# The methodology of quantitative risk assessment studies

Maxime Rigaud, Jurgen Buekers, Jos Bessems, Xavier Basagaña, Sandrine Mathy, Mark Nieuwenhuijsen, Rémy Slama

## ► To cite this version:

Maxime Rigaud, Jurgen Buekers, Jos Bessems, Xavier Basagaña, Sandrine Mathy, et al.. The methodology of quantitative risk assessment studies. Environmental Health, 2024, 23 (1), pp.13. 10.1186/s12940-023-01039-x. hal-04523440

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# The methodology of quantitative risk assessment studies

Maxime Rigaud, Jurgen Buekers, Jos Bessems, Xavier Basagaña, Sandrine

Mathy, Mark Nieuwenhuijsen, Rémy Slama

► To cite this version:

Maxime Rigaud, Jurgen Buekers, Jos Bessems, Xavier Basagaña, Sandrine Mathy, et al. The methodology of quantitative risk assessment studies. Environmental Health, 2024, 23 (1), pp.13. 10.1186/s12940-023-01039-x. hal-04523440

HAL Id: hal-04523440

https://hal.inrae.fr/hal-04523440v1

Submitted on 28 Mar 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

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Distributed under a Creative Commons Attribution 4.0 International License
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# The methodology of quantitative risk assessment studies

Maxime Rigaud<fnref n="1" />, Jurgen Buekers<fnref n="2" />, Jos Bessems<fnref n="2" />, Xavier Basagaña<fnref n="3" />,<fnref n="4" />,<fnref n="5" />, Sandrine Mathy<fnref n="6" />, Mark Nieuwenhuijsen<fnref n="3" />,<fnref n="4" />,<fnref n="5" /> and Rémy Slama<fnref n="1" />*

**Abstract**

Once an external factor has been deemed likely to influence human health and a dose response function is available, an assessment of its health impact or that of policies aimed at influencing this and possibly other factors in a specific population can be obtained through a quantitative risk assessment, or health impact assessment (HIA) study. The health impact is usually expressed as a number of disease cases or disability-adjusted life-years (DALYs) attributable to or expected from the exposure or policy. We review the methodology of quantitative risk assessment studies based on human data. The main steps of such studies include definition of counterfactual scenarios related to the exposure or policy, exposure(s) assessment, quantification of risks (usually relying on literature-based dose response functions), possibly economic assessment, followed by uncertainty analyses. We discuss issues and make recommendations relative to the accuracy and geographic scale at which factors are assessed, which can strongly influence the study results. If several factors are considered simultaneously, then correlation, mutual influences and possibly synergy between them should be taken into account. Gaps or issues in the methodology of quantitative risk assessment studies include 1) proposing a formal approach to the quantitative handling of the level of evidence regarding each exposure-health pair (essential to consider emerging factors); 2) contrasting risk assessment based on human dose-response functions with that relying on toxicological data; 3) clarification of terminology of health impact assessment and human-based risk assessment studies, which are actually very similar, and 4) other technical issues related to the simultaneous consideration of several factors, in particular when they are causally linked.

**Keywords** Dose-response, Environment, Hazard, Health impact, Policy, Risk

**Introduction**

The main aims of environmental health research are i) to identify positive or negative determinants of health-related states (environmental factors in a broad sense encompassing physical, chemical, social, behavioral, systemic factors); ii) to understand the mechanisms underlying the effects of these factors; iii) to quantify the corresponding population impact, which can either be a burden or benefit. This quantification can be done e.g., in terms of number of deaths or disease cases or of healthy years of life lost attributable to the factor or set of factors; and iv) to identify interventions (which can be of all natures and act e.g., on the body, behaviors, knowledge, representations, values, the social, physical and chemical

Rémy Slama
remy.slama@inserm.fr

<footnote>*Correspondence:</footnote>

<footnote n="1">¹ Inserm, University of Grenoble Alpes, CNRS, IAB, Team of Environmental Epidemiology Applied to Reproduction and Respiratory Health, Grenoble, France</footnote>

<footnote n="2">² VITO, Flemish Institute for Technological Research, Unit Health, Mol, Belgium</footnote>

<footnote n="3">³ ISGlobal, Barcelona 08003, Spain</footnote>

<footnote n="4">⁴ Universitat Pompeu Fabra (UPF), Barcelona 08003, Spain</footnote>

<footnote n="5">⁵ CIBER Epidemiología y Salud Pública (CIBERESP), Madrid 28029, Spain</footnote>

<footnote n="6">⁶ CNRS, University Grenoble Alpes, INRAe, Grenoble INP, GAEL, Grenoble, France</footnote>
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# The methodology of quantitative risk assessment studies

Maxime Rigaud<fnref n="1" />, Jurgen Buekers<fnref n="2" />, Jos Bessems<fnref n="2" />, Xavier Basagaña<fnref n="3" />,<fnref n="4" />,<fnref n="5" />, Sandrine Mathy<fnref n="6" />, Mark Nieuwenhuijsen<fnref n="3" />,<fnref n="4" />,<fnref n="5" /> and Rémy Slama<fnref n="1" />*

## Abstract

Once an external factor has been deemed likely to influence human health and a dose response function is available, an assessment of its health impact or that of policies aimed at influencing this and possibly other factors in a specific population can be obtained through a quantitative risk assessment, or health impact assessment (HIA) study. The health impact is usually expressed as a number of disease cases or disability-adjusted life-years (DALYs) attributable to or expected from the exposure or policy. We review the methodology of quantitative risk assessment studies based on human data. The main steps of such studies include definition of counterfactual scenarios related to the exposure or policy, exposure(s) assessment, quantification of risks (usually relying on literature-based dose response functions), possibly economic assessment, followed by uncertainty analyses. We discuss issues and make recommendations relative to the accuracy and geographic scale at which factors are assessed, which can strongly influence the study results. If several factors are considered simultaneously, then correlation, mutual influences and possibly synergy between them should be taken into account. Gaps or issues in the methodology of quantitative risk assessment studies include 1) proposing a formal approach to the quantitative handling of the level of evidence regarding each exposure-health pair (essential to consider emerging factors); 2) contrasting risk assessment based on human dose-response functions with that relying on toxicological data; 3) clarification of terminology of health impact assessment and human-based risk assessment studies, which are actually very similar, and 4) other technical issues related to the simultaneous consideration of several factors, in particular when they are causally linked.

**Keywords** Dose-response, Environment, Hazard, Health impact, Policy, Risk

## Introduction

The main aims of environmental health research are i) to identify positive or negative determinants of health-related states (environmental factors in a broad sense encompassing physical, chemical, social, behavioral, systemic factors); ii) to understand the mechanisms underlying the effects of these factors; iii) to quantify the corresponding population impact, which can either be a burden or benefit. This quantification can be done e.g., in terms of number of deaths or disease cases or of healthy years of life lost attributable to the factor or set of factors; and iv) to identify interventions (which can be of all natures and act e.g., on the body, behaviors, knowledge, representations, values, the social, physical and chemical

Rémy Slama
remy.slama@inserm.fr

<footnote>*Correspondence:</footnote>

<footnote n="1">¹ Inserm, University of Grenoble Alpes, CNRS, IAB, Team of Environmental Epidemiology Applied to Reproduction and Respiratory Health, Grenoble, France</footnote>

<footnote n="2">² VITO, Flemish Institute for Technological Research, Unit Health, Mol, Belgium</footnote>

<footnote n="3">³ ISGlobal, Barcelona 08003, Spain</footnote>

<footnote n="4">⁴ Universitat Pompeu Fabra (UPF), Barcelona 08003, Spain</footnote>

<footnote n="5">⁵ CIBER Epidemiología y Salud Pública (CIBERESP), Madrid 28029, Spain</footnote>

<footnote n="6">⁶ CNRS, University Grenoble Alpes, INRAe, Grenoble INP, GAEL, Grenoble, France</footnote>
environments, the economy) allowing to limit this impact and preserve or improve the health of populations and limit health inequalities.

In the classical view of the 1983 Redbook of the US National Research Council on risk assessment [1, 2], aim i) corresponds to hazard identification and aim iii) to risk assessment. Aim iv) is usually seen as being tackled by health impact assessment (HIA) studies, or analytical HIA studies [3] but as we will discuss (see "Issues related to terminology" below, last section), from a methodological point of view, the approaches used to tackle aims iii) and iv) are essentially similar. We will therefore use (quantitative) risk assessment to point to studies filling specifically the aim of steps iii) (quantification of population impact of existing factors) and iv) (which corresponds to the quantification of the expected impact of hypothetical policies or interventions). The overall aim of quantitative risk assessment as broadly defined can be described as the quantification of the population impact of any type of factor, exposure, policy or program, hypothesized or already present.

Risk assessment studies typically allow to answer questions such as "How many cases of these diseases are attributable (yesterday/today/tomorrow) to this (exposure) factor or policy?", or "How many disease cases would be avoided today/in the future if this (exposure) factor was/had been brought to a certain level, or if this policy was/had been implemented, all other things not influenced by this factor or policy being kept identical?". These questions relate to the consequences of interventions (more precisely about the comparison of counterfactual situations), and not about associations or effects (i.e., hazards, for example: can exposure to this factor cause liver cancer?), as is typical for epidemiological study designs such as cohorts and case-control studies. Such measures of associations, or dose-response functions, are essential but not sufficient to assess the risk. Indeed, dose-response functions alone generally do not allow providing a relevant hierarchy of the disease burden, or impact, associated with each factor: the impact can be higher for an exposure with a mild dose-response function curve than for an exposure with a steep dose-response function, if the first exposure is more frequent than the latter exposure.

For many, if not all risk factors that influence the occurrence of a health-related event, it is not possible to identify if the occurrence of this event in a given subject has been caused by the risk factor; indeed, disease causes generally do not leave a specific (unambiguous) signature in the body, even for strong associations such as the induction of lung cancer by active tobacco smoking. Therefore, one cannot add up cases identified from death certificates or other routine medical data to estimate the

disease or mortality burden attributable to an exposure or policy. Similarly, *before-after* observational studies can be used to document quantitatively health changes in a given population, following e.g., a heat wave, a major air pollution episode [4], a decrease in air pollution following the temporary closure of an industrial site, an abrupt change in regulation [5] or an event such as the Olympic Games. However, they are no general solution here; indeed, they may allow to identify a hazard but they are limited to documenting observed (factual) changes and not to studying other (counterfactual) scenarios.

Consequently, one has to rely on more indirect – modelling – approaches. This can be done combining knowledge about the overall frequency of the health parameter considered in the specific population under study, about the distribution of exposure and about dose-response function(s) associated with the factor(s), typically stemming from long-term studies such as cohorts (or animal studies in the case of animal-based risk assessment approaches). Risk assessment studies are related to three research and activity streams: that of the epidemiological concept of population attributable fraction, or etiologic fraction, dating back from the mid-twentieth century [6–8], that of chemical risk assessment derived from toxicological studies [9], and the practice of environmental impact assessment in relation to a planned policy or project, in which the consideration of the health impacts possibly induced by the planned policy or project has become more frequent, in addition to the consideration of its environmental impacts [3, 10].

These quantitative risk assessment studies contribute to integrating and translating knowledge generated from environmental health research in a form more relevant for policy making. They can be used to define or compare risk management strategies or projects, policies, infrastructures of various kinds with possible health consequences (Fig. 1). The risk assessment step can be followed by (or include) an economic assessment step, in which the estimated health impact is translated into an economic cost, providing an economic assessment of the impact of the factor or policy considered.

Many risk assessment studies have been conducted in relation to atmospheric pollutants, urban policies, metals, tobacco smoke, alcohol consumption, dietary factors, access to clean water. Although many chemicals are likely to influence health, the consideration of chemical exposures in (human-based) risk assessment studies appears relatively limited [12, 13]. The most recent worldwide environmental burden of disease assessment coordinated by the IHME (Institute for Health Metrics and Evaluation, Seattle, USA) considered 87 risk factors and combinations of risk factors, including air pollutants, non-optimal temperatures,
environments, the economy) allowing to limit this impact and preserve or improve the health of populations and limit health inequalities.

In the classical view of the 1983 Redbook of the US National Research Council on risk assessment [1, 2], aim i) corresponds to hazard identification and aim iii) to risk assessment. Aim iv) is usually seen as being tackled by health impact assessment (HIA) studies, or analytical HIA studies [3] but as we will discuss (see "Issues related to terminology" below, last section), from a methodological point of view, the approaches used to tackle aims iii) and iv) are essentially similar. We will therefore use (quantitative) risk assessment to point to studies filling specifically the aim of steps iii) (quantification of population impact of existing factors) and iv) (which corresponds to the quantification of the expected impact of hypothetical policies or interventions). The overall aim of quantitative risk assessment as broadly defined can be described as the quantification of the population impact of any type of factor, exposure, policy or program, hypothesized or already present.

Risk assessment studies typically allow to answer questions such as "How many cases of these diseases are attributable (yesterday/today/tomorrow) to this (exposure) factor or policy?", or "How many disease cases would be avoided today/in the future if this (exposure) factor was/had been brought to a certain level, or if this policy was/had been implemented, all other things not influenced by this factor or policy being kept identical?". These questions relate to the consequences of interventions (more precisely about the comparison of counterfactual situations), and not about associations or effects (i.e., hazards, for example: can exposure to this factor cause liver cancer?), as is typical for epidemiological study designs such as cohorts and case-control studies. Such measures of associations, or dose-response functions, are essential but not sufficient to assess the risk. Indeed, dose-response functions alone generally do not allow providing a relevant hierarchy of the disease burden, or impact, associated with each factor: the impact can be higher for an exposure with a mild dose-response function curve than for an exposure with a steep dose-response function, if the first exposure is more frequent than the latter exposure.

For many, if not all risk factors that influence the occurrence of a health-related event, it is not possible to identify if the occurrence of this event in a given subject has been caused by the risk factor; indeed, disease causes generally do not leave a specific (unambiguous) signature in the body, even for strong associations such as the induction of lung cancer by active tobacco smoking. Therefore, one cannot add up cases identified from death certificates or other routine medical data to estimate the

disease or mortality burden attributable to an exposure or policy. Similarly, *before-after* observational studies can be used to document quantitatively health changes in a given population, following e.g., a heat wave, a major air pollution episode [4], a decrease in air pollution following the temporary closure of an industrial site, an abrupt change in regulation [5] or an event such as the Olympic Games. However, they are no general solution here; indeed, they may allow to identify a hazard but they are limited to documenting observed (factual) changes and not to studying other (counterfactual) scenarios.

Consequently, one has to rely on more indirect – modelling – approaches. This can be done combining knowledge about the overall frequency of the health parameter considered in the specific population under study, about the distribution of exposure and about dose-response function(s) associated with the factor(s), typically stemming from long-term studies such as cohorts (or animal studies in the case of animal-based risk assessment approaches). Risk assessment studies are related to three research and activity streams: that of the epidemiological concept of population attributable fraction, or etiologic fraction, dating back from the mid-twentieth century [6–8], that of chemical risk assessment derived from toxicological studies [9], and the practice of environmental impact assessment in relation to a planned policy or project, in which the consideration of the health impacts possibly induced by the planned policy or project has become more frequent, in addition to the consideration of its environmental impacts [3, 10].

These quantitative risk assessment studies contribute to integrating and translating knowledge generated from environmental health research in a form more relevant for policy making. They can be used to define or compare risk management strategies or projects, policies, infrastructures of various kinds with possible health consequences (Fig. 1). The risk assessment step can be followed by (or include) an economic assessment step, in which the estimated health impact is translated into an economic cost, providing an economic assessment of the impact of the factor or policy considered.

Many risk assessment studies have been conducted in relation to atmospheric pollutants, urban policies, metals, tobacco smoke, alcohol consumption, dietary factors, access to clean water. Although many chemicals are likely to influence health, the consideration of chemical exposures in (human-based) risk assessment studies appears relatively limited [12, 13]. The most recent worldwide environmental burden of disease assessment coordinated by the IHME (Institute for Health Metrics and Evaluation, Seattle, USA) considered 87 risk factors and combinations of risk factors, including air pollutants, non-optimal temperatures,
<figure><img src="image_3.png" /><figcaption>**Fig. 1** Position of quantitative risk assessment in the process of risk characterization and management. Risk assessment can be used to assess the impacts of the “factors” considered (leftmost box) and of policies aiming at managing and limiting their impacts. Adapted from [11]</figcaption></figure>

lead, unsafe water, sanitation and handwashing, but no other chemical factors except those considered in an occupational setting [14]. However, the production volume of synthetic chemicals is still increasing and is expected to triple in 2050 compared to 2010 [15], and widespread human exposure is documented by bio-monitoring studies [16, 17].

Several reviews about risk assessment and HIA studies have been published [10, 18–23]. For example, Harris-Roxas et al. provided a narrative of the historical origins of health impact assessment, strengths and opportunities [20], Nieuwenhuijsen [21] reviewed issues related to the participatory nature of HIA studies, while Briggs [19] provided a conceptual framework for integrated environmental health impact assessment. With the exception of issues related to the challenging concepts of etiologic fraction/excess cases [7, 8], very few reviews focused on methodological issues related to the technicalities of the execution of the assessment itself, while, with the development of more refined approaches to assess exposures, the identification of a growing number of hazards through toxicological and biomarker-based epidemiological studies or epidemiological studies based on fine-scale (e.g., air pollution) modeling, there is a need to review options and strategies related to input data and handling of uncertainties at each step of risk assessment studies.

We therefore aimed to perform a literature review (see [24]) of the methodology of quantitative risk assessment studies, discussing sequentially each step posterior to issue framing [19]. Qualitative health impact assessment approaches and those based on animal (toxicological) dose-response functions were not considered, with the exception of a few points illustrating in which respect the latter diverge from

assessments based on human dose-response functions. We conclude by summarizing the identified methodological gaps, in particular related to the handling of emerging factors with partial data, and issues related to terminology.

## Key issues and options at each step

### Overall methodology of quantitative risk assessment studies

The main technical steps of quantitative risk assessment, include:

1. Definition/identification of the factor(s) (environmental factors/infrastructure/plan/policy) considered;

2. Definition of the study area and study population;

3. Description of the counterfactual situations compared and of the study period (may be merged with step 1);

4. Assessment/description of “exposures” in the study population under each counterfactual scenario;

5. Identification of the hazards (health outcomes) induced by the factors considered and of the corresponding dose-response functions and level of evidence;

6. Assessment of “baseline” (usually, current) disease frequency or of the DALYs attributable to the health outcomes considered, if needed;

7. Quantification of health risk or impact (e.g., in number of disease cases or DALYs);

8. Quantification of the social and economic impacts;

9. Uncertainty analysis;

10. Reporting/communication.
<figure><img src="image_4.png" /><figcaption>**Fig. 1** Position of quantitative risk assessment in the process of risk characterization and management. Risk assessment can be used to assess the impacts of the “factors” considered (leftmost box) and of policies aiming at managing and limiting their impacts. Adapted from [11]</figcaption></figure>

lead, unsafe water, sanitation and handwashing, but no other chemical factors except those considered in an occupational setting [14]. However, the production volume of synthetic chemicals is still increasing and is expected to triple in 2050 compared to 2010 [15], and widespread human exposure is documented by bio-monitoring studies [16, 17].

Several reviews about risk assessment and HIA studies have been published [10, 18–23]. For example, Harris-Roxas et al. provided a narrative of the historical origins of health impact assessment, strengths and opportunities [20], Nieuwenhuijsen [21] reviewed issues related to the participatory nature of HIA studies, while Briggs [19] provided a conceptual framework for integrated environmental health impact assessment. With the exception of issues related to the challenging concepts of etiologic fraction/excess cases [7, 8], very few reviews focused on methodological issues related to the technicalities of the execution of the assessment itself, while, with the development of more refined approaches to assess exposures, the identification of a growing number of hazards through toxicological and biomarker-based epidemiological studies or epidemiological studies based on fine-scale (e.g., air pollution) modeling, there is a need to review options and strategies related to input data and handling of uncertainties at each step of risk assessment studies.

We therefore aimed to perform a literature review (see [24]) of the methodology of quantitative risk assessment studies, discussing sequentially each step posterior to issue framing [19]. Qualitative health impact assessment approaches and those based on animal (toxicological) dose-response functions were not considered, with the exception of a few points illustrating in which respect the latter diverge from

assessments based on human dose-response functions. We conclude by summarizing the identified methodological gaps, in particular related to the handling of emerging factors with partial data, and issues related to terminology.

## Key issues and options at each step

### Overall methodology of quantitative risk assessment studies

The main technical steps of quantitative risk assessment, include:

1. Definition/identification of the factor(s) (environmental factors/infrastructure/plan/policy) considered;

2. Definition of the study area and study population;

3. Description of the counterfactual situations compared and of the study period (may be merged with step 1);

4. Assessment/description of “exposures” in the study population under each counterfactual scenario;

5. Identification of the hazards (health outcomes) induced by the factors considered and of the corresponding dose-response functions and level of evidence;

6. Assessment of “baseline” (usually, current) disease frequency or of the DALYs attributable to the health outcomes considered, if needed;

7. Quantification of health risk or impact (e.g., in number of disease cases or DALYs);

8. Quantification of the social and economic impacts;

9. Uncertainty analysis;

10. Reporting/communication.
Note that some reviews [19, 25] include preparatory or organizational steps, which are not detailed here. Public involvement (not discussed here) can be present at virtually each of these steps. The steps of identification of the exposures, outcomes, area and population considered (numbered 1–3 above) and protocol definition are sometimes referred to as “scoping” step. Note also that the order of some steps is somewhat arbitrary. For example step 2 may come first.

Not all quantitative risk assessment studies follow all of these steps in practice, depending on their scope and the chosen approach. In practice, some studies may stop before completing the risk assessment step – for example many “risk assessment” exercises conducted by national agencies actually only correspond to the identification of hazards associated with the exposure or policy considered without quantification of the corresponding risk, e.g., because robust dose–response functions are lacking (see Sect. "Issues related to terminology" for further discussion). In case a policy is indeed implemented, a “policy implementation phase”, monitoring the implementation of the policy and possibly its actual impact, is sometimes added.

We will review steps 2 to 9, corresponding to the “appraisal steps” in the WHO terminology [25].

These steps are depicted in Fig. 2. We first consider the simple case of a single environmental factor for which exposure levels are available or can be assessed (exposure being here understood in its strict meaning of the contact of an environmental factor with the human body). From the knowledge about exposure in the population under study and various other essential pieces of information detailed below, an estimation of the corresponding health impact will be provided, and generally compared to the impact under an alternative (or counterfactual) scenario (e.g., corresponding to the same population in which exposure is set to zero or another reference value, sometimes called TMREL, or Theoretical Minimum Risk Exposure Level,

see Selection of the target scenario(s) – exposure levels). This health impact may be positive or negative, restricted to a specific symptom or disease, or consider several diseases or integrated measures of health such as Disability Adjusted Life Years (DALYs), which integrate years lost due to both death and disability.

Numerous variations around this basic scheme exist: one can start upstream of human exposure (box 4 in Fig. 2), for example from the environmental level of the factor (e.g., the amount of contamination of food by metals or the average atmospheric concentration of particulate matter [26], box 3A), further upstream, considering a source of potentially harmful or beneficial factors (e.g., a factory that emits several pollutants, the presence of green space [27]; box 2), or a behavior, possibly influencing exposures, such as burning incense, use of tanning cabins, use of electronic screens or cigarette smoking [28] (box 3B), or a policy/infrastructure or foreseen societal or environmental change (box 1), such as the ban of coal burning or of inefficient woodstoves in a specific area [29] or of flavored tobacco [30], the building of a school, or the temperature changes expected from climate change a few decades ahead [31], this policy, infrastructure or environmental or societal change being either real or hypothetical. In this latter case, some assessment (e.g., though modelling) of the variations of all the chemical, physical, psychosocial factors that may change as a result of the policy may be required, if it is not already available, e.g. as a result of a pre-existing environmental impact assessment study. One can also start downstream of exposure(s), in particular from a body dose or from the organ dose or the excreted level of an exposure biomarker. Depending on the starting point, specific data and modelling may be required, typically to translate the information about this starting point (say, a behavior or the presence of a factory) into an exposure metric that can be translated into a health risk, which will generally be the exposure metric for which reliable dose–response functions exist. Downstream of the

<figure><img src="image_4.png" /><figcaption>**Fig. 2** Overview of the main steps of risk assessment studies. The starting point of the study (or the counterfactual scenarios) can be formulated in terms of policy, program, project (1), environmental emissions (2), environmental level (3A), behavior (3B), human exposure (4)</figcaption></figure>
Note that some reviews [19, 25] include preparatory or organizational steps, which are not detailed here. Public involvement (not discussed here) can be present at virtually each of these steps. The steps of identification of the exposures, outcomes, area and population considered (numbered 1–3 above) and protocol definition are sometimes referred to as “scoping” step. Note also that the order of some steps is somewhat arbitrary. For example step 2 may come first.

Not all quantitative risk assessment studies follow all of these steps in practice, depending on their scope and the chosen approach. In practice, some studies may stop before completing the risk assessment step – for example many “risk assessment” exercises conducted by national agencies actually only correspond to the identification of hazards associated with the exposure or policy considered without quantification of the corresponding risk, e.g., because robust dose–response functions are lacking (see Sect. "Issues related to terminology" for further discussion). In case a policy is indeed implemented, a “policy implementation phase”, monitoring the implementation of the policy and possibly its actual impact, is sometimes added.

We will review steps 2 to 9, corresponding to the “appraisal steps” in the WHO terminology [25].

These steps are depicted in Fig. 2. We first consider the simple case of a single environmental factor for which exposure levels are available or can be assessed (exposure being here understood in its strict meaning of the contact of an environmental factor with the human body). From the knowledge about exposure in the population under study and various other essential pieces of information detailed below, an estimation of the corresponding health impact will be provided, and generally compared to the impact under an alternative (or counterfactual) scenario (e.g., corresponding to the same population in which exposure is set to zero or another reference value, sometimes called TMREL, or Theoretical Minimum Risk Exposure Level,

see Selection of the target scenario(s) – exposure levels). This health impact may be positive or negative, restricted to a specific symptom or disease, or consider several diseases or integrated measures of health such as Disability Adjusted Life Years (DALYs), which integrate years lost due to both death and disability.

Numerous variations around this basic scheme exist: one can start upstream of human exposure (box 4 in Fig. 2), for example from the environmental level of the factor (e.g., the amount of contamination of food by metals or the average atmospheric concentration of particulate matter [26], box 3A), further upstream, considering a source of potentially harmful or beneficial factors (e.g., a factory that emits several pollutants, the presence of green space [27]; box 2), or a behavior, possibly influencing exposures, such as burning incense, use of tanning cabins, use of electronic screens or cigarette smoking [28] (box 3B), or a policy/infrastructure or foreseen societal or environmental change (box 1), such as the ban of coal burning or of inefficient woodstoves in a specific area [29] or of flavored tobacco [30], the building of a school, or the temperature changes expected from climate change a few decades ahead [31], this policy, infrastructure or environmental or societal change being either real or hypothetical. In this latter case, some assessment (e.g., though modelling) of the variations of all the chemical, physical, psychosocial factors that may change as a result of the policy may be required, if it is not already available, e.g. as a result of a pre-existing environmental impact assessment study. One can also start downstream of exposure(s), in particular from a body dose or from the organ dose or the excreted level of an exposure biomarker. Depending on the starting point, specific data and modelling may be required, typically to translate the information about this starting point (say, a behavior or the presence of a factory) into an exposure metric that can be translated into a health risk, which will generally be the exposure metric for which reliable dose–response functions exist. Downstream of the

<figure><img src="image_5.png" /><figcaption>**Fig. 2** Overview of the main steps of risk assessment studies. The starting point of the study (or the counterfactual scenarios) can be formulated in terms of policy, program, project (1), environmental emissions (2), environmental level (3A), behavior (3B), human exposure (4)</figcaption></figure>
health risk assessment, one may wish to also consider
economic and other societal impacts.

Compared situations

Principle of counterfactual comparisons

To estimate the impact of a given factor or policy, one needs to subtract the number of disease cases expected under the hypothesis that the policy is present or the factor(s) has a given distribution in the study population from the number of cases expected in the situation assuming that the policy is absent or different, or that the factor(s) has a different distribution. Either of these situations may correspond to reality as observed at a given time point. For this estimation to be relevant (i.e., for it to correspond to an estimation of the causal effect of the “change” implemented), the comparison has to be done in the same population and at the same time point. Otherwise, trends in the health outcome unrelated to the considered policy or factor may exist and bias the comparison between both situations. As an illustration, comparing the number of air pollution-related diseases in 10 years, after a road infrastructure has been built, with the situation today, in the absence of the infrastructure, would not distinguish the impact on health of changes in the traffic fleet in time from the impact of the infrastructure per se. In the terminology of causal inference theory, this corresponds to considering counterfactual situations. The reliance on counterfactual thinking is a basis for causal inference: the causal effect of a factor A corresponds to the difference between the situation in the presence of A and a (counterfactual) situation in which everything is similar with the exception that A has been removed [32, 33]. Note that the epidemiological concept of population attributable fraction developed before the application of counterfactual thinking to the health field, with the possible consequence that the counterfactual scenarios are not always explicit when estimating population attributable fractions.

The comparison can apply to the past, the current
period, or to another period in the future. Therefore, the
two main options are:

* *Counterfactual approach at the current period or in the past:* The number of disease cases (or healthy years lost because of specific diseases or another health metric) at the current time $t_0$ in a hypothetical (“counterfactual”) world similar to the current world but for the fact that the factor is absent, or altered, or the policy has been implemented, is compared to the number of disease cases (or healthy years lost or another health metric) in the real world considered at the same time $t_0$; $t_0$ needs not to be to the time when the study is performed but can correspond to some

time point in the past. We group the situations corre-
sponding to $t_0$ corresponding to current or past situa-
tions because in principle real data on exposures and
health can be accessed for the default scenario. See
e.g., examples in [34, 35].

* *Counterfactual approach with future scenarios:* Here, the number of disease cases (or healthy years lost because of specific diseases or another health metric) at a specific time $t_1$ in the future in the study population in which the factor has been removed or altered, or the policy has been implemented, is compared to what would be observed at the same time assuming a specific reference scenario [29, 36, 37]. Time $t_1$ might correspond to the time when the planned policy is expected to have been implemented, or some time later when a new stationary state is assumed to have been reached.

$t_0$ and $t_1$ are usually not time points but time periods over which impacts are summed; they may typically correspond to a one-year period, but may also correspond to a long duration, which may correspond to the life expectancy of the planned infrastructure, in which case the risk assessment may be repeated during each year of the study period to allow integration of the impact and possibly infrastructure or policy costs over this period. This is in particular relevant if the costs and benefits vary over time (the costs being possibly borne in the beginning and the positive impacts reaped after a longer duration). Such an integration allows to provide a relevant average of the yearly impacts and costs. An example is the assessment of the health, economic impact and cost of measures to limit air pollution over the 2017–2045 period, assuming that the measures have been implemented at the start of the study period [29].

The two options above may actually be combined,
by providing estimates of the situation at time t₁ in the
future under various scenarios, together with an estimate
providing to another earlier time t₀ such as the current
time. As an illustration, Martinez-Solanas et al. estimated
the impact of non-optimal (both cold and warm) tem-
peratures at the end of the twenty-first century under
three greenhouse gas emission scenarios, but also at the
historical period (1971–2005), allowing both to compare
two possible futures with different levels of action against
greenhouse gas emissions, as well as to compare the cur-
rent situations with some possible futures [31].

Note that the first situation typically corresponds to
attributable fraction calculations [7] done on the basis
of the measure of association (e.g., a relative risk) esti-
mated in an epidemiological study, using the exposure in
the population from which the relative risk has been esti-
mated. Also note that the observational study equivalent
health risk assessment, one may wish to also consider
economic and other societal impacts.

Compared situations

Principle of counterfactual comparisons

To estimate the impact of a given factor or policy, one
needs to subtract the number of disease cases expected
under the hypothesis that the policy is present or the
factor(s) has a given distribution in the study popula-
tion from the number of cases expected in the situation
assuming that the policy is absent or different, or that the
factor(s) has a different distribution. Either of these situ-
ations may correspond to reality as observed at a given
time point. For this estimation to be relevant (i.e., for it
to correspond to an estimation of the causal effect of the
“change” implemented), the comparison has to be done
in the same population and at the same time point. Oth-
erwise, trends in the health outcome unrelated to the
considered policy or factor may exist and bias the com-
parison between both situations. As an illustration, com-
paring the number of air pollution-related diseases in
10 years, after a road infrastructure has been built, with
the situation today, in the absence of the infrastructure,
would not distinguish the impact on health of changes in
the traffic fleet in time from the impact of the infrastruc-
ture per se. In the terminology of causal inference theory,
this corresponds to considering counterfactual situa-
tions. The reliance on counterfactual thinking is a basis
for causal inference: the causal effect of a factor A cor-
responds to the difference between the situation in the
presence of A and a (counterfactual) situation in which
everything is similar with the exception that A has been
removed [32, 33]. Note that the epidemiological concept
of population attributable fraction developed before the
application of counterfactual thinking to the health field,
with the possible consequence that the counterfactual
scenarios are not always explicit when estimating popula-
tion attributable fractions.

The comparison can apply to the past, the current
period, or to another period in the future. Therefore, the
two main options are:

* *Counterfactual approach at the current period or in the past:* The number of disease cases (or healthy years lost because of specific diseases or another health metric) at the current time $t_0$ in a hypothetical (“counterfactual”) world similar to the current world but for the fact that the factor is absent, or altered, or the policy has been implemented, is compared to the number of disease cases (or healthy years lost or another health metric) in the real world considered at the same time $t_0$; $t_0$ needs not to be to the time when the study is performed but can correspond to some

time point in the past. We group the situations corre-
sponding to $t_0$ corresponding to current or past situa-
tions because in principle real data on exposures and
health can be accessed for the default scenario. See
e.g., examples in [34, 35].

* *Counterfactual approach with future scenarios:* Here, the number of disease cases (or healthy years lost because of specific diseases or another health metric) at a specific time $t_1$ in the future in the study population in which the factor has been removed or altered, or the policy has been implemented, is compared to what would be observed at the same time assuming a specific reference scenario [29, 36, 37]. Time $t_1$ might correspond to the time when the planned policy is expected to have been implemented, or some time later when a new stationary state is assumed to have been reached.

$t_0$ and $t_1$ are usually not time points but time periods over which impacts are summed; they may typically correspond to a one-year period, but may also correspond to a long duration, which may correspond to the life expectancy of the planned infrastructure, in which case the risk assessment may be repeated during each year of the study period to allow integration of the impact and possibly infrastructure or policy costs over this period. This is in particular relevant if the costs and benefits vary over time (the costs being possibly borne in the beginning and the positive impacts reaped after a longer duration). Such an integration allows to provide a relevant average of the yearly impacts and costs. An example is the assessment of the health, economic impact and cost of measures to limit air pollution over the 2017–2045 period, assuming that the measures have been implemented at the start of the study period [29].

The two options above may actually be combined,
by providing estimates of the situation at time $t_1$ in the
future under various scenarios, together with an estimate
providing to another earlier time $t_0$ such as the current
time. As an illustration, Martinez-Solanas et al. estimated
the impact of non-optimal (both cold and warm) tem-
peratures at the end of the twenty-first century under
three greenhouse gas emission scenarios, but also at the
historical period (1971–2005), allowing both to compare
two possible futures with different levels of action against
greenhouse gas emissions, as well as to compare the cur-
rent situations with some possible futures [31].

Note that the first situation typically corresponds to
attributable fraction calculations [7] done on the basis
of the measure of association (e.g., a relative risk) esti-
mated in an epidemiological study, using the exposure in
the population from which the relative risk has been esti-
mated. Also note that the observational study equivalent
to the second situation corresponds to what is called the *difference-in-differences* approach [38]; in this observational approach, in order to estimate the impact of a real intervention, a community or group experiencing an intervention is compared to itself before the intervention, while another group that did not experience the intervention to correct this before-after comparison for temporal trends in the health outcome of interest).

A specificity of the second (“future”) option relates to the temporal evolutions of the study area. These possibly include changes in the demography (age structure and hence also possibly raw disease risk, as the incidence of most diseases varies with age), in specific disease risk factors besides the one in focus and also possibly regarding the dose response function, in particular for health outcomes very sensitive to societal changes, such as mortality. Such evolutions may be difficult to predict, in particular over periods of several decades or more. Illustrations include studies of long-term effects of ozone depletion [37] or of climate change, in which sociodemographic changes as well as societal adaptation to high temperatures [39] are expected.

### Selection of the target scenario(s) – exposure levels

The scenarios correspond to the counterfactual situations that one wishes to compare to answer the study aim. One scenario will typically correspond to the *current* or *baseline* situation (if one is interested in the effect of a factor present today), or to the extension over time of the current situation, the so-called “business as usual” scenario, if the question asked pertains to a policy or infrastructure that would be implemented or built in the future. The alternative scenario(s) will correspond to the hypothetical situation in which the policy considered has been implemented (the policy being e.g., the construction of an infrastructure, a change in urban design, or a lowering of the pollution levels, if the study aims at quantifying the impact of a specific exposure). Of course, several counterfactual scenarios can be considered and compared (see examples in Table 1 or [29]).

An essential question here, for actions on one or several specific factors, relates to the targeted levels (or distribution) of the factor. In the case of a study aiming to quantify the current impact of a factor that has monotonous effects on all diseases considered, the counterfactual situation in which no one is exposed to the factor can be considered. This would correspond to the ban of the substance or the behavior considered, assuming that

<table><caption>**Table 1** A series of 10 scenarios compared in a risk assessment study of the impact of atmospheric pollution (fine particulate matter, or PM<sub>2.5</sub>). From [40]</caption><thead><tr><th>Scenario number</th><th>Scenario description</th><th>Scenario name</th><th>PM<sub>2.5</sub> yearly level reduction</th></tr></thead><tbody><tr><td>S1</td><td>Spatially homogeneous target value in the whole area</td><td>"WHO guideline"</td><td>Down to WHO yearly guideline (10 µg/m<sup>3</sup> at the time of this publication)</td></tr><tr><td>S2</td><td></td><td>"No anthropogenic PM<sub>2.5</sub> emissions"</td><td>Down to lowest nation-wide levels (4.9 µg/m<sup>3</sup>)<sup>a</sup></td></tr><tr><td>S3</td><td></td><td>"Quiet neighborhood"</td><td>Down to lowest study area district levels (10th percentile of exposure)<sup>b</sup></td></tr><tr><td>S4</td><td rowspan="2">Homogeneous PM<sub>2.5</sub> decreases in the whole area</td><td>"-1 µg/m<sup>3</sup>"</td><td>Baseline<sup>c</sup> -1 µg/m<sup>3</sup></td></tr><tr><td>S5</td><td>"-2 µg/m<sup>3</sup>"</td><td>Baseline<sup>c</sup> -2 µg/m<sup>3</sup></td></tr><tr><td>S6</td><td rowspan="3">Targeted reduction in PM<sub>2.5</sub>-related mortality in the whole area<sup>d</sup></td><td>"-1/3 of mortality"</td><td rowspan="3">Equivalent to decreasing homogeneously and sufficiently the baseline<sup>c</sup> exposure to achieve the indicated health objective<sup>e</sup></td></tr><tr><td>S7</td><td>"-1/2 of mortality"</td></tr><tr><td>S8</td><td>"-2/3 of mortality"</td></tr><tr><td>S9</td><td>2008/50/EU Directive<sup>f</sup></td><td>In the whole study area"</td><td>Baseline<sup>c</sup> -15%</td></tr><tr><td>S10</td><td>"2020 target"</td><td>Restricted to PM<sub>2.5</sub> exposure hotspots"</td><td>Baseline<sup>c</sup> -15%, only if baseline ≥ 90th centile of PM<sub>2.5</sub> levels<sup>g</sup></td></tr></tbody></table>

<footnote><sup>a</sup> Corresponding to the 5th percentile of PM<sub>2.5</sub> concentration distribution among French rural towns</footnote>

<footnote><sup>b</sup> The 10th percentile of PM<sub>2.5</sub> exposure by Housing Block Regrouped for Statistical Information (IRIS) in the study area (corresponding to 10.3 and 12.4 µg/m<sup>3</sup> in Grenoble and Lyon conurbations, respectively)</footnote>

<footnote><sup>c</sup> Baseline corresponds to the PM<sub>2.5</sub> exposure average for the 2015–2017 period, taken as a reference in the present study</footnote>

<footnote><sup>d</sup> Mortality reduction targets expressed as a proportion of the non-accidental death cases attributable to PM<sub>2.5</sub> exposure that can be prevented under the scenario S2: "No anthropogenic PM<sub>2.5</sub> emissions"</footnote>

<footnote><sup>e</sup> S6: -2.9 and -3.3 µg/m<sup>3</sup> in Grenoble and Lyon conurbations, respectively; S7: -4.4 and -5.1 µg/m<sup>3</sup>; S8: -6.0 and -6.9 µg/m<sup>3</sup></footnote>

<footnote><sup>f</sup> Inspired by the 2008/50/EU Directive, which targets relative PM<sub>2.5</sub> yearly average decreases to obtain by 2020. The decrease value depends on the exposure average for the last three years (2015–2017): -15% in the case of Grenoble and Lyon conurbations</footnote>

<footnote><sup>g</sup> The 90th percentile corresponded to 16.0 and 17.4 µg/m<sup>3</sup> in Grenoble and Lyon conurbations, respectively</footnote>
to the second situation corresponds to what is called the *difference-in-differences* approach [38]; in this observational approach, in order to estimate the impact of a real intervention, a community or group experiencing an intervention is compared to itself before the intervention, while another group that did not experience the intervention to correct this before-after comparison for temporal trends in the health outcome of interest).

A specificity of the second (“future”) option relates to the temporal evolutions of the study area. These possibly include changes in the demography (age structure and hence also possibly raw disease risk, as the incidence of most diseases varies with age), in specific disease risk factors besides the one in focus and also possibly regarding the dose response function, in particular for health outcomes very sensitive to societal changes, such as mortality. Such evolutions may be difficult to predict, in particular over periods of several decades or more. Illustrations include studies of long-term effects of ozone depletion [37] or of climate change, in which sociodemographic changes as well as societal adaptation to high temperatures [39] are expected.

### Selection of the target scenario(s) – exposure levels

The scenarios correspond to the counterfactual situations that one wishes to compare to answer the study aim. One scenario will typically correspond to the *current* or *baseline* situation (if one is interested in the effect of a factor present today), or to the extension over time of the current situation, the so-called “business as usual” scenario, if the question asked pertains to a policy or infrastructure that would be implemented or built in the future. The alternative scenario(s) will correspond to the hypothetical situation in which the policy considered has been implemented (the policy being e.g., the construction of an infrastructure, a change in urban design, or a lowering of the pollution levels, if the study aims at quantifying the impact of a specific exposure). Of course, several counterfactual scenarios can be considered and compared (see examples in Table 1 or [29]).

An essential question here, for actions on one or several specific factors, relates to the targeted levels (or distribution) of the factor. In the case of a study aiming to quantify the current impact of a factor that has monotonous effects on all diseases considered, the counterfactual situation in which no one is exposed to the factor can be considered. This would correspond to the ban of the substance or the behavior considered, assuming that

<table><caption>**Table 1** A series of 10 scenarios compared in a risk assessment study of the impact of atmospheric pollution (fine particulate matter, or PM<sub>2.5</sub>). From [40]</caption><thead><tr><th>Scenario number</th><th>Scenario description</th><th>Scenario name</th><th>PM<sub>2.5</sub> yearly level reduction</th></tr></thead><tbody><tr><td>S1</td><td>Spatially homogeneous target value in the whole area</td><td>"WHO guideline"</td><td>Down to WHO yearly guideline (10 µg/m<sup>3</sup> at the time of this publication)</td></tr><tr><td>S2</td><td></td><td>"No anthropogenic PM<sub>2.5</sub> emissions"</td><td>Down to lowest nation-wide levels (4.9 µg/m<sup>3</sup>)<sup>a</sup></td></tr><tr><td>S3</td><td></td><td>"Quiet neighborhood"</td><td>Down to lowest study area district levels (10th percentile of exposure)<sup>b</sup></td></tr><tr><td>S4</td><td rowspan="2">Homogeneous PM<sub>2.5</sub> decreases in the whole area</td><td>"-1 µg/m<sup>3</sup>"</td><td>Baseline<sup>c</sup> -1 µg/m<sup>3</sup></td></tr><tr><td>S5</td><td>"-2 µg/m<sup>3</sup>"</td><td>Baseline<sup>c</sup> -2 µg/m<sup>3</sup></td></tr><tr><td>S6</td><td rowspan="3">Targeted reduction in PM<sub>2.5</sub>-related mortality in the whole area<sup>d</sup></td><td>"-1/3 of mortality"</td><td rowspan="3">Equivalent to decreasing homogeneously and sufficiently the baseline<sup>c</sup> exposure to achieve the indicated health objective<sup>e</sup></td></tr><tr><td>S7</td><td>"-1/2 of mortality"</td></tr><tr><td>S8</td><td>"-2/3 of mortality"</td></tr><tr><td>S9</td><td>2008/50/EU Directive<sup>f</sup></td><td>In the whole study area"</td><td>Baseline<sup>c</sup> -15%</td></tr><tr><td>S10</td><td>"2020 target"</td><td>Restricted to PM<sub>2.5</sub> exposure hotspots"</td><td>Baseline<sup>c</sup> -15%, only if baseline ≥ 90th centile of PM<sub>2.5</sub> levels<sup>g</sup></td></tr></tbody></table>

<footnote><sup>a</sup> Corresponding to the 5th percentile of PM<sub>2.5</sub> concentration distribution among French rural towns</footnote>

<footnote><sup>b</sup> The 10th percentile of PM<sub>2.5</sub> exposure by Housing Block Regrouped for Statistical Information (IRIS) in the study area (corresponding to 10.3 and 12.4 µg/m<sup>3</sup> in Grenoble and Lyon conurbations, respectively)</footnote>

<footnote><sup>c</sup> Baseline corresponds to the PM<sub>2.5</sub> exposure average for the 2015–2017 period, taken as a reference in the present study</footnote>

<footnote><sup>d</sup> Mortality reduction targets expressed as a proportion of the non-accidental death cases attributable to PM<sub>2.5</sub> exposure that can be prevented under the scenario S2: "No anthropogenic PM<sub>2.5</sub> emissions"</footnote>

<footnote><sup>e</sup> S6: -2.9 and -3.3 µg/m<sup>3</sup> in Grenoble and Lyon conurbations, respectively; S7: -4.4 and -5.1 µg/m<sup>3</sup>; S8: -6.0 and -6.9 µg/m<sup>3</sup></footnote>

<footnote><sup>f</sup> Inspired by the 2008/50/EU Directive, which targets relative PM<sub>2.5</sub> yearly average decreases to obtain by 2020. The decrease value depends on the exposure average for the last three years (2015–2017): -15% in the case of Grenoble and Lyon conurbations</footnote>

<footnote><sup>g</sup> The 90th percentile corresponded to 16.0 and 17.4 µg/m<sup>3</sup> in Grenoble and Lyon conurbations, respectively</footnote>
the substance is not persistent in the body or the envi-
ronment, and that the compliance to the regulation is
perfect. Other scenarios are however worth considering
in specific situations; in particular, one may wish to con-
sider levels strictly higher than zero as an alternative to
the current situation if the factor corresponds to a sub-
stance persistent in the body or the environment (so that
a ban would not lead to the immediate disappearance of
the pollutant, as is the case for DDT [dichlorodiphenyl-
trichloroethane] or PCBs [polychlorinated biphenyls]),
if it has both human and natural sources (as is the case
for particulate matter, which are also emitted by volcanic
eruptions) or if exposure to the factor does not have a
monotonic association with disease occurrence (as is the
case for outdoor temperature, exposure to sun radiations
or level of essential elements in the body). The meth-
odology of the Global burden of disease (GBD) project
coordinated by IHME refers to a *Theoretical Minimum
Risk Exposure Level* (TMREL) defined as the exposure
level that “minimizes risk at the population level, or [...]
captures the maximum attributable burden” [14]. Alter-
natives exist, such as considering a *feasible minimum*
(which may however require a specific approach in order
to be rigorously identified), or specific existing guideline
levels (e.g., WHO air quality guidelines [41]).

In the case of particulate matter (PM), studies in the
early 2000s typically used WHO PM guideline value
(then 10 µg/m³ for PM₂.₅) as the target, which then
seemed a remote target – although this value did not
correspond to a “no-effect level”, which has not been evi-
denced for PM₂.₅. Today, as exposures in many Western
cities decreased close or below 10 µg/m³, lower reference
values are often chosen, such as the 2021 WHO guide-
line value of 5 µg/m³, the lowest observed value, or the
fifth percentile of the values observed across the cities of
the country (which, in the case of PM, will lead to very
different reference values in India and Canada, making
between-country comparisons difficult), or an estimate
of the levels that would be observed in the absence of
anthropogenic source of PM. Since the “target” value has
of course generally a very large impact on estimates, it is
crucial for it to be explicitly quoted when summarizing
the study results. Mueller et al. [36] give the example of
a policy that would simultaneously target noise, air pol-
lution, green space and heat exposure, as well as physical
activity, taking for each exposure factor levels interna-
tionally recommended (in general by WHO) as counter-
factual scenario (see Figure S1).

Considering environmental and societal side effects
of policies

Ideally, the counterfactual scenarios should consider
possible side effects and remote consequences of the

considered intervention. For example, a risk assess-
ment of a ban of bisphenol A (totally or for specific uses)
could consider several counterfactual scenarios, one in
which the consumer products containing bisphenol A
are simply banned (possibly trying to consider the soci-
etal cost of such a ban if the products product a benefit
to society), and others in which bisphenol A is replaced
by other compounds, including some that also have pos-
sible adverse effects, such as bisphenol S. Studies on the
expected impacts of climate change mitigation strategies,
such as the limitation of fossil fuels use, may consider
health effects due to the expected long-term improve-
ment in climate, but also those related to changes in air
pollution levels possibly resulting from the limitation of
fossil fuels use, and also the possible consequences of
increases in physical activity if this limitation of fossil
fuels is expected to be followed by shifts from individual
cars to other more active modes of transportation.

Study area and population

The study area should be coherent with the policy or fac-
tor considered, trying to include the whole population
likely to undergo positive or negative impacts from the
factor or policy. Its choice should also take into account
the entity (institution, community, administration, pop-
ulation...) able to take a decision regarding this policy.
Choosing an area larger than that targeted by a policy
makes sense, as it may allow to consider unplanned
effects on the surrounding areas (for example, in the
case of a policy planning to ban the most polluting vehi-
cles from a city, an increase in the traffic of these vehi-
cles in the surrounding cities), and to provide estimates
specific to various sub-areas, which are also relevant
because sometimes the exact area concerned with a pos-
sible policy is not always decided a priori – in which case
the study may help making this decision. However, one
should also keep in mind that considering a study area
larger than that in which the policy will be implemented
may entail possible dilution effects – i.e., the impact may
appear lower than it is actually in the population targeted
by the policy, if expressed on a multiplicative scale, that
is, as a change in the proportion of deaths or DALYs in
the area. When considering a policy decided at the city
level, estimating the health impact in the city and pos-
sibly the surrounding ones is for example relevant; for a
European policy, one may consider the whole Europe, or
a (possibly random) group of regions if limiting the size
of the study population limits bias, costs or uncertainties,
which is not always the case for risk assessment studies
contrarily to field studies.

In addition to factors related to health (see Assess-
ment of disease frequency) and to exposure to the factor
or policy considered (such as possibly fine-scale data on
the substance is not persistent in the body or the envi-
ronment, and that the compliance to the regulation is
perfect. Other scenarios are however worth considering
in specific situations; in particular, one may wish to con-
sider levels strictly higher than zero as an alternative to
the current situation if the factor corresponds to a sub-
stance persistent in the body or the environment (so that
a ban would not lead to the immediate disappearance of
the pollutant, as is the case for DDT [dichlorodiphenyl-
trichloroethane] or PCBs [polychlorinated biphenyls]),
if it has both human and natural sources (as is the case
for particulate matter, which are also emitted by volcanic
eruptions) or if exposure to the factor does not have a
monotonic association with disease occurrence (as is the
case for outdoor temperature, exposure to sun radiations
or level of essential elements in the body). The meth-
odology of the Global burden of disease (GBD) project
coordinated by IHME refers to a *Theoretical Minimum
Risk Exposure Level* (TMREL) defined as the exposure
level that “minimizes risk at the population level, or [...]
captures the maximum attributable burden” [14]. Alter-
natives exist, such as considering a *feasible minimum*
(which may however require a specific approach in order
to be rigorously identified), or specific existing guideline
levels (e.g., WHO air quality guidelines [41]).

In the case of particulate matter (PM), studies in the
early 2000s typically used WHO PM guideline value
(then 10 µg/m³ for PM₂.₅) as the target, which then
seemed a remote target – although this value did not
correspond to a “no-effect level”, which has not been evi-
denced for PM₂.₅. Today, as exposures in many Western
cities decreased close or below 10 µg/m³, lower reference
values are often chosen, such as the 2021 WHO guide-
line value of 5 µg/m³, the lowest observed value, or the
fifth percentile of the values observed across the cities of
the country (which, in the case of PM, will lead to very
different reference values in India and Canada, making
between-country comparisons difficult), or an estimate
of the levels that would be observed in the absence of
anthropogenic source of PM. Since the “target” value has
of course generally a very large impact on estimates, it is
crucial for it to be explicitly quoted when summarizing
the study results. Mueller et al. [36] give the example of
a policy that would simultaneously target noise, air pol-
lution, green space and heat exposure, as well as physical
activity, taking for each exposure factor levels interna-
tionally recommended (in general by WHO) as counter-
factual scenario (see Figure S1).

Considering environmental and societal side effects
of policies

Ideally, the counterfactual scenarios should consider
possible side effects and remote consequences of the

considered intervention. For example, a risk assess-
ment of a ban of bisphenol A (totally or for specific uses)
could consider several counterfactual scenarios, one in
which the consumer products containing bisphenol A
are simply banned (possibly trying to consider the soci-
etal cost of such a ban if the products product a benefit
to society), and others in which bisphenol A is replaced
by other compounds, including some that also have pos-
sible adverse effects, such as bisphenol S. Studies on the
expected impacts of climate change mitigation strategies,
such as the limitation of fossil fuels use, may consider
health effects due to the expected long-term improve-
ment in climate, but also those related to changes in air
pollution levels possibly resulting from the limitation of
fossil fuels use, and also the possible consequences of
increases in physical activity if this limitation of fossil
fuels is expected to be followed by shifts from individual
cars to other more active modes of transportation.

Study area and population

The study area should be coherent with the policy or fac-
tor considered, trying to include the whole population
likely to undergo positive or negative impacts from the
factor or policy. Its choice should also take into account
the entity (institution, community, administration, pop-
ulation...) able to take a decision regarding this policy.
Choosing an area larger than that targeted by a policy
makes sense, as it may allow to consider unplanned
effects on the surrounding areas (for example, in the
case of a policy planning to ban the most polluting vehi-
cles from a city, an increase in the traffic of these vehi-
cles in the surrounding cities), and to provide estimates
specific to various sub-areas, which are also relevant
because sometimes the exact area concerned with a pos-
sible policy is not always decided a priori – in which case
the study may help making this decision. However, one
should also keep in mind that considering a study area
larger than that in which the policy will be implemented
may entail possible dilution effects – i.e., the impact may
appear lower than it is actually in the population targeted
by the policy, if expressed on a multiplicative scale, that
is, as a change in the proportion of deaths or DALYs in
the area. When considering a policy decided at the city
level, estimating the health impact in the city and pos-
sibly the surrounding ones is for example relevant; for a
European policy, one may consider the whole Europe, or
a (possibly random) group of regions if limiting the size
of the study population limits bias, costs or uncertainties,
which is not always the case for risk assessment studies
contrarily to field studies.

In addition to factors related to health (see Assess-
ment of disease frequency) and to exposure to the factor
or policy considered (such as possibly fine-scale data on
population density), it is usually relevant to collect information on population size, sociodemographic (documenting e.g., age and social-category distribution) and behavioral factors. Although seldom done in practice in the context of risk assessment studies, it is worth considering conducting a specific survey to document specific characteristics of the study population not available in administrative or health databases. For example, if the intervention may as a side effect impact physical activity (which has a non-linear relation to health), it is useful to document the distribution of physical activity in the population.

## Exposure (risk factors) assessment

### Identification of exposures

In the simple case of a risk assessment study considering a single pre-identified factor A, before assessing the impact (Health impact), one has to:

* assess the expected exposure to factor A in the study population under the considered counterfactual scenarios (see Exposure assessment tools – general considerations to Reliance on exposure biomarkers);

* identify all health endpoints and possibly biological parameters H₁, H₂... Hᵢ that can or could be influenced by A (see Identifying all health-related events possibly influenced by the considered exposures);

* assess the level of evidence regarding the possible effect of A on H₁, of A on H₂... Hᵢ (see Estimating the strength of evidence about the effect of factors on health);

* assess the incidence of the health endpoints in the considered population, and the dose response function of all exposure-outcome pairs (A, H₁), (A, H₂)... (A, Hᵢ) (see Exposure-response functions).

As described in Fig. 2, the level of intervention can correspond to either the emission of factor A (e.g., what a chemical plant is allowed to emit on a yearly basis, box 1), its concentration in a milieu (e.g., air, water, food, box 3A), human exposure to A (referring, strictly speaking, to the contact of humans with the factor, integrating both the duration of the contact and the level of the compound, box 4); A may also correspond to a behavior (e.g., having sexual intercourse without using condoms, box 3B). We will here refer to all of these situations with the same simplifying terminology of exposure in the loose sense, keeping in mind that this differs from its strict definition given above, and that depending on the situation, one may have to do some modelling to translate the intervention into a metric compatible with the

exposure response function to be used (see Exposure assessment tools – general considerations below).

If the starting point of the study is now a family of factors (e.g., endocrine disruptors, or environmental factors, as in the case of Environmental burden of disease assessments), then one may first have to list/identify which factors fall under this definition. This step can in practice be challenging and may require a specific technical study.

If the study aims at assessing the impact of a policy, one has to first analyze if and how the policy may translate in terms of environmental (understood in the broad sense) impacts – that is, identify which chemical, physical and social factors A₁, A₂... Aᵢ may be influenced by the policy, and quantify the expected amplitude of the variations in these factors once the policy has been implemented. For example, if one aims at estimating the impact of banning a fraction of gasoline- and diesel-powered cars or trucks from an area, then one will generally have to rely on atmospheric dispersion models to estimate which changes in specific atmospheric pollutants will be induced by this ban, in addition to consider other consequences of the ban, e.g. related to physical activity. This actually corresponds to a study in itself (an environmental and social impact assessment), which may be already available, possibly because of legal requirements. One would then have to perform the three steps listed above (see end of Study area and population) for each of the factors A₁, A₂... Aᵢ, influenced by the policy, which may imply to assess and synthesize the evidence regarding a large number of exposure-outcome pairs (Aᵢ, Hᵢ).

The consideration of several risk factors has implications in the way the health impact is estimated, which are discussed in Consideration of multiple risks factors below.

### Exposure assessment tools – general considerations

Whatever the starting point of the study (i.e., the targeted intervention or factor), the estimation of the health impact should ideally rely on some estimate of the exposure metric coherent with the dose-response function considered (see Exposure-response functions below), which should itself be chosen to minimize the uncertainties and bias in the final risk estimate. If, for example, the evaluated intervention corresponds to the closing of a plant emitting hazardous gases, one could attempt estimating the spatial distribution of the air concentration of the corresponding gases in the area surrounding the plant, averaged over a relevant time period, to convert this spatial distribution into an estimate of population exposure taking into account the spatial distribution of density of the target population (e.g., general population or any specific subgroup) in the study area, and possibly any relevant information
population density), it is usually relevant to collect information on population size, sociodemographic (documenting e.g., age and social-category distribution) and behavioral factors. Although seldom done in practice in the context of risk assessment studies, it is worth considering conducting a specific survey to document specific characteristics of the study population not available in administrative or health databases. For example, if the intervention may as a side effect impact physical activity (which has a non-linear relation to health), it is useful to document the distribution of physical activity in the population.

## Exposure (risk factors) assessment

### Identification of exposures

In the simple case of a risk assessment study considering a single pre-identified factor A, before assessing the impact (Health impact), one has to:

* assess the expected exposure to factor A in the study population under the considered counterfactual scenarios (see Exposure assessment tools – general considerations to Reliance on exposure biomarkers);

* identify all health endpoints and possibly biological parameters $H_1, H_2... H_i$ that can or could be influenced by A (see Identifying all health-related events possibly influenced by the considered exposures);

* assess the level of evidence regarding the possible effect of A on $H_1$, of A on $H_2... H_i$ (see Estimating the strength of evidence about the effect of factors on health);

* assess the incidence of the health endpoints in the considered population, and the dose response function of all exposure-outcome pairs (A, $H_1$), (A, $H_2$)... (A, $H_i$) (see Exposure-response functions).

As described in Fig. 2, the level of intervention can correspond to either the emission of factor A (e.g., what a chemical plant is allowed to emit on a yearly basis, box 1), its concentration in a milieu (e.g., air, water, food, box 3A), human exposure to A (referring, strictly speaking, to the contact of humans with the factor, integrating both the duration of the contact and the level of the compound, box 4); A may also correspond to a behavior (e.g., having sexual intercourse without using condoms, box 3B). We will here refer to all of these situations with the same simplifying terminology of exposure in the loose sense, keeping in mind that this differs from its strict definition given above, and that depending on the situation, one may have to do some modelling to translate the intervention into a metric compatible with the

exposure response function to be used (see Exposure assessment tools – general considerations below).

If the starting point of the study is now a family of factors (e.g., endocrine disruptors, or environmental factors, as in the case of Environmental burden of disease assessments), then one may first have to list/identify which factors fall under this definition. This step can in practice be challenging and may require a specific technical study.

If the study aims at assessing the impact of a policy, one has to first analyze if and how the policy may translate in terms of environmental (understood in the broad sense) impacts – that is, identify which chemical, physical and social factors $A_1, A_2... A_i$ may be influenced by the policy, and quantify the expected amplitude of the variations in these factors once the policy has been implemented. For example, if one aims at estimating the impact of banning a fraction of gasoline- and diesel-powered cars or trucks from an area, then one will generally have to rely on atmospheric dispersion models to estimate which changes in specific atmospheric pollutants will be induced by this ban, in addition to consider other consequences of the ban, e.g. related to physical activity. This actually corresponds to a study in itself (an environmental and social impact assessment), which may be already available, possibly because of legal requirements. One would then have to perform the three steps listed above (see end of Study area and population) for each of the factors $A_1, A_2... A_i$, influenced by the policy, which may imply to assess and synthesize the evidence regarding a large number of exposure-outcome pairs ($A_i, H_i$).

The consideration of several risk factors has implications in the way the health impact is estimated, which are discussed in Consideration of multiple risks factors below.

### Exposure assessment tools – general considerations

Whatever the starting point of the study (i.e., the targeted intervention or factor), the estimation of the health impact should ideally rely on some estimate of the exposure metric coherent with the dose-response function considered (see Exposure-response functions below), which should itself be chosen to minimize the uncertainties and bias in the final risk estimate. If, for example, the evaluated intervention corresponds to the closing of a plant emitting hazardous gases, one could attempt estimating the spatial distribution of the air concentration of the corresponding gases in the area surrounding the plant, averaged over a relevant time period, to convert this spatial distribution into an estimate of population exposure taking into account the spatial distribution of density of the target population (e.g., general population or any specific subgroup) in the study area, and possibly any relevant information
on the time-space activity budget of the local popula-
tions, and then estimate the population risk from this
estimated distribution of population exposure and a
dose-response function chosen in coherence with this
exposure metric. Similarly, if the intervention aims at
changing a behavior such as having unprotected sexual
intercourse, one would ideally need to obtain estimates
of such behaviors before and after the hypothetical
intervention, to provide an estimate of the incidence of
a sexually transmitted disease.

All the tools of exposure science and etiological epi-
demiological studies can in principle be used to assess
exposures, from environmental models to question-
naires, dosimeters and biomarkers, keeping in mind that
they differ in terms of resolution, accuracy, cost, potential
for bias...

As risk assessment studies are expected to provide an
estimate relevant in a given population, representative-
ness of the group in which exposure is assessed with
respect to this target population is a desired feature, con-
trarily to etiological epidemiological studies, for which
representativeness is usually not required [42]. For this
reason, “simpler” rather than more accurate and cum-
bersome approaches to exposure assessment than those
used in etiological studies may be preferred, since the
later, although more accurate at the individual level, may
entail selection bias and thus have in some instances
more limited validity at the population level. Conse-
quently, environmental models or data, which may be
developed without always requiring contact with the
population, are very frequently used in risk assessment
studies of environmental factors; we discuss below issues
related to the spatial resolution of such models without
entering into details of models development and validity
not specific to risk assessment studies [43]; for behav-
iors, questionnaires may be used, while for many chemi-
cal exposures, data from biomarkers or exposure models
may be preferred.

In addition to issues related to the validity of the
exposure metric itself, errors may arise because of par-
ticipation (selection) bias induced by the selection of
the population for which this metric is available (e.g.,
answering a questionnaire or providing biospecimens to
assess exposure biomarkers). Simply identifying a repre-
sentative sampling base may be challenging in some areas
if no relevant public database exists or if access cannot
be granted; even if such a relevant sampling base exists, a
participation rate of 100% cannot be expected, and refus-
ing to participate can a priori be expected to be associ-
ated with sociodemographic characteristics and possibly
with the exposure of interest. Tools such as reweighing
approaches may be used to limit the impact of such selec-
tion bias on the estimated exposure distribution.

Again, whatever the approach used, the estimate of
exposure provided should be coherent with the hazard
identified and the dose response function to be used in
the following steps (i.e., a dose-response function based
on yearly exposure averages should not be combined
with a weekly estimate of exposure).

Issues related to the assessment of environmental factors
through questionnaires

Questionnaires may be used to assess behaviors, such
as the frequency of use of specific modes of transpor-
tation (which would be relevant if one aims to quan-
tify the impact of a policy entailing a shift in the share
of specific modes of transportation), diet, smoking or
physical activity and also psychosocial factors. Just like
for environmental models, validation studies are par-
ticularly relevant to discuss and possibly quantify (see
below, sensitivity analyses, Sensitivity and uncertainty
analyses) any bias possibly induced by the question-
naire used, keeping in mind that the validity of ques-
tionnaires may be population-specific, as the validity
of replies will depend on the social desirability of the
considered behavior (for example, replies to question-
naires on alcohol consumption may be dependent on
the social perception of alcohol consumption in the
given cultural background), as well as evolve over time
in a given society, limiting the validity of temporal
comparisons.

When it comes to assessing exposure to specific
chemical or physical factors, questionnaires may be
very limited. Indeed, one is generally not aware of
one's own exposure to a chemical, in particular if expo-
sure occurs through several routes (e.g., in the case of
bisphenol A, PCBs, or specific pesticides), and can-
not provide any quantitative estimate of her/his own
exposure; additionally, one's perception of exposures
may be strongly influenced by social or psychologi-
cal factors (e.g., one's perception of the noxiousness of
the factor, or the existence of a disease that one con-
siders to be imputable to the considered exposure),
which may bias the estimated impact (assuming that
perception is not of interest by itself). As an illustra-
tion, a European study showed limited agreement of
one's self-declared exposure to traffic with an objective
assessment of exposure, to extents that varied between
countries [44]. The fact that questionnaires alone are
typically limited to assess exposures to chemical and
physical factors does not imply that they cannot be
used in combination with other sources of informa-
tion to provide a relevant exposure estimate (see Reli-
ance on environmental models and surveys below).
Moreover, questionnaires (including those relying on
smartphone-based applications) are essential to assess
on the time-space activity budget of the local popula-
tions, and then estimate the population risk from this
estimated distribution of population exposure and a
dose-response function chosen in coherence with this
exposure metric. Similarly, if the intervention aims at
changing a behavior such as having unprotected sexual
intercourse, one would ideally need to obtain estimates
of such behaviors before and after the hypothetical
intervention, to provide an estimate of the incidence of
a sexually transmitted disease.

All the tools of exposure science and etiological epi-
demiological studies can in principle be used to assess
exposures, from environmental models to question-
naires, dosimeters and biomarkers, keeping in mind that
they differ in terms of resolution, accuracy, cost, potential
for bias...

As risk assessment studies are expected to provide an
estimate relevant in a given population, representative-
ness of the group in which exposure is assessed with
respect to this target population is a desired feature, con-
trarily to etiological epidemiological studies, for which
representativeness is usually not required [42]. For this
reason, “simpler” rather than more accurate and cum-
bersome approaches to exposure assessment than those
used in etiological studies may be preferred, since the
later, although more accurate at the individual level, may
entail selection bias and thus have in some instances
more limited validity at the population level. Conse-
quently, environmental models or data, which may be
developed without always requiring contact with the
population, are very frequently used in risk assessment
studies of environmental factors; we discuss below issues
related to the spatial resolution of such models without
entering into details of models development and validity
not specific to risk assessment studies [43]; for behav-
iors, questionnaires may be used, while for many chemi-
cal exposures, data from biomarkers or exposure models
may be preferred.

In addition to issues related to the validity of the
exposure metric itself, errors may arise because of par-
ticipation (selection) bias induced by the selection of
the population for which this metric is available (e.g.,
answering a questionnaire or providing biospecimens to
assess exposure biomarkers). Simply identifying a repre-
sentative sampling base may be challenging in some areas
if no relevant public database exists or if access cannot
be granted; even if such a relevant sampling base exists, a
participation rate of 100% cannot be expected, and refus-
ing to participate can a priori be expected to be associ-
ated with sociodemographic characteristics and possibly
with the exposure of interest. Tools such as reweighing
approaches may be used to limit the impact of such selec-
tion bias on the estimated exposure distribution.

Again, whatever the approach used, the estimate of
exposure provided should be coherent with the hazard
identified and the dose response function to be used in
the following steps (i.e., a dose-response function based
on yearly exposure averages should not be combined
with a weekly estimate of exposure).

Issues related to the assessment of environmental factors
through questionnaires

Questionnaires may be used to assess behaviors, such
as the frequency of use of specific modes of transpor-
tation (which would be relevant if one aims to quan-
tify the impact of a policy entailing a shift in the share
of specific modes of transportation), diet, smoking or
physical activity and also psychosocial factors. Just like
for environmental models, validation studies are par-
ticularly relevant to discuss and possibly quantify (see
below, sensitivity analyses, Sensitivity and uncertainty
analyses) any bias possibly induced by the question-
naire used, keeping in mind that the validity of ques-
tionnaires may be population-specific, as the validity
of replies will depend on the social desirability of the
considered behavior (for example, replies to question-
naires on alcohol consumption may be dependent on
the social perception of alcohol consumption in the
given cultural background), as well as evolve over time
in a given society, limiting the validity of temporal
comparisons.

When it comes to assessing exposure to specific
chemical or physical factors, questionnaires may be
very limited. Indeed, one is generally not aware of
one's own exposure to a chemical, in particular if expo-
sure occurs through several routes (e.g., in the case of
bisphenol A, PCBs, or specific pesticides), and can-
not provide any quantitative estimate of her/his own
exposure; additionally, one's perception of exposures
may be strongly influenced by social or psychologi-
cal factors (e.g., one's perception of the noxiousness of
the factor, or the existence of a disease that one con-
siders to be imputable to the considered exposure),
which may bias the estimated impact (assuming that
perception is not of interest by itself). As an illustra-
tion, a European study showed limited agreement of
one's self-declared exposure to traffic with an objective
assessment of exposure, to extents that varied between
countries [44]. The fact that questionnaires alone are
typically limited to assess exposures to chemical and
physical factors does not imply that they cannot be
used in combination with other sources of informa-
tion to provide a relevant exposure estimate (see Reli-
ance on environmental models and surveys below).
Moreover, questionnaires (including those relying on
smartphone-based applications) are essential to assess
behavioral factors such as dietary patterns, alcohol or tobacco consumption, physical exercise, transportation patterns, sexual activity... These often rely on data collected independently from the health impact assessment study, but there is no reason for investigators planning such a study not to envision an ad-hoc questionnaire survey.

## Reliance on environmental models and surveys

In some areas, public authorities or other institutions developed “databases” regarding specific factors that may be a relevant source of information about the exposure of interest. These databases may be built from various sources and approaches. These include data on sources of specific hazards (e.g., maps on the location of pollution sources or on the chemical composition of cosmetics or other consumers’ products), environmental monitoring (e.g., databases on water contamination (typically based on measurements in the water distribution network, job-exposure matrices in an occupational setting or models), corresponding to boxes 2, 3A and 3B of Fig. 2 (the case of human biomonitoring is discussed specifically below). When available, databases on sources and environmental models and measurements have the advantage of being possibly representative of a specific milieu, in particular if they are based on environmental measurements or models, which can more easily be developed on a representative basis than measurements implying the participation of human subjects; they also have the advantage to rely on information often not known to the inhabitants of the study area (e.g., the level of contamination of the air or drinking water or food by specific compounds) and to possibly cover large spatial areas and extended temporal windows. They may provide source-specific information, which may be relevant if the health impact assessment study considers a possible intervention limited to a specific source of exposure; for example, atmospheric pollution dispersion models typically combine emissions from urban heating, traffic, industry... and may be used to predict environmental levels that would be observed assuming that emissions from one or several specific sources are decreased [29]. They possibly allow avoiding directly contacting individuals to collect information on their exposure, although in many situations it is actually relevant to combine such environmental models with questionnaire data: for example, questionnaires are essential to combine models or data on food contamination or dietary characteristics with individual information on food consumption patterns [45], models or measurements in drinking water benefit from information on water use (sources and amount of water drunk, frequency and temperature of baths and showers... [46], and atmospheric pollution models may be relevantly combined with individual information on time space activity, to integrate individual

exposures across the places where each individual spends time [47, 48]. Indeed, environmental models typically provide an estimate of an environmental level and not an estimate of personal exposure in the strict meaning. Other issues related to their use is that such models do not exist for all environmental factors and areas and that their spatial resolution may be limited.

## Environmental models—Issues related to spatial scale

Indeed, the spatial resolutions of such models vary between models. In the case of atmospheric pollutants, early risk assessment studies typically relied on data from background monitoring stations, which cover a generally small fraction of territories and are sometimes distant by several kilometers one from another. In addition, background monitoring stations are by definition located in “background” sites, which are located far (typically, a couple hundred meters or more) from air pollution “hot spots” (see Fig. 3). On the one hand, relying on data from background monitoring stations may underestimate health impacts, as these background stations are not meant to represent people living or spending time close to air pollution hot spots such as industrial sources or high-traffic roads. On the other hand, stations located close to specific sources to monitor their activity are not meant to provide an estimate valid for a large area.

In the last decades, models providing a finer-scale resolution, such as geostatistical models based on measurement campaigns in a large number of points, land-use regression or dispersion models were developed [49]. These have a much finer spatial resolution (Fig. 4). In a study in two French urban areas, assessing exposures from background monitoring stations entailed an underestimation of the mortality attributable to fine particulate matter by 10 to 20%, compared to fine-scale models with spatial resolutions taking into account variations in the pollutants’ concentration with a spatial scale of about 10 m [34]. Identifying the most relevant approach for risk assessment purposes is not straightforward. Even some fine-scale approaches may entail some error, as these may represent a “smoothed” version of the actual spatial contrasts in air pollution, and as smoothing typically entails a poor representation of the extreme values. These models with a very fine spatial resolution may be limited in terms of temporal resolution, which may be an issue for some health outcomes. Moreover and maybe counter-intuitively, relying on spatially very fine models may not be desirable in risk assessment studies in which there is no available data on the time-space activity of individuals. Indeed, if, in the absence of such individual time-space activity data, one has to
behavioral factors such as dietary patterns, alcohol or tobacco consumption, physical exercise, transportation patterns, sexual activity... These often rely on data collected independently from the health impact assessment study, but there is no reason for investigators planning such a study not to envision an ad-hoc questionnaire survey.

## Reliance on environmental models and surveys

In some areas, public authorities or other institutions developed “databases” regarding specific factors that may be a relevant source of information about the exposure of interest. These databases may be built from various sources and approaches. These include data on sources of specific hazards (e.g., maps on the location of pollution sources or on the chemical composition of cosmetics or other consumers’ products), environmental monitoring (e.g., databases on water contamination (typically based on measurements in the water distribution network, job-exposure matrices in an occupational setting or models), corresponding to boxes 2, 3A and 3B of Fig. 2 (the case of human biomonitoring is discussed specifically below). When available, databases on sources and environmental models and measurements have the advantage of being possibly representative of a specific milieu, in particular if they are based on environmental measurements or models, which can more easily be developed on a representative basis than measurements implying the participation of human subjects; they also have the advantage to rely on information often not known to the inhabitants of the study area (e.g., the level of contamination of the air or drinking water or food by specific compounds) and to possibly cover large spatial areas and extended temporal windows. They may provide source-specific information, which may be relevant if the health impact assessment study considers a possible intervention limited to a specific source of exposure; for example, atmospheric pollution dispersion models typically combine emissions from urban heating, traffic, industry... and may be used to predict environmental levels that would be observed assuming that emissions from one or several specific sources are decreased [29]. They possibly allow avoiding directly contacting individuals to collect information on their exposure, although in many situations it is actually relevant to combine such environmental models with questionnaire data: for example, questionnaires are essential to combine models or data on food contamination or dietary characteristics with individual information on food consumption patterns [45], models or measurements in drinking water benefit from information on water use (sources and amount of water drunk, frequency and temperature of baths and showers... [46], and atmospheric pollution models may be relevantly combined with individual information on time space activity, to integrate individual

exposures across the places where each individual spends time [47, 48]. Indeed, environmental models typically provide an estimate of an environmental level and not an estimate of personal exposure in the strict meaning. Other issues related to their use is that such models do not exist for all environmental factors and areas and that their spatial resolution may be limited.

## Environmental models—Issues related to spatial scale

Indeed, the spatial resolutions of such models vary between models. In the case of atmospheric pollutants, early risk assessment studies typically relied on data from background monitoring stations, which cover a generally small fraction of territories and are sometimes distant by several kilometers one from another. In addition, background monitoring stations are by definition located in “background” sites, which are located far (typically, a couple hundred meters or more) from air pollution “hot spots” (see Fig. 3). On the one hand, relying on data from background monitoring stations may underestimate health impacts, as these background stations are not meant to represent people living or spending time close to air pollution hot spots such as industrial sources or high-traffic roads. On the other hand, stations located close to specific sources to monitor their activity are not meant to provide an estimate valid for a large area.

In the last decades, models providing a finer-scale resolution, such as geostatistical models based on measurement campaigns in a large number of points, land-use regression or dispersion models were developed [49]. These have a much finer spatial resolution (Fig. 4). In a study in two French urban areas, assessing exposures from background monitoring stations entailed an underestimation of the mortality attributable to fine particulate matter by 10 to 20%, compared to fine-scale models with spatial resolutions taking into account variations in the pollutants’ concentration with a spatial scale of about 10 m [34]. Identifying the most relevant approach for risk assessment purposes is not straightforward. Even some fine-scale approaches may entail some error, as these may represent a “smoothed” version of the actual spatial contrasts in air pollution, and as smoothing typically entails a poor representation of the extreme values. These models with a very fine spatial resolution may be limited in terms of temporal resolution, which may be an issue for some health outcomes. Moreover and maybe counter-intuitively, relying on spatially very fine models may not be desirable in risk assessment studies in which there is no available data on the time-space activity of individuals. Indeed, if, in the absence of such individual time-space activity data, one has to
<figure><img src="image_5.png" /><figcaption>**Fig. 3** Cross-sectional variations of fine particulate matter (PM<sub>2.5</sub>) throughout the urban area of Lyon, as estimated from a fine-scale dispersion model, and typical locations of background permanent monitoring stations (black circles). Adapted from [40]</figcaption></figure>

assume that individuals are exposed at the concentration assessed at the location of their home address, then models that tend to smooth concentration over rather large areas may be more accurate for the purpose of risk assessment than models very fine spatially used ignoring the other places where individuals spend time.

## Integrating environmental models with data on population density

As already mentioned, environmental models do not provide an estimate of the population exposure in the strict sense, if only because population density varies with space so that simply averaging the environmental levels over the study area, which gives the same weight to each location (and is equivalent to assume that the population is homogeneously distributed spatially across the study area) may poorly approximate population exposure. Getting closer to population exposure may imply to combine the estimated environmental level with data on population density (i.e., weighting concentrations with population density), which will allow considering the fact that the population is not evenly distributed in a given area. Kulhánová et al. [51] have illustrated these issues in a study of the lung cancer risk attributable to fine particulate matter exposure in France. Compared to a model that took into account PM<sub>2.5</sub> exposure at a 2 km

resolution and population density, a model ignoring the spatial distribution of homes within each *département* (geographical units of 200,000 to one million inhabitants) underestimated the population attributable fraction by about one third; when the variations in population sizes *between départements* was ignored, so that one assumed that everyone in the country was exposed to the median level observed at the country level, the estimated population attributable fraction was divided by 3.6, compared to the original one taking into account population density and fine-scale air pollution data (see Table 2). A large part of this bias was due to ignoring population density.

Note that at this step, the environmental levels and population density data can be combined with other spatially referenced data, such as information on sociodemographic characteristics, as a way to provide an estimate of how exposure distribution varies across these sociodemographic characteristics.

## Reliance on personal dosimeters

Exposure assessment may also rely on personal sensors and dosimeters [54]. Generally, these have the advantages to provide an estimate of exposure that does not rely on detailed data on the sources of the factor, which are not always available (for many chemicals whose sources are not always monitored, such as benzene and other volatile compounds or pesticides), not
<figure><img src="image_6.png" /><figcaption>**Fig. 3** Cross-sectional variations of fine particulate matter (PM<sub>2.5</sub>) throughout the urban area of Lyon, as estimated from a fine-scale dispersion model, and typical locations of background permanent monitoring stations (black circles). Adapted from [40]</figcaption></figure>

assume that individuals are exposed at the concentration assessed at the location of their home address, then models that tend to smooth concentration over rather large areas may be more accurate for the purpose of risk assessment than models very fine spatially used ignoring the other places where individuals spend time.

## Integrating environmental models with data on population density

As already mentioned, environmental models do not provide an estimate of the population exposure in the strict sense, if only because population density varies with space so that simply averaging the environmental levels over the study area, which gives the same weight to each location (and is equivalent to assume that the population is homogeneously distributed spatially across the study area) may poorly approximate population exposure. Getting closer to population exposure may imply to combine the estimated environmental level with data on population density (i.e., weighting concentrations with population density), which will allow considering the fact that the population is not evenly distributed in a given area. Kulhánová et al. [51] have illustrated these issues in a study of the lung cancer risk attributable to fine particulate matter exposure in France. Compared to a model that took into account PM<sub>2.5</sub> exposure at a 2 km

resolution and population density, a model ignoring the spatial distribution of homes within each *département* (geographical units of 200,000 to one million inhabitants) underestimated the population attributable fraction by about one third; when the variations in population sizes *between départements* was ignored, so that one assumed that everyone in the country was exposed to the median level observed at the country level, the estimated population attributable fraction was divided by 3.6, compared to the original one taking into account population density and fine-scale air pollution data (see Table 2). A large part of this bias was due to ignoring population density.

Note that at this step, the environmental levels and population density data can be combined with other spatially referenced data, such as information on sociodemographic characteristics, as a way to provide an estimate of how exposure distribution varies across these sociodemographic characteristics.

## Reliance on personal dosimeters

Exposure assessment may also rely on personal sensors and dosimeters [54]. Generally, these have the advantages to provide an estimate of exposure that does not rely on detailed data on the sources of the factor, which are not always available (for many chemicals whose sources are not always monitored, such as benzene and other volatile compounds or pesticides), not
<figure><img src="image_6.png" /><figcaption>**Fig. 4** Spatial resolutions of various air pollution (nitrogen dioxide) exposure models developed in a middle size city. a Estimates based on permanent background monitoring stations; b geostatistical model relying on a fine-scale measurement campaign; c dispersion model taking into account emission and meteorological conditions; d Land-use regression model relying on the same measurement points as geostatistical model (b) [50]</figcaption></figure>

on a modeling of the dispersion of the factor from its sources to the human environment, contrarily to the approaches discussed above in 2.4.4 to 2.4.6. Since dosimeters are carried by individuals, they efficiently allow taking into account the variability in exposure due to people moving between different environment [47]. They also allow to capture indoor levels of the factor of interest, which is of importance (for factors whose levels indoors and outdoors differ, such as ozone, benzene, radiations, temperature, noise...) given that people spend the vast majority of time indoors, at least in Northern countries. This increased “spatial” resolution compared to the above-mentioned environmental models (which typically capture outdoor levels, and generally at one location only if the time space activity

of the population is not assessed) generally comes at the cost of possible limitations in terms of temporal resolution. In particular, it may be cumbersome to assess long-term exposure (which may be toxicologically relevant for specific outcomes) using personal dosimeters, which are typically carried over short-term (typically, from a day to a week) periods; these measurement periods may be repeated over time to improve the accuracy of the assessment as a proxy of long-term exposure [55], as discussed below for exposure biomarkers. Dosimeters are particularly relevant for media-specific exposures or factors, such as atmospheric pollutants including particulate matter [56, 57] or nitrogen oxides [47, 58], benzene [59, 60] and other volatile organic compounds [61], non-ionizing radiation such
<figure><img src="image_7.png" /><figcaption>**Fig. 4** Spatial resolutions of various air pollution (nitrogen dioxide) exposure models developed in a middle size city. a Estimates based on permanent background monitoring stations; b geostatistical model relying on a fine-scale measurement campaign; c dispersion model taking into account emission and meteorological conditions; d Land-use regression model relying on the same measurement points as geostatistical model (b) [50]</figcaption></figure>

on a modeling of the dispersion of the factor from its sources to the human environment, contrarily to the approaches discussed above in 2.4.4 to 2.4.6. Since dosimeters are carried by individuals, they efficiently allow taking into account the variability in exposure due to people moving between different environment [47]. They also allow to capture indoor levels of the factor of interest, which is of importance (for factors whose levels indoors and outdoors differ, such as ozone, benzene, radiations, temperature, noise...) given that people spend the vast majority of time indoors, at least in Northern countries. This increased “spatial” resolution compared to the above-mentioned environmental models (which typically capture outdoor levels, and generally at one location only if the time space activity

of the population is not assessed) generally comes at the cost of possible limitations in terms of temporal resolution. In particular, it may be cumbersome to assess long-term exposure (which may be toxicologically relevant for specific outcomes) using personal dosimeters, which are typically carried over short-term (typically, from a day to a week) periods; these measurement periods may be repeated over time to improve the accuracy of the assessment as a proxy of long-term exposure [55], as discussed below for exposure biomarkers. Dosimeters are particularly relevant for media-specific exposures or factors, such as atmospheric pollutants including particulate matter [56, 57] or nitrogen oxides [47, 58], benzene [59, 60] and other volatile organic compounds [61], non-ionizing radiation such
<table><caption>**Table 2** Illustration of the influence of the spatial resolution of the exposure model and of the consideration of data on population density in health impact assessment studies (adapted from [51])</caption><thead><tr><th>Hypothesis</th><th>PM<sub>2.5</sub> exposure: 5th–50th–95th percentiles (µg/m<sup>3</sup>)</th><th>PAF (%) (95% CI)</th><th>Number of attributable lung cancer cases (95% CI)</th><th>Relative difference compared to main model (%)</th></tr></thead><tbody><tr><td colspan="5"><strong>Approach 1: population-weighted PM<sub>2.5</sub> concentration (main model)</strong></td></tr><tr><td>IRIS scale</td><td>8.3 – 13.8 – 21.8</td><td>3.6 (1.7–5.4)</td><td>1,466 (679–2,193)</td><td>–</td></tr><tr><td colspan="5"><strong>Sensitivity analyses</strong></td></tr><tr><td colspan="5"><strong>Approach 2: population-weighted median PM<sub>2.5</sub> concentration</strong></td></tr><tr><td>Department scale</td><td>9.7 – 13.8 – 19.1</td><td>3.6 (1.7–5.4)</td><td>1,471 (680–2,203)</td><td>0.4</td></tr><tr><td>Country scale</td><td>13.8 – 13.8 – 13.8</td><td>3.2 (1.5–4.9)</td><td>1,303 (598–1,965)</td><td>-11.1</td></tr><tr><td colspan="5"><strong>Approach 3: median PM<sub>2.5</sub> concentration without population weighing</strong></td></tr><tr><td>Department scale</td><td>6.0 – 11.1 – 16.4</td><td>2.4 (1.1–3.6)</td><td>964 (445–1,446)</td><td>-34.2</td></tr><tr><td>Country scale</td><td>11.2 – 11.2 – 11.2</td><td>1.0 (0.5–1.6)</td><td>416 (190–631)</td><td>-71.6</td></tr><tr><td colspan="5"><strong>Approach 4: alternative RR of lung cancer (1.40 per 10 µg/m<sup>3</sup> increase in PM<sub>2.5</sub>, instead of 1.09)</strong></td></tr><tr><td>Neighbourhood</td><td>8.3 – 13.8 – 21.8</td><td>12.9 (0.2–25.3)</td><td>5,232 (78–10,221)</td><td>256.8</td></tr></tbody></table>

The table gives the estimated population attributable fraction (PAF) of lung cancer cases attributable to fine particulate matter (PM<sub>2.5</sub>) exposure in France among subjects aged 30 years and more, for the year 2015 [51]

In approach 1 (main model), the PAF is estimated using a fine scale PM<sub>2.5</sub> dispersion model (2 km grid) at the country level, averaged at the "IRIS" (neighborhood) scale and weighted by population density. In approach 2, exposure is smoothed by assuming that all IRIS of each département have the same PM<sub>2.5</sub> concentration (corresponding to the median population-weighted value in each département), or that all départements in the country have the same PM<sub>2.5</sub> concentration value ("country scale"). In approach 3, values also correspond to the median value at the département (respectively, country) levels, with the only difference compared to approach 2 that median value are estimated without weighting with population density

Approach 4 differs from approach 1 in that an alternative RR of 1.40 per 10 µg/m³ increase, obtained from a meta-analysis from ESCAPE project including 14 cohorts from eight European countries [52] is used, while a RR of 1.09 is used in model 1 [53]

CI Confidence interval, PAF Population attributable fraction, RR Relative risk

as ultra-violet [62] or ionizing radiation [63], temperature, noise [64]... Contrarily to environmental models, their use in the context of a health impact assessment study implies to recruit a population sample as representative of the target population as possible. Their use in risk assessment studies appears quite limited so far outside the occupational setting [61].

## Reliance on exposure biomarkers

In the case of chemicals with multiple routes of exposure such as specific pesticides, which may be present in food, water and air, exposure biomarkers (the assessment of the compound or of its metabolite(s) in a tissue or fluid of the organism) may be a relevant approach. With the development of biomonitoring studies [65–67] and of cohorts collecting biospecimens [68], exposure biomarkers may be expected to be increasingly used in quantitative risk assessment studies related to chemicals.

Biomarkers study typically provide an estimate of the circulating or excreted level of the compound, which is not exposure in the strict sense but is related to it, while also depending on toxicokinetic factors, that typically vary between subjects [69]. Biomarkers integrate multiple routes of exposure, in that the level of a compound or its metabolites in a given body compartment will generally depend on the doses entering the body by ingestion, inhalation, dermal contact... (with many

specificities according to the compound and tissue in which the metabolites are assessed). This may or may not be seen as an advantage, depending on the study aim, which may relate to exposure as a whole or to route-specific exposure (e.g., that due to food contamination). Considering these different routes is in principle possible via environmental models and measurements, but may be very cumbersome in terms of data collection and modeling work (consider for example a study on the impact of pesticides, which would have to estimate pesticide levels in water, possibly in the air, in food and to assess eating behaviors to try to reconstruct an individual's exposure). A limitation of exposure biomarkers is related to the short half-life of many chemicals in the body, which implies that a spot biospecimen will generally be a poor proxy of long-term internal dose [70]. This is an issue for etiological studies, in which dose response functions assessed using a single biomarker in each subject are expected to suffer from bias towards the null [70]. This issue may also impact risk assessment studies. Indeed, even in the context of classical-type error, which may be hypothesized for biomarkers, although the population average exposure may not be biased when a spot measurement is done in each subject, the estimation of other features of the exposure distribution, such as variance and hence the estimation of specific exposure percentages, is expected to be biased. Like questionnaire-based
<table><caption>**Table 2** Illustration of the influence of the spatial resolution of the exposure model and of the consideration of data on population density in health impact assessment studies (adapted from [51])</caption><thead><tr><th>Hypothesis</th><th>PM<sub>2.5</sub> exposure: 5th–50th–95th percentiles (µg/m<sup>3</sup>)</th><th>PAF (%) (95% CI)</th><th>Number of attributable lung cancer cases (95% CI)</th><th>Relative difference compared to main model (%)</th></tr></thead><tbody><tr><td colspan="5"><strong>Approach 1: population-weighted PM<sub>2.5</sub> concentration (main model)</strong></td></tr><tr><td>IRIS scale</td><td>8.3 – 13.8 – 21.8</td><td>3.6 (1.7–5.4)</td><td>1,466 (679–2,193)</td><td>–</td></tr><tr><td colspan="5"><strong>Sensitivity analyses</strong></td></tr><tr><td colspan="5"><strong>Approach 2: population-weighted median PM<sub>2.5</sub> concentration</strong></td></tr><tr><td>Department scale</td><td>9.7 – 13.8 – 19.1</td><td>3.6 (1.7–5.4)</td><td>1,471 (680–2,203)</td><td>0.4</td></tr><tr><td>Country scale</td><td>13.8 – 13.8 – 13.8</td><td>3.2 (1.5–4.9)</td><td>1,303 (598–1,965)</td><td>-11.1</td></tr><tr><td colspan="5"><strong>Approach 3: median PM<sub>2.5</sub> concentration without population weighing</strong></td></tr><tr><td>Department scale</td><td>6.0 – 11.1 – 16.4</td><td>2.4 (1.1–3.6)</td><td>964 (445–1,446)</td><td>-34.2</td></tr><tr><td>Country scale</td><td>11.2 – 11.2 – 11.2</td><td>1.0 (0.5–1.6)</td><td>416 (190–631)</td><td>-71.6</td></tr><tr><td colspan="5"><strong>Approach 4: alternative RR of lung cancer (1.40 per 10 µg/m<sup>3</sup> increase in PM<sub>2.5</sub>, instead of 1.09)</strong></td></tr><tr><td>Neighbourhood</td><td>8.3 – 13.8 – 21.8</td><td>12.9 (0.2–25.3)</td><td>5,232 (78–10,221)</td><td>256.8</td></tr></tbody></table>

The table gives the estimated population attributable fraction (PAF) of lung cancer cases attributable to fine particulate matter (PM<sub>2.5</sub>) exposure in France among subjects aged 30 years and more, for the year 2015 [51]

In approach 1 (main model), the PAF is estimated using a fine scale PM<sub>2.5</sub> dispersion model (2 km grid) at the country level, averaged at the "IRIS" (neighborhood) scale and weighted by population density. In approach 2, exposure is smoothed by assuming that all IRIS of each département have the same PM<sub>2.5</sub> concentration (corresponding to the median population-weighted value in each département), or that all départements in the country have the same PM<sub>2.5</sub> concentration value ("country scale"). In approach 3, values also correspond to the median value at the département (respectively, country) levels, with the only difference compared to approach 2 that median value are estimated without weighting with population density

Approach 4 differs from approach 1 in that an alternative RR of 1.40 per 10 µg/m³ increase, obtained from a meta-analysis from ESCAPE project including 14 cohorts from eight European countries [52] is used, while a RR of 1.09 is used in model 1 [53]

CI: Confidence interval, PAF: Population attributable fraction, RR: Relative risk

as ultra-violet [62] or ionizing radiation [63], temperature, noise [64]... Contrarily to environmental models, their use in the context of a health impact assessment study implies to recruit a population sample as representative of the target population as possible. Their use in risk assessment studies appears quite limited so far outside the occupational setting [61].

## Reliance on exposure biomarkers

In the case of chemicals with multiple routes of exposure such as specific pesticides, which may be present in food, water and air, exposure biomarkers (the assessment of the compound or of its metabolite(s) in a tissue or fluid of the organism) may be a relevant approach. With the development of biomonitoring studies [65–67] and of cohorts collecting biospecimens [68], exposure biomarkers may be expected to be increasingly used in quantitative risk assessment studies related to chemicals.

Biomarkers study typically provide an estimate of the circulating or excreted level of the compound, which is not exposure in the strict sense but is related to it, while also depending on toxicokinetic factors, that typically vary between subjects [69]. Biomarkers integrate multiple routes of exposure, in that the level of a compound or its metabolites in a given body compartment will generally depend on the doses entering the body by ingestion, inhalation, dermal contact... (with many

specificities according to the compound and tissue in which the metabolites are assessed). This may or may not be seen as an advantage, depending on the study aim, which may relate to exposure as a whole or to route-specific exposure (e.g., that due to food contamination). Considering these different routes is in principle possible via environmental models and measurements, but may be very cumbersome in terms of data collection and modeling work (consider for example a study on the impact of pesticides, which would have to estimate pesticide levels in water, possibly in the air, in food and to assess eating behaviors to try to reconstruct an individual's exposure). A limitation of exposure biomarkers is related to the short half-life of many chemicals in the body, which implies that a spot biospecimen will generally be a poor proxy of long-term internal dose [70]. This is an issue for etiological studies, in which dose response functions assessed using a single biomarker in each subject are expected to suffer from bias towards the null [70]. This issue may also impact risk assessment studies. Indeed, even in the context of classical-type error, which may be hypothesized for biomarkers, although the population average exposure may not be biased when a spot measurement is done in each subject, the estimation of other features of the exposure distribution, such as variance and hence the estimation of specific exposure percentages, is expected to be biased. Like questionnaire-based
approaches, and generally to a larger extent, biomarker-
based approach are dependent on individual's participa-
tion and are therefore prone to selection biases; these
may, again, be partly corrected if information on the fac-
tors associated with participation is available. Just like for
all other approaches to assess exposures, behaviors and
other health drivers, although rarely done, there is no
reason beyond logistics and funding not to consider an
ad-hoc biomonitoring survey as part of the HIA, on the
contrary. We are not aware of specific quantitative evalu-
ation of the bias associated with all the possible exposure
assessment tools to a priori justify the choice of the expo-
sure metric used in a given risk assessment study.

Exposure-response functions

Identifying all health-related events possibly influenced
by the considered exposures

For each factor (in the broad sense of chemical, physical,
psychosocial, behavioral factor) primarily considered or
identified at the previous stages as possibly influenced
by the considered intervention, all health-related events
that this factor might influence (the “health effects”, or
hazards, a qualitative notion not to be mistaken with the
quantitative health impacts) need to be identified. This
identification should cover proximal and more remote
effects, and positive (beneficial) as well as negative (det-
rimental) effects. For several environmental factors, the
list of possible health effects may be long; for example,
lead is a cause of neurological, nephrotoxic, cardiac,
reproductive... effects, while particulate matter can affect
cardiac, respiratory, metabolic and possibly reproductive
and neurodevelopmental function [71]. Complex policies
may entail numerous health consequences; for example,
acting on traffic will affect air pollutants, but also noise,
traffic accidents, greenhouse gas emissions, that may
have long-term health effects (even if the correspond-
ing impact may be limited, depending on the considered
spatial scale). Even if the study does not provide a quan-
titative assessment of all the effects of a given exposure,
identifying all of these effects is important. This identi-
fication of possible health effects should in principle rely
on a systematic review that should encompass the human
literature but also toxicology and possibly in vitro or in
silico studies that may inform on mechanisms and point
to specific health effects. Such an identification of all
likely effects of the factor, change or intervention con-
sidered may rely on a recent well-conducted published
review.

Estimating the strength of evidence about the effect
of factors on health

The identification of each health effect possibly influ-
enced by each considered factor should come with some

assessment of the corresponding level of evidence. The
assessment of the level of evidence evolved in the last
decades from experts' opinion to more formalized sys-
tematic reviews, possibly followed by meta-analyses and
evidence integration approaches combining streams of
evidence from various disciplines such as in silico data,
in vivo and in vitro toxicology, environmental sciences,
epidemiology... (see e.g., [72, 73] or the chapter 6 of [74]
for a presentation of these approaches). Given the some-
times very large effort required by the implementation
of such approaches, in particular for factors about which
a vast literature exists, it is relevant to rely on existing
assessments of the level of evidence, whenever a recent
one with a transparent and relevant methodology is avail-
able. If not, the time and effort required for this step
should not be underestimated, so that a review of the lit-
erature from all relevant disciplines, experts from these
disciplines can be gathered to synthesize and weight the
evidence and provide an assessment on a pre-specified
grading scale (e.g., in terms of probability of causation).
In case several factors are considered, then the number
of exposure outcome pairs considered can be very large.
An example of the assessment of the strength of evidence
about endocrine disruptors is provided in Trasande et al.
[75] and in Table 3.

Handling of the strength of evidence about the effect
of environmental factors on health

In the past, a common practice was to only consider
exposure-outcome pairs ($A_i$, $H_j$) for which the strength
of the evidence regarding the effect of $A_i$ on $H_j$ was very
strong or deemed causal. Another common option is
to focus on a specific a priori chosen health outcome
induced by the exposure, acknowledging that other
effects are ignored; for example, many studies quantified
the impact of tobacco smoke on lung cancer only, while
other effects, e.g., on cardiovascular diseases, are certain.

The obvious consequence of these practices is to bias
the estimated impact of the exposure or policy, generally
in the direction of an underestimation (assuming that
all associations go in the same direction, e.g., a negative
effect of exposures on health). This is obvious for the sec-
ond option above, but is also true for the first one. This is
because in some cases, the discarded exposure-outcome
associations will eventually turn out to correspond to
very likely effects, as research continues, while the sym-
metrical situation of an effect deemed very likely or cer-
tain becoming unlikely as research unfolds is arguably
much rarer in practice [76].

Possible alternatives to only considering very likely
exposure-response pairs include:
approaches, and generally to a larger extent, biomarker-
based approach are dependent on individual's participa-
tion and are therefore prone to selection biases; these
may, again, be partly corrected if information on the fac-
tors associated with participation is available. Just like for
all other approaches to assess exposures, behaviors and
other health drivers, although rarely done, there is no
reason beyond logistics and funding not to consider an
ad-hoc biomonitoring survey as part of the HIA, on the
contrary. We are not aware of specific quantitative evalu-
ation of the bias associated with all the possible exposure
assessment tools to a priori justify the choice of the expo-
sure metric used in a given risk assessment study.

Exposure-response functions

Identifying all health-related events possibly influenced
by the considered exposures

For each factor (in the broad sense of chemical, physical,
psychosocial, behavioral factor) primarily considered or
identified at the previous stages as possibly influenced
by the considered intervention, all health-related events
that this factor might influence (the “health effects”, or
hazards, a qualitative notion not to be mistaken with the
quantitative health impacts) need to be identified. This
identification should cover proximal and more remote
effects, and positive (beneficial) as well as negative (det-
rimental) effects. For several environmental factors, the
list of possible health effects may be long; for example,
lead is a cause of neurological, nephrotoxic, cardiac,
reproductive... effects, while particulate matter can affect
cardiac, respiratory, metabolic and possibly reproductive
and neurodevelopmental function [71]. Complex policies
may entail numerous health consequences; for example,
acting on traffic will affect air pollutants, but also noise,
traffic accidents, greenhouse gas emissions, that may
have long-term health effects (even if the correspond-
ing impact may be limited, depending on the considered
spatial scale). Even if the study does not provide a quan-
titative assessment of all the effects of a given exposure,
identifying all of these effects is important. This identi-
fication of possible health effects should in principle rely
on a systematic review that should encompass the human
literature but also toxicology and possibly in vitro or in
silico studies that may inform on mechanisms and point
to specific health effects. Such an identification of all
likely effects of the factor, change or intervention con-
sidered may rely on a recent well-conducted published
review.

Estimating the strength of evidence about the effect
of factors on health

The identification of each health effect possibly influ-
enced by each considered factor should come with some

assessment of the corresponding level of evidence. The
assessment of the level of evidence evolved in the last
decades from experts' opinion to more formalized sys-
tematic reviews, possibly followed by meta-analyses and
evidence integration approaches combining streams of
evidence from various disciplines such as in silico data,
in vivo and in vitro toxicology, environmental sciences,
epidemiology... (see e.g., [72, 73] or the chapter 6 of [74]
for a presentation of these approaches). Given the some-
times very large effort required by the implementation
of such approaches, in particular for factors about which
a vast literature exists, it is relevant to rely on existing
assessments of the level of evidence, whenever a recent
one with a transparent and relevant methodology is avail-
able. If not, the time and effort required for this step
should not be underestimated, so that a review of the lit-
erature from all relevant disciplines, experts from these
disciplines can be gathered to synthesize and weight the
evidence and provide an assessment on a pre-specified
grading scale (e.g., in terms of probability of causation).
In case several factors are considered, then the number
of exposure outcome pairs considered can be very large.
An example of the assessment of the strength of evidence
about endocrine disruptors is provided in Trasande et al.
[75] and in Table 3.

Handling of the strength of evidence about the effect
of environmental factors on health

In the past, a common practice was to only consider
exposure-outcome pairs (Aᵢ, Hⱼ) for which the strength
of the evidence regarding the effect of Aᵢ on Hⱼ was very
strong or deemed causal. Another common option is
to focus on a specific a priori chosen health outcome
induced by the exposure, acknowledging that other
effects are ignored; for example, many studies quantified
the impact of tobacco smoke on lung cancer only, while
other effects, e.g., on cardiovascular diseases, are certain.

The obvious consequence of these practices is to bias
the estimated impact of the exposure or policy, generally
in the direction of an underestimation (assuming that
all associations go in the same direction, e.g., a negative
effect of exposures on health). This is obvious for the sec-
ond option above, but is also true for the first one. This is
because in some cases, the discarded exposure-outcome
associations will eventually turn out to correspond to
very likely effects, as research continues, while the sym-
metrical situation of an effect deemed very likely or cer-
tain becoming unlikely as research unfolds is arguably
much rarer in practice [76].

Possible alternatives to only considering very likely
exposure-response pairs include:
<table><caption>**Table 3** Estimated strength of evidence regarding the effect of endocrine disruptors on health</caption><thead><tr><th>Exposure</th><th>Outcome</th><th>Strength of human evidence</th><th>Strength of toxicological evidence</th><th>Probability of causation, %</th></tr></thead><tbody><tr><td>PBDEs</td><td>IQ loss and intellectual disability</td><td>Moderate-to-high</td><td>Strong</td><td>70-100</td></tr><tr><td>Organophosphate pesticides</td><td>IQ loss and intellectual disability</td><td>Moderate-to-high</td><td>Strong</td><td>70-100</td></tr><tr><td>DDE</td><td>Childhood obesity</td><td>Moderate</td><td>Moderate</td><td>40-69</td></tr><tr><td>DDE</td><td>Adult diabetes</td><td>Low</td><td>Moderate</td><td>20-39</td></tr><tr><td>Di-2-ethylhexylphthalate</td><td>Adult obesity</td><td>Low</td><td>Strong</td><td>40-69</td></tr><tr><td>Di-2-ethylhexylphthalate</td><td>Adult diabetes</td><td>Low</td><td>Strong</td><td>40-69</td></tr><tr><td>Bisphenol A</td><td>Childhood obesity</td><td>Very low-to-low</td><td>Strong</td><td>20-69</td></tr><tr><td>PBDEs</td><td>Testicular cancer</td><td>Very low-to-low</td><td>Weak</td><td>0-19</td></tr><tr><td>PBDEs</td><td>Cryptorchidism</td><td>Low</td><td>Strong</td><td>40-69</td></tr><tr><td>Benzyl and butyl-phthalates</td><td>Male infertility, resulting in increased assisted reproductive technology</td><td>Low</td><td>Strong</td><td>40-69</td></tr><tr><td>Phthalates</td><td>Low testosterone, resulting in increased early mortality</td><td>Low</td><td>Strong</td><td>40-69</td></tr></tbody></table>

The overall probability of causation (last column) was based on the toxicological and epidemiological evidence. From Trasande et al. [75] (extract)

a) Considering all exposure-outcome pairs for which the estimated level of evidence is above a certain level (e.g., “likely association” or above, keeping in mind that diverse approaches are used to obtain these causality gradings and that various scales of evidence are used by various institutions), and estimating the corresponding impacts of these likely effects just like for the exposure-outcome pairs with a very high level of evidence. A special case consists in considering all exposure-outcome pairs for which there is at least “some evidence” of an association; in this case, there is potential for an overestimation of the overall impact (again, assuming that all associations go in the same direction);

b) Performing sensitivity (additional) analyses considering exposure-outcome pairs with decreasing levels of evidence, and report the estimated impact of the exposure or policy considering only very likely effects, as well as the impact estimated considering also likely effects and suspected effects;

c) Considering all exposure-outcome pairs for which the estimated level of evidence is above a certain level in the risk assessment and summing their impacts, weighing the sum by a weight increasing with the level of evidence of the corresponding effect, so that in the overall impact more weight is given to impacts from exposure-outcome pairs with a high level of evidence and less to the less likely ones.

Many studies more or less explicitly correspond to approach a). For example, the GBD methodology currently focuses on exposure-outcome pairs for which there is “convincing or probable evidence” [14]. An example of

approach c), which is an intermediate one between the two first alternatives above, is a study of the cost of exposure to endocrine disruptors in the European Union [12, 75]. In this study, the health impact (and corresponding cost) attributable to exposure to each considered endocrine disruptors has been assessed using a Monte-Carlo approach in which, at each simulation run, the impact of a given exposure-outcome pair was possibly set to zero, according to the estimated probability of causation (with more likely effects being less often set to zero), and the overall impact was estimated averaging over many simulation runs and summed across exposure-outcome pairs. For example, in the case of a dose-response function of an exposure-outcome pair for which the strength of evidence had been rated to be about 50%, then the corresponding attributable cases were taken into consideration in only half of the simulation runs [75]. This approach seems relevant if a large number of factors is considered and if one assumes that the literature is not systematically biased. Indeed, if twenty factors are considered and the evidence is properly evaluated, then, assuming that the weight of evidence is estimated to be 50% for all factors, one may expect that eventually 10 of these factors turn out to really have an impact, so that counting half of the effect of the twenty factors may fall closer to the true impact (corresponding to that of ten factors) than if all twenty factors are ignored because the strength of evidence is not high enough. Note that the assumption regarding the fact that the literature is not biased can be debated for environmental factors, as for many factors, the weight of evidence typically tends to increase over time, rather than vary up or down randomly, and as a literature review of environmental alerts concluded
<table><caption>**Table 3** Estimated strength of evidence regarding the effect of endocrine disruptors on health</caption><thead><tr><th>Exposure</th><th>Outcome</th><th>Strength of human evidence</th><th>Strength of toxicological evidence</th><th>Probability of causation, %</th></tr></thead><tbody><tr><td>PBDEs</td><td>IQ loss and intellectual disability</td><td>Moderate-to-high</td><td>Strong</td><td>70-100</td></tr><tr><td>Organophosphate pesticides</td><td>IQ loss and intellectual disability</td><td>Moderate-to-high</td><td>Strong</td><td>70-100</td></tr><tr><td>DDE</td><td>Childhood obesity</td><td>Moderate</td><td>Moderate</td><td>40-69</td></tr><tr><td>DDE</td><td>Adult diabetes</td><td>Low</td><td>Moderate</td><td>20-39</td></tr><tr><td>Di-2-ethylhexylphthalate</td><td>Adult obesity</td><td>Low</td><td>Strong</td><td>40-69</td></tr><tr><td>Di-2-ethylhexylphthalate</td><td>Adult diabetes</td><td>Low</td><td>Strong</td><td>40-69</td></tr><tr><td>Bisphenol A</td><td>Childhood obesity</td><td>Very low-to-low</td><td>Strong</td><td>20-69</td></tr><tr><td>PBDEs</td><td>Testicular cancer</td><td>Very low-to-low</td><td>Weak</td><td>0-19</td></tr><tr><td>PBDEs</td><td>Cryptorchidism</td><td>Low</td><td>Strong</td><td>40-69</td></tr><tr><td>Benzyl and butyl-phthalates</td><td>Male infertility, resulting in increased assisted reproductive technology</td><td>Low</td><td>Strong</td><td>40-69</td></tr><tr><td>Phthalates</td><td>Low testosterone, resulting in increased early mortality</td><td>Low</td><td>Strong</td><td>40-69</td></tr></tbody></table>

The overall probability of causation (last column) was based on the toxicological and epidemiological evidence. From Trasande et al. [75] (extract)

a) Considering all exposure-outcome pairs for which the estimated level of evidence is above a certain level (e.g., “likely association” or above, keeping in mind that diverse approaches are used to obtain these causality gradings and that various scales of evidence are used by various institutions), and estimating the corresponding impacts of these likely effects just like for the exposure-outcome pairs with a very high level of evidence. A special case consists in considering all exposure-outcome pairs for which there is at least “some evidence” of an association; in this case, there is potential for an overestimation of the overall impact (again, assuming that all associations go in the same direction);

b) Performing sensitivity (additional) analyses considering exposure-outcome pairs with decreasing levels of evidence, and report the estimated impact of the exposure or policy considering only very likely effects, as well as the impact estimated considering also likely effects and suspected effects;

c) Considering all exposure-outcome pairs for which the estimated level of evidence is above a certain level in the risk assessment and summing their impacts, weighing the sum by a weight increasing with the level of evidence of the corresponding effect, so that in the overall impact more weight is given to impacts from exposure-outcome pairs with a high level of evidence and less to the less likely ones.

Many studies more or less explicitly correspond to approach a). For example, the GBD methodology currently focuses on exposure-outcome pairs for which there is “convincing or probable evidence” [14]. An example of

approach c), which is an intermediate one between the two first alternatives above, is a study of the cost of exposure to endocrine disruptors in the European Union [12, 75]. In this study, the health impact (and corresponding cost) attributable to exposure to each considered endocrine disruptors has been assessed using a Monte-Carlo approach in which, at each simulation run, the impact of a given exposure-outcome pair was possibly set to zero, according to the estimated probability of causation (with more likely effects being less often set to zero), and the overall impact was estimated averaging over many simulation runs and summed across exposure-outcome pairs. For example, in the case of a dose-response function of an exposure-outcome pair for which the strength of evidence had been rated to be about 50%, then the corresponding attributable cases were taken into consideration in only half of the simulation runs [75]. This approach seems relevant if a large number of factors is considered and if one assumes that the literature is not systematically biased. Indeed, if twenty factors are considered and the evidence is properly evaluated, then, assuming that the weight of evidence is estimated to be 50% for all factors, one may expect that eventually 10 of these factors turn out to really have an impact, so that counting half of the effect of the twenty factors may fall closer to the true impact (corresponding to that of ten factors) than if all twenty factors are ignored because the strength of evidence is not high enough. Note that the assumption regarding the fact that the literature is not biased can be debated for environmental factors, as for many factors, the weight of evidence typically tends to increase over time, rather than vary up or down randomly, and as a literature review of environmental alerts concluded
that “false alarms” tended to be very rare in environmen-
tal health [76]. This would rather support not restrict-
ing the risk assessment to “certain” exposure-outcome
associations, and also consider those with a lower level
of evidence, possibly taking the level of evidence in the
estimation as described above in c). Considering associa-
tions with less than certain level of evidence also allows
to quantify the possible impact of suspected hazards,
which is relevant to prioritize environmental factors for
which research efforts should be dedicated [77]. In prac-
tice, the ability to implement the approaches depends on
the availability of relevant data on exposures (which can
be collected in the context of the risk assessment if not
already available), exposure response functions (which
may be very long and cumbersome to obtain if they are
not already available) and baseline population health;
this means that whatever the option chosen to handle
the weight of evidence regarding each exposure-health
outcome pair, the list of effectively considered pairs
may be further restricted because of these issues related
to data availability; this is expected to bias the health
impact estimate (see Assessing the impact of policies
versus the impact of exposures for further discussion).
Transparency on all possibly affected outcomes is any-
way warranted, even if not all of them can eventually be
incorporated in the estimated overall impact.

Exposure-response functions

Exposure to chemical, physical and behavioral factors is now generally assessed on quantitative scales, and the expected impact of policies or plans on environmental and societal factor can often be translated in terms of quantitative variations in drivers of health. The ERF provides an estimate of the effect (positive or detrimental) associated with the exposure at each level (the terms of dose, concentration or exposure response function (DRF, CRF, ERF) or curve are here used synonymously). Issues related to the ERF relate to the validity of its assessment, including the slope and shape and to its applicability to the study population.

In the context of a risk assessment study, contrarily
to the estimation of exposure which may in some cases
be done ad hoc, it is generally not realistic to expect to
generate from scratch a new ERF (whose estimation may
require the follow-up of large populations over periods
of years or decades) so that one has to rely on external
ERFs. If no ERF is available, then one may either 1) try to
derive an ERF from existing toxicological (animal) stud-
ies [78], if any or 2) perform a qualitative HIA. If several
ERFs are available, then performing a meta-analysis of
these ERFs to obtain a more robust one should be consid-
ered. This step may be done on the basis of the systematic
review possibly performed to assess the level of evidence

(see Estimating the strength of evidence about the effect
of factors on health above).

We will here assume that some ERFs (or relative risks or any equivalent measure of association) are available. The choice of the exposure response function may have large influences, as illustrated by a review of air pollution HIAs illustrating that the estimated health impact of fine particulate matter in Europe varies by a ratio of two when switching between exposure-response functions based on two large studies [79] (see also Table 2). Three dimensions to consider are those of the sample size from which the ERF has been estimated, the potential for bias of the ERF, e.g., in relation to the adjustment factors considered, and that of its applicability to the study population. Researchers are typically left with the choice between an ERF estimated on a local (or nearby) population, which possibly relies on a small population (hence a large variance), or more global estimates, such as those from meta-analyses, which may be more robust (based on larger populations) but ignore possible differences in sensitivity between the local population and the rest of the world (and therefore are possibly biased). This can be seen as an illustration of the classical bias-variance trade-off. In an ideal situation in which many studies providing an ERF are available, one would characterize the potential for bias of each individual study (evidence evaluation, see e.g., chapter 5 in [74]) and then perform meta-analyses, in which the poor-quality studies would be discarded if they tend to produce different ERF estimates than the studies with better quality. The potential for heterogeneity in the ERF across populations and geographical areas should also be characterized (see Fig. 5), allowing to decide whether it appears more relevant to derive the ERF from a small group of studies in settings very similar to the setting of the HIA, or from a larger group of studies covering a wider diversity of settings.

It may be relevant to also consider other factors, such
as the range of exposures in the studies from which the
ERF is based, trying to base the ERF on studies with an
exposure range similar to that of the population in which
the risk assessment is conducted, and avoiding to extrap-
olate ERFs outside the exposure levels where the bulk of
the original data lie. In the case of risk assessment stud-
ies focusing on factors of other nature, such as social or
behavioral factors, for which the hypothesis of heteroge-
neity in sensitivity across large areas is more likely, the
meta-analysis may not be the preferred option.

The concept underlying the exposure assessment
in the study from which the exposure response func-
tion is based should be similar to that used in the risk
assessment study. For example, if “exposure” in the
study from which the exposure-response curve origi-
nates corresponds to lead environmental level, then
that “false alarms” tended to be very rare in environmen-
tal health [76]. This would rather support not restrict-
ing the risk assessment to “certain” exposure-outcome
associations, and also consider those with a lower level
of evidence, possibly taking the level of evidence in the
estimation as described above in c). Considering associa-
tions with less than certain level of evidence also allows
to quantify the possible impact of suspected hazards,
which is relevant to prioritize environmental factors for
which research efforts should be dedicated [77]. In prac-
tice, the ability to implement the approaches depends on
the availability of relevant data on exposures (which can
be collected in the context of the risk assessment if not
already available), exposure response functions (which
may be very long and cumbersome to obtain if they are
not already available) and baseline population health;
this means that whatever the option chosen to handle
the weight of evidence regarding each exposure-health
outcome pair, the list of effectively considered pairs
may be further restricted because of these issues related
to data availability; this is expected to bias the health
impact estimate (see Assessing the impact of policies
versus the impact of exposures for further discussion).
Transparency on all possibly affected outcomes is any-
way warranted, even if not all of them can eventually be
incorporated in the estimated overall impact.

Exposure-response functions

Exposure to chemical, physical and behavioral factors is
now generally assessed on quantitative scales, and the
expected impact of policies or plans on environmental
and societal factor can often be translated in terms of
quantitative variations in drivers of health. The ERF pro-
vides an estimate of the effect (positive or detrimental)
associated with the exposure at each level (the terms of
dose, concentration or exposure response function (DRF,
CRF, ERF) or curve are here used synonymously). Issues
related to the ERF relate to the validity of its assessment,
including the slope and shape and to its applicability to
the study population.

In the context of a risk assessment study, contrarily
to the estimation of exposure which may in some cases
be done ad hoc, it is generally not realistic to expect to
generate from scratch a new ERF (whose estimation may
require the follow-up of large populations over periods
of years or decades) so that one has to rely on external
ERFs. If no ERF is available, then one may either 1) try to
derive an ERF from existing toxicological (animal) stud-
ies [78], if any or 2) perform a qualitative HIA. If several
ERFs are available, then performing a meta-analysis of
these ERFs to obtain a more robust one should be consid-
ered. This step may be done on the basis of the systematic
review possibly performed to assess the level of evidence

(see Estimating the strength of evidence about the effect
of factors on health above).

We will here assume that some ERFs (or relative risks
or any equivalent measure of association) are available.
The choice of the exposure response function may have
large influences, as illustrated by a review of air pollu-
tion HIAs illustrating that the estimated health impact
of fine particulate matter in Europe varies by a ratio of
two when switching between exposure-response func-
tions based on two large studies [79] (see also Table 2).
Three dimensions to consider are those of the sample size
from which the ERF has been estimated, the potential
for bias of the ERF, e.g., in relation to the adjustment fac-
tors considered, and that of its applicability to the study
population. Researchers are typically left with the choice
between an ERF estimated on a local (or nearby) popula-
tion, which possibly relies on a small population (hence
a large variance), or more global estimates, such as those
from meta-analyses, which may be more robust (based
on larger populations) but ignore possible differences in
sensitivity between the local population and the rest of
the world (and therefore are possibly biased). This can be
seen as an illustration of the classical bias-variance trade-
off. In an ideal situation in which many studies providing
an ERF are available, one would characterize the poten-
tial for bias of each individual study (evidence evaluation,
see e.g., chapter 5 in [74]) and then perform meta-analy-
ses, in which the poor-quality studies would be discarded
if they tend to produce different ERF estimates than the
studies with better quality. The potential for heteroge-
neity in the ERF across populations and geographical
areas should also be characterized (see Fig. 5), allowing
to decide whether it appears more relevant to derive the
ERF from a small group of studies in settings very similar
to the setting of the HIA, or from a larger group of stud-
ies covering a wider diversity of settings.

It may be relevant to also consider other factors, such
as the range of exposures in the studies from which the
ERF is based, trying to base the ERF on studies with an
exposure range similar to that of the population in which
the risk assessment is conducted, and avoiding to extrap-
olate ERFs outside the exposure levels where the bulk of
the original data lie. In the case of risk assessment stud-
ies focusing on factors of other nature, such as social or
behavioral factors, for which the hypothesis of heteroge-
neity in sensitivity across large areas is more likely, the
meta-analysis may not be the preferred option.

The concept underlying the exposure assessment
in the study from which the exposure response func-
tion is based should be similar to that used in the risk
assessment study. For example, if “exposure” in the
study from which the exposure-response curve origi-
nates corresponds to lead environmental level, then
<figure><img src="image_7.png" /><figcaption>**Fig. 5** Meta-analysis of the relative-risk (RR) of lung cancer associated with PM<sub>2.5</sub> exposure, by region [53]</figcaption></figure>

it is generally not advised to rely on lead biomarkers (which assess the levels circulating in the body and not environmental levels) in the risk assessment study; the length of the exposure window should also be similar, as this length generally influences the estimated exposure variability. If both entities differ, then in some cases it may be possible to convert one into the other, using a formula derived from a study in which both entities have been assessed in the same population, or using toxicokinetic modelling. Contrarily to what is sometimes said, this requirement of a similarity of exposure concepts does not imply that the specific approaches used to assess exposures need to be identical. The measurement approaches can differ, provided one is not biased with respect to the other. For example, if the exposure considered is fine particulate matter and the exposure-response function stems from a cohort study in which exposure was assessed relying on permanent monitoring station, then a dispersion model could in principle be used to assess fine particulate matter levels in the risk assessment study. In this example, both the permanent monitoring stations and the dispersion models provide an estimate of the same entity (the environmental level), and since etiologic

studies relying on permanent monitoring stations are not expected to be strongly biased compared to studies using environmental models with a finer scale such as a dispersion model (assuming that the concept of Berkson error [80] applies), the exposure-response function stemming from the study using monitoring stations is in expectation similar to the one that would have been obtained if a dispersion model had been used instead to assess exposure.

### Non-linear exposure-response functions

The studied factor may have non-linear associations with the health outcome considered on a given (e.g., additive or multiplicative) scale. Note that such deviations from linearity are not always investigated in etiological studies (possibly for reasons related to limited statistical power). As an illustration, a 2001 review on the ERF of physical activity effects on mortality indicates that only 17 of the 44 studies conducted a test of linear trend [81]. A more recent and robust review does a meta-analysis on studies with larger population samples and finds a better fit for the curve $y=-x^{0.25}$, with steeper effect of moderate, as opposed to higher, physical activity on mortality [82].
<figure><img src="image_8.png" /><figcaption>**Fig. 5** Meta-analysis of the relative-risk (RR) of lung cancer associated with PM<sub>2.5</sub> exposure, by region [53]</figcaption></figure>

it is generally not advised to rely on lead biomarkers (which assess the levels circulating in the body and not environmental levels) in the risk assessment study; the length of the exposure window should also be similar, as this length generally influences the estimated exposure variability. If both entities differ, then in some cases it may be possible to convert one into the other, using a formula derived from a study in which both entities have been assessed in the same population, or using toxicokinetic modelling. Contrarily to what is sometimes said, this requirement of a similarity of exposure concepts does not imply that the specific approaches used to assess exposures need to be identical. The measurement approaches can differ, provided one is not biased with respect to the other. For example, if the exposure considered is fine particulate matter and the exposure-response function stems from a cohort study in which exposure was assessed relying on permanent monitoring station, then a dispersion model could in principle be used to assess fine particulate matter levels in the risk assessment study. In this example, both the permanent monitoring stations and the dispersion models provide an estimate of the same entity (the environmental level), and since etiologic

studies relying on permanent monitoring stations are not expected to be strongly biased compared to studies using environmental models with a finer scale such as a dispersion model (assuming that the concept of Berkson error [80] applies), the exposure-response function stemming from the study using monitoring stations is in expectation similar to the one that would have been obtained if a dispersion model had been used instead to assess exposure.

### Non-linear exposure-response functions

The studied factor may have non-linear associations with the health outcome considered on a given (e.g., additive or multiplicative) scale. Note that such deviations from linearity are not always investigated in etiological studies (possibly for reasons related to limited statistical power). As an illustration, a 2001 review on the ERF of physical activity effects on mortality indicates that only 17 of the 44 studies conducted a test of linear trend [81]. A more recent and robust review does a meta-analysis on studies with larger population samples and finds a better fit for the curve $y=-x^{0.25}$, with steeper effect of moderate, as opposed to higher, physical activity on mortality [82].
<figure><img src="image_8.png" /><figcaption>**Fig. 6** Illustration of non-linear exposure response functions: A) Fine particulate matter and mortality [85]; B) Temperature and mortality in Rome [86], C) Physical activity and cardiovascular events [87]. MET: Metabolic equivalents; RR: Relative risk</figcaption></figure>

Non-linear dose-response functions are all the more likely when the underlying mechanisms of action are complex and as the range of exposure values increases. Ignoring this non-linear relation can significantly impact the estimated risk [83], hence potentially misestimating the risks or benefits of the change, depending on the distribution of the exposure in the population.

Non-linear ERFs have been exhibited for several risk factors. This is the case for temperature and air pollution effects on mortality in particular, and also effects of physical activity on health (Fig. 6); they may also be expected e.g., for endocrine disruptors [84].

Note that many risk assessment studies, at least from a certain period in the past, used to assume the existence of thresholds (hence, a non-linear dose-response) in the non-carcinogenic health effects of chemicals, and a lack of threshold of carcinogenic effects. There is to our knowledge no toxicological justification to such general claims. The “threshold” model can be seen as being related to the misconception that the NOAEL (no observed adverse effect level) estimated in some regulatory toxicology studies corresponds to a true “no effect” exposure level. In fact, a NOAEL generally corresponds to a level with an effect, whose size depends in particular on the number of animals used in the experiment aiming to estimate the NOAEL [88].

## Assessment of disease frequency

The ideal situation corresponds to that of an area where a register (or any other system allowing an exhaustive assessment of new disease cases on a representative basis) exists. Such registers exist in many countries for cancers but, outside Scandinavian countries, are rarer for other diseases. Just like for the case of the assessment of exposures, tools typically used in etiologic cohort studies may provide a

relevant estimate of the disease frequency, with the same *caveat* as above, namely that etiologic studies are rarely representative of a given area, which would be a limitation if the disease frequency obtained in such a study is to be used in a risk assessment exercise. Alternatively, one can rely directly on estimates of the disease burden, such as those provided by the Global burden of disease project (https://www.healthdata.org/results/gbd_summaries/2019).

The disease frequency can correspond to different entities, generally related to incidence (the number of cases appearing during a given time period in a population) or prevalence (the number of cases present at a given time point, whatever the time when the disease started). In principle, incidence should be targeted. The entity used to assess disease frequency should be coherent with the measure of association (the exposure-response function) chosen. For example, a hazard rate stemming from a cohort study (or an incident case control study) assesses the change in the disease hazard (the strength of approximation of new cases) and needs to be combined with a measure of incidence and not prevalence.

## Health impact

### Concepts of impact

The health impact (or risk) is the core estimate of a risk assessment study. It is a challenging notion, both from a conceptual and estimation perspective, not to mention issues related to the use of this expression with possibly different meanings across scientific and public health communities. When it comes to the human-derived risk assessment studies discussed here, the core product corresponds to notions close to the epidemiologic notion of attributable fraction. Following Greenland [8], we shall remind that this expression covers different concepts: the etiologic fraction, the excess fraction, the incidence
<figure><img src="image_9.png" /><figcaption>**Fig. 6** Illustration of non-linear exposure response functions: A) Fine particulate matter and mortality [85]; B) Temperature and mortality in Rome [86], C) Physical activity and cardiovascular events [87]. MET: Metabolic equivalents; RR: Relative risk</figcaption></figure>

Non-linear dose-response functions are all the more likely when the underlying mechanisms of action are complex and as the range of exposure values increases. Ignoring this non-linear relation can significantly impact the estimated risk [83], hence potentially misestimating the risks or benefits of the change, depending on the distribution of the exposure in the population.

Non-linear ERFs have been exhibited for several risk factors. This is the case for temperature and air pollution effects on mortality in particular, and also effects of physical activity on health (Fig. 6); they may also be expected e.g., for endocrine disruptors [84].

Note that many risk assessment studies, at least from a certain period in the past, used to assume the existence of thresholds (hence, a non-linear dose-response) in the non-carcinogenic health effects of chemicals, and a lack of threshold of carcinogenic effects. There is to our knowledge no toxicological justification to such general claims. The “threshold” model can be seen as being related to the misconception that the NOAEL (no observed adverse effect level) estimated in some regulatory toxicology studies corresponds to a true “no effect” exposure level. In fact, a NOAEL generally corresponds to a level with an effect, whose size depends in particular on the number of animals used in the experiment aiming to estimate the NOAEL [88].

## Assessment of disease frequency

The ideal situation corresponds to that of an area where a register (or any other system allowing an exhaustive assessment of new disease cases on a representative basis) exists. Such registers exist in many countries for cancers but, outside Scandinavian countries, are rarer for other diseases. Just like for the case of the assessment of exposures, tools typically used in etiologic cohort studies may provide a

relevant estimate of the disease frequency, with the same *caveat* as above, namely that etiologic studies are rarely representative of a given area, which would be a limitation if the disease frequency obtained in such a study is to be used in a risk assessment exercise. Alternatively, one can rely directly on estimates of the disease burden, such as those provided by the Global burden of disease project (https://www.healthdata.org/results/gbd_summaries/2019).

The disease frequency can correspond to different entities, generally related to incidence (the number of cases appearing during a given time period in a population) or prevalence (the number of cases present at a given time point, whatever the time when the disease started). In principle, incidence should be targeted. The entity used to assess disease frequency should be coherent with the measure of association (the exposure-response function) chosen. For example, a hazard rate stemming from a cohort study (or an incident case control study) assesses the change in the disease hazard (the strength of approximation of new cases) and needs to be combined with a measure of incidence and not prevalence.

## Health impact

### Concepts of impact

The health impact (or risk) is the core estimate of a risk assessment study. It is a challenging notion, both from a conceptual and estimation perspective, not to mention issues related to the use of this expression with possibly different meanings across scientific and public health communities. When it comes to the human-derived risk assessment studies discussed here, the core product corresponds to notions close to the epidemiologic notion of attributable fraction. Following Greenland [8], we shall remind that this expression covers different concepts: the etiologic fraction, the excess fraction, the incidence
density fraction, to which one shall add the expected (healthy) years of life lost.

The excess fraction corresponds to the proportion of cases that would not have become a case during the study period in the absence of exposure, while the etiologic fraction includes these excess cases as well as the cases due to exposure that would also have occurred during the study period in the absence of exposure, but at a later time point during this period. These two fractions can strongly differ because the etiologic fraction includes, in addition to the “excess cases”, the cases which would have happened also in the absence of exposure, but for which exposure made the incidence happen earlier than if the subject had not been exposed. These cases for which exposure simply made the case happen earlier in the study period may correspond to a large fraction of cases for complex diseases (as opposed to diseases with a simpler etiology such as infectious diseases), and their number increases with the duration of the study period. This is illustrated with the extreme example of a study of a factor increasing mortality or any other inevitable outcome: if the study period is very long, so that all members of the considered population are dead at the end of this period, then the excess fraction will become zero (because everyone eventually dies, even in the absence of the considered exposure) (see for example Fig. 2.6c in [89]), while the etiologic fraction may be non-null if the exposure does influence mortality [8]. For this reason, some advise not to use the excess fraction as a metric, or the similar yearly number of avoided cases in a population [89]. Although this metric is indeed limited when it comes to estimating a meaningful health impact (that may be used to quantify an economic impact), when comparing the impact of various factors, it is possible that in many common situations the ranking of risk factors is preserved across metrics. In any case, it is of course crucial to only compare exposures in terms of impact assessed using exactly the same metric. Although in principle more relevant, the estimation of the etiologic fraction requires specific biological knowledge or hypotheses [8].

The incidence density fraction, defined as $(ID_{E+}-ID_E)/ID_{E+}$, where $ID_{E+}$ (respectively, $ID_E$) is the incidence in the exposed (respectively, unexposed) group, has different interpretations, depending on whether one relies on instantaneous or average incidence densities [8]. Estimating attributable life-years (or healthy life-years) associated with the exposure or policy may appear as a relevant option for many public health purposes [8] and should be attempted. One reason is that this metric does not suffer from the above-mentioned limitation related to the fact that, since everyone eventually dies (the deaths are postponed, not avoided), the long-term gain expressed as a total number of deaths avoided from the reduction of

exposure to a harmful environmental factor will appear much smaller than could be thought at first sight when considering the number of deaths avoided during a given year. The number of avoided life-years, by depending both on the number of deaths postponed each year and on the delay in their occurrence induced by the environmental change, takes into account the two dimensions of the problem. The same goes for the change in life expectancy [89]. Note that a given number of (healthy) life-years lost may translate into very different impacts on life expectancy, depending on how the life-years lost are distributed in the population (something that cannot be determined without strong assumptions). As an illustration, the UK committee on the medical effects of air pollution (COMEAP) concluded that anthropogenic fine particulate matter ($PM_{2.5}$) at the level observed in 2008 in the UK was associated with an effect on mortality equivalent to nearly 29,000 deaths at typical ages in 2008, and that, depending on how this burden is spread in the whole population, this might correspond to impacts on life expectancy ranging from 6 months (if the air pollution effects was distributed across all deaths) to 11.5 years (if $PM_{2.5}$ were only implied in 29,000 deaths) [89].

## Estimation

The risk estimation relies on a more or less sophisticated combination of the exposure distribution under each counterfactual scenario with the ERF and with an estimate of the baseline disease frequency in the considered population, whether explicitly or hidden in the externally available disease burden. This estimation is repeated under each of counterfactual scenario, and the risk difference between the targeted and “baseline” scenario is computed. In practice, several ways to estimate the risk are used, which are not all strictly valid in theory. The main types of approaches correspond to:

*   **PAF-based formulas:** An analytical (formula-based) estimation of a “population attributable fraction” associated with the exposure, multiplied either by the incidence of the disease or by an externally available estimate of the disease burden in the population (i.e., the impact of the disease in the considered population irrespective of all its possible causes, typically, expressed in DALYs);

*   **Person-years method:** A simulation of the whole population in which new disease cases occur each year during the course of the study period under various counterfactual scenarios, from which attributable cases, differences in life expectancy, DALYs and other specific measures of risk can be estimated. This approach has the advantage of allowing to take into
density fraction, to which one shall add the expected (healthy) years of life lost.

The excess fraction corresponds to the proportion of cases that would not have become a case during the study period in the absence of exposure, while the etiologic fraction includes these excess cases as well as the cases due to exposure that would also have occurred during the study period in the absence of exposure, but at a later time point during this period. These two fractions can strongly differ because the etiologic fraction includes, in addition to the “excess cases”, the cases which would have happened also in the absence of exposure, but for which exposure made the incidence happen earlier than if the subject had not been exposed. These cases for which exposure simply made the case happen earlier in the study period may correspond to a large fraction of cases for complex diseases (as opposed to diseases with a simpler etiology such as infectious diseases), and their number increases with the duration of the study period. This is illustrated with the extreme example of a study of a factor increasing mortality or any other inevitable outcome: if the study period is very long, so that all members of the considered population are dead at the end of this period, then the excess fraction will become zero (because everyone eventually dies, even in the absence of the considered exposure) (see for example Fig. 2.6c in [89]), while the etiologic fraction may be non-null if the exposure does influence mortality [8]. For this reason, some advise not to use the excess fraction as a metric, or the similar yearly number of avoided cases in a population [89]. Although this metric is indeed limited when it comes to estimating a meaningful health impact (that may be used to quantify an economic impact), when comparing the impact of various factors, it is possible that in many common situations the ranking of risk factors is preserved across metrics. In any case, it is of course crucial to only compare exposures in terms of impact assessed using exactly the same metric. Although in principle more relevant, the estimation of the etiologic fraction requires specific biological knowledge or hypotheses [8].

The incidence density fraction, defined as $(ID_{E+}-ID_E)/ID_{E+}$, where $ID_{E+}$ (respectively, $ID_E$) is the incidence in the exposed (respectively, unexposed) group, has different interpretations, depending on whether one relies on instantaneous or average incidence densities [8]. Estimating attributable life-years (or healthy life-years) associated with the exposure or policy may appear as a relevant option for many public health purposes [8] and should be attempted. One reason is that this metric does not suffer from the above-mentioned limitation related to the fact that, since everyone eventually dies (the deaths are postponed, not avoided), the long-term gain expressed as a total number of deaths avoided from the reduction of

exposure to a harmful environmental factor will appear much smaller than could be thought at first sight when considering the number of deaths avoided during a given year. The number of avoided life-years, by depending both on the number of deaths postponed each year and on the delay in their occurrence induced by the environmental change, takes into account the two dimensions of the problem. The same goes for the change in life expectancy [89]. Note that a given number of (healthy) life-years lost may translate into very different impacts on life expectancy, depending on how the life-years lost are distributed in the population (something that cannot be determined without strong assumptions). As an illustration, the UK committee on the medical effects of air pollution (COMEAP) concluded that anthropogenic fine particulate matter ($PM_{2.5}$) at the level observed in 2008 in the UK was associated with an effect on mortality equivalent to nearly 29,000 deaths at typical ages in 2008, and that, depending on how this burden is spread in the whole population, this might correspond to impacts on life expectancy ranging from 6 months (if the air pollution effects was distributed across all deaths) to 11.5 years (if $PM_{2.5}$ were only implied in 29,000 deaths) [89].

## Estimation

The risk estimation relies on a more or less sophisticated combination of the exposure distribution under each counterfactual scenario with the ERF and with an estimate of the baseline disease frequency in the considered population, whether explicitly or hidden in the externally available disease burden. This estimation is repeated under each of counterfactual scenario, and the risk difference between the targeted and “baseline” scenario is computed. In practice, several ways to estimate the risk are used, which are not all strictly valid in theory. The main types of approaches correspond to:

*   **PAF-based formulas:** An analytical (formula-based) estimation of a “population attributable fraction” associated with the exposure, multiplied either by the incidence of the disease or by an externally available estimate of the disease burden in the population (i.e., the impact of the disease in the considered population irrespective of all its possible causes, typically, expressed in DALYs);

*   **Person-years method:** A simulation of the whole population in which new disease cases occur each year during the course of the study period under various counterfactual scenarios, from which attributable cases, differences in life expectancy, DALYs and other specific measures of risk can be estimated. This approach has the advantage of allowing to take into
account the dynamics between death rates, population size and age structure [89].

Note that alternative approaches exist, such as compartmental models (generally, but not exclusively, used for infectious diseases) or approaches based on individual, as opposed to population-based modeling, such as microsimulations (see e.g. Mueller et al. [90] for a review). Compartmental models assume that subjects switch between mutually exclusive states (e.g., susceptible, infected, recovered, dead, for an infectious disease) and model the trajectory of each individual from the population across these states via deterministic or probabilistic approaches. They are particularly relevant to model the impact of interventions that may influence infectious diseases, and will not be detailed here (see [91] for an example). The lifetable (or person-years) approach mentioned below can in a way be seen as a particular example of compartmental models.

As already mentioned, one general issue relates to the consistency between the various metrics used; for example, the data on baseline disease frequency need to correspond to an estimate of disease incidence if the exposure-response function is derived from an etiologic study assessing the occurrence of new disease cases, such as a cohort or incident case-controls study.

The “PAF-based formula” approach can be illustrated taking the simple example in which a binary exposure level is changed from 1 to 0 (e.g., all smokers stop smoking) in the counterfactual situation and in which the overall burden associated with the disease, assumed to correspond to a dichotomous outcome (with/without disease) is available. The health impact is generally estimated in two steps, the first one corresponding to the estimation of the PAF, which, in a situation without confounding, is defined as:

$$PAF = \frac{P(Y = 1) - P(Y = 1/X = 0)}{P(Y = 1)} \quad (1)$$

Where Y corresponds to the disease, P(Y=1) is the proportion of subjects developing the disease in the study period and X is the exposure of interest, with X=0 corresponding to non-exposed subjects. Equivalently, the PAF can be defined as:

$$PAF = \frac{P(X = 1) \times (R_e - R_u)}{P(Y = 1)} \quad (2)$$

Were $R_e$ and $R_u$ are the risks of disease in the exposed and unexposed subgroups, respectively.

Note that the assumption about the lack of confounding can be conveniently ignored by relying on the structural causal modeling framework [92] and the do operator:

$$PAF = \frac{P(Y = 1) - P(Y = 1/\text{do}(X = 0))}{P(Y = 1)} \quad (3)$$

where do(X=0) refers to a situation in which X is set to 0 through a minimally invasive intervention (in the terminology of Pearl [92]), all other variables possibly influencing X remaining constant; of course, the “reference” value X=0 can be replaced by any other value or distribution, in the case of an exposure with more than two categories.

Coming back to the situation in which X is binary, the PAF is generally estimated relying on Levin's formula, which can be derived from the previous ones:

$$PAF = \frac{P \times (RR - 1)}{1 + P \times (RR - 1)} \quad (4)$$

Where P is the prevalence of exposure in the population, or P(X=1), RR the relative risk associated with exposure (assumed here to be dichotomous). (Note that Rockhill et al. [6] explain that this formula is not valid in the context of confounding. This is true when one applies the formula (4) in the study population from which the RR is estimated but not, as in a risk assessment exercise, if one uses (4) to estimate the attributable fraction in a given population using a RR assumed to be unbiased estimated from another population.

The health impact is then estimated by combining the estimated PAF with the burden of the considered disease, BD, in the study population, generally available or approximated from external sources (or estimated via an ad-hoc study):

$$\text{Health Impact} = PAF \times BD \quad (5)$$

The unit of BD (e.g., deaths, DALYs, etc.) defines the unit of measure of the health impact.

In the case of a categorical assessment of exposure, the health impact is estimated as above in each exposure category, after which the overall impact is estimated by summing over all exposure levels. If exposure is continuous, formula (1) above is generalized by integrating the PAF over all exposure levels as shown here:

$$PAF = \frac{\int_{x=0}^{m} RR(x) \times P_{S1}(x)dx - \int_{x=0}^{m} RR(x) \times P_{S2}(x)dx}{\int_{x=0}^{m} RR(x) \times P_{S1}(x)dx} \quad (6)$$

Where m is the maximal exposure level, $P_{S1}$ is the observed distribution of exposure level (or baseline scenario), $P_{S2}$ the distribution of exposure under the counterfactual hypothesis (which may correspond to a uniform distribution with all subjects at zero if zero is the targeted level) and RR the exposure-response function, with RR(x) providing the relative risk when exposure is x.
account the dynamics between death rates, population size and age structure [89].

Note that alternative approaches exist, such as compartmental models (generally, but not exclusively, used for infectious diseases) or approaches based on individual, as opposed to population-based modeling, such as microsimulations (see e.g. Mueller et al. [90] for a review). Compartmental models assume that subjects switch between mutually exclusive states (e.g., susceptible, infected, recovered, dead, for an infectious disease) and model the trajectory of each individual from the population across these states via deterministic or probabilistic approaches. They are particularly relevant to model the impact of interventions that may influence infectious diseases, and will not be detailed here (see [91] for an example). The lifetable (or person-years) approach mentioned below can in a way be seen as a particular example of compartmental models.

As already mentioned, one general issue relates to the consistency between the various metrics used; for example, the data on baseline disease frequency need to correspond to an estimate of disease incidence if the exposure-response function is derived from an etiologic study assessing the occurrence of new disease cases, such as a cohort or incident case-controls study.

The “PAF-based formula” approach can be illustrated taking the simple example in which a binary exposure level is changed from 1 to 0 (e.g., all smokers stop smoking) in the counterfactual situation and in which the overall burden associated with the disease, assumed to correspond to a dichotomous outcome (with/without disease) is available. The health impact is generally estimated in two steps, the first one corresponding to the estimation of the PAF, which, in a situation without confounding, is defined as:

$$PAF = \frac{P(Y = 1) - P(Y = 1/X = 0)}{P(Y = 1)} \qquad (1)$$

Where Y corresponds to the disease, P(Y=1) is the proportion of subjects developing the disease in the study period and X is the exposure of interest, with X=0 corresponding to non-exposed subjects. Equivalently, the PAF can be defined as:

$$PAF = \frac{P(X = 1) \times (R_e - R_u)}{P(Y = 1)} \qquad (2)$$

Were $R_e$ and $R_u$ are the risks of disease in the exposed and unexposed subgroups, respectively.

Note that the assumption about the lack of confounding can be conveniently ignored by relying on the structural causal modeling framework [92] and the do operator:

$$PAF = \frac{P(Y = 1) - P(Y = 1/\text{do}(X = 0))}{P(Y = 1)} \qquad (3)$$

where do(X=0) refers to a situation in which X is set to 0 through a minimally invasive intervention (in the terminology of Pearl [92]), all other variables possibly influencing X remaining constant; of course, the “reference” value X=0 can be replaced by any other value or distribution, in the case of an exposure with more than two categories.

Coming back to the situation in which X is binary, the PAF is generally estimated relying on Levin's formula, which can be derived from the previous ones:

$$PAF = \frac{P \times (RR - 1)}{1 + P \times (RR - 1)} \qquad (4)$$

Where P is the prevalence of exposure in the population, or P(X=1), RR the relative risk associated with exposure (assumed here to be dichotomous). (Note that Rockhill et al. [6] explain that this formula is not valid in the context of confounding. This is true when one applies the formula (4) in the study population from which the RR is estimated but not, as in a risk assessment exercise, if one uses (4) to estimate the attributable fraction in a given population using a RR assumed to be unbiased estimated from another population.

The health impact is then estimated by combining the estimated PAF with the burden of the considered disease, BD, in the study population, generally available or approximated from external sources (or estimated via an ad-hoc study):

$$\text{Health Impact} = PAF \times BD \qquad (5)$$

The unit of BD (e.g., deaths, DALYs, etc.) defines the unit of measure of the health impact.

In the case of a categorical assessment of exposure, the health impact is estimated as above in each exposure category, after which the overall impact is estimated by summing over all exposure levels. If exposure is continuous, formula (1) above is generalized by integrating the PAF over all exposure levels as shown here:

$$PAF = \frac{\int_{x=0}^{m} RR(x) \times P_{S1}(x)dx - \int_{x=0}^{m} RR(x) \times P_{S2}(x)dx}{\int_{x=0}^{m} RR(x) \times P_{S1}(x)dx} \qquad (6)$$

Where m is the maximal exposure level, $P_{S1}$ is the observed distribution of exposure level (or baseline scenario), $P_{S2}$ the distribution of exposure under the counterfactual hypothesis (which may correspond to a uniform distribution with all subjects at zero if zero is the targeted level) and RR the exposure-response function, with RR(x) providing the relative risk when exposure is x.