If the health parameter Y is continuous (e.g., blood pressure, birth weight...), then the impact of X on the average value of Y can be estimated as:

$$Health\ Impact = \int_{x=0}^{m} \beta(x) \times P_{S1}(x)dx - \int_{x=0}^{m} \beta(x) \times P_{S2}(x)dx = \int_{x=0}^{m} \beta(x) \times [P_{S1}(x) - P_{S2}(x)]dx \quad (7)$$

Where β corresponds to the exposure-response function describing the average value of the outcome Y as a function of the outcome. In the case of a binary exposure with prevalence P, the right-hand side of this formula simplifies to β x P. This value can be multiplied by the population size if one wants to express the impact in terms of units of Y (e.g., IQ points) due to the exposure in the population as a whole.

The person-years approach consists in simulating the cohorts corresponding to each of the considered counterfactual scenarios throughout the study period, with new disease cases appearing each year. It has several key advantages over the formula-based approach, including: 1) to make all assumptions more explicit; 2) to avoid issues related to the estimation of the expected number of cases [7, 93], since the number of subjects still at risk in each cohort is explicitly estimated; 3) to be more flexible in coping with various exposures simultaneously, assuming various correlation structures between them, with scenarios implying gradual changes in exposure over time, considering sociodemographic changes in the study population, without having to work out an analytical solution. The cost of this approach is that it is generally much more complex to implement and compute.

The estimation needs to be repeated for the other health outcomes identified at the hazard identification step (Identification of exposures above) as being possibly influenced by the considered factor. It can also be repeated for other factors, as we now discuss.

## Consideration of multiple risks factors

If several factors are considered (e.g., because one is interested in a prespecified set of exposures, or because the policy evaluated is expected to influence several physical, chemical, psychosocial factors), the estimation needs to be repeated for each of these factors, at least those for which the level of evidence regarding effects on one health outcome are above the selected level, if any (see Handling of the strength of evidence about the effect of environmental factors on health). A central issue here relates to the situation in which two or more of these factors can influence the same health outcome. Indeed, care is required to acknowledge the fact that the fraction of cases of a specific disease attributable to different

risk factors can generally not be summed. This is a consequence of the multiplicative nature of risk and of the multifactorial nature of most diseases [94]; moreover,

$$PAF = 1 - \prod_{r=1}^{R} (1 - PAF_{r}) \quad (8)$$

care is needed to consider possible relations, and in particular correlation, effect measure modifications or mediation between risk factors.

Again, the PAF-based formula and the person-years method can be used when considering several factors influencing the same health outcome, with the latter being more flexible. Regarding the former approach, if population attributable fractions have been estimated for each of the R risk factors influencing the considered outcome, and under some hypotheses (see below), then these can be aggregated with formula (6):

Where PAF_r is the population attributable risk fraction associated with risk factor r estimated independently from the other risk factors. This approach makes strong assumption: that all risk factors act independently (in particular, that no effect of one factor is to some extent mediated by another factor, or modified by another factor) and are not correlated. Note that this formula is identical to that used in toxicology for the so-called case of independent action [95]. Under these assumptions, if two independent factors have attributable fraction of the cases of 40 and 50% respectively, then their joint action corresponds to an attributable fraction of 70% (40% plus 50% of the remaining 60%).

Some of these assumptions may not hold in real situations.

A first issue relates to the situation in which exposures to the considered factors (say, x_1 and x_2) are correlated. Formula (8) assumes that the fraction of cases attributable to B is the same in the whole population and in the population from which factor A has been removed (independent action), which does not hold if A and B are correlated because then the prevalence of exposure to B is not the same in the two populations. From this it appears that information on the relations between exposures to the considered factors (here, x_1 and x_2) in the study population is required to estimate the fraction of cases attributable to x_1 and x_2. Specifically, their joint distribution P(x_1, x_2) needs to be considered in the PAF estimation, as described in Ezzati et al. [96]. Formula (6) can be adapted by replacing each integral by:
If the health parameter Y is continuous (e.g., blood pressure, birth weight...), then the impact of X on the average value of Y can be estimated as:

$$Health \ Impact = \int_{x=0}^{m} \beta(x) \times P_{S1}(x)dx - \int_{x=0}^{m} \beta(x) \times P_{S2}(x)dx = \int_{x=0}^{m} \beta(x) \times [P_{S1}(x) - P_{S2}(x)]dx \quad (7)$$

Where β corresponds to the exposure-response function describing the average value of the outcome Y as a function of the outcome. In the case of a binary exposure with prevalence P, the right-hand side of this formula simplifies to β x P. This value can be multiplied by the population size if one wants to express the impact in terms of units of Y (e.g., IQ points) due to the exposure in the population as a whole.

The person-years approach consists in simulating the cohorts corresponding to each of the considered counterfactual scenarios throughout the study period, with new disease cases appearing each year. It has several key advantages over the formula-based approach, including: 1) to make all assumptions more explicit; 2) to avoid issues related to the estimation of the expected number of cases [7, 93], since the number of subjects still at risk in each cohort is explicitly estimated; 3) to be more flexible in coping with various exposures simultaneously, assuming various correlation structures between them, with scenarios implying gradual changes in exposure over time, considering sociodemographic changes in the study population, without having to work out an analytical solution. The cost of this approach is that it is generally much more complex to implement and compute.

The estimation needs to be repeated for the other health outcomes identified at the hazard identification step (Identification of exposures above) as being possibly influenced by the considered factor. It can also be repeated for other factors, as we now discuss.

### Consideration of multiple risks factors

If several factors are considered (e.g., because one is interested in a prespecified set of exposures, or because the policy evaluated is expected to influence several physical, chemical, psychosocial factors), the estimation needs to be repeated for each of these factors, at least those for which the level of evidence regarding effects on one health outcome are above the selected level, if any (see Handling of the strength of evidence about the effect of environmental factors on health). A central issue here relates to the situation in which two or more of these factors can influence the same health outcome. Indeed, care is required to acknowledge the fact that the fraction of cases of a specific disease attributable to different

risk factors can generally not be summed. This is a consequence of the multiplicative nature of risk and of the multifactorial nature of most diseases [94]; moreover,

$$PAF = 1 - \prod_{r=1}^{R} (1 - PAF_{r}) \quad (8)$$

care is needed to consider possible relations, and in particular correlation, effect measure modifications or mediation between risk factors.

Again, the PAF-based formula and the person-years method can be used when considering several factors influencing the same health outcome, with the latter being more flexible. Regarding the former approach, if population attributable fractions have been estimated for each of the R risk factors influencing the considered outcome, and under some hypotheses (see below), then these can be aggregated with formula (6):

Where PAF_r is the population attributable risk fraction associated with risk factor r estimated independently from the other risk factors. This approach makes strong assumption: that all risk factors act independently (in particular, that no effect of one factor is to some extent mediated by another factor, or modified by another factor) and are not correlated. Note that this formula is identical to that used in toxicology for the so-called case of independent action [95]. Under these assumptions, if two independent factors have attributable fraction of the cases of 40 and 50% respectively, then their joint action corresponds to an attributable fraction of 70% (40% plus 50% of the remaining 60%).

Some of these assumptions may not hold in real situations.

A first issue relates to the situation in which exposures to the considered factors (say, x_1 and x_2) are correlated. Formula (8) assumes that the fraction of cases attributable to B is the same in the whole population and in the population from which factor A has been removed (independent action), which does not hold if A and B are correlated because then the prevalence of exposure to B is not the same in the two populations. From this it appears that information on the relations between exposures to the considered factors (here, x_1 and x_2) in the study population is required to estimate the fraction of cases attributable to x_1 and x_2. Specifically, their joint distribution P(x_1, x_2) needs to be considered in the PAF estimation, as described in Ezzati et al. [96]. Formula (6) can be adapted by replacing each integral by:
$$ \int_{x_1=0}^{m_1} \int_{x_2=0}^{m_2} RR_1(x_1)RR_2(x_2)P(x_1,x_2)dx_1dx_2 \quad (9) $$

this implies of course that information on the joint (and not only marginal) distribution of all relevant factors is available or collected in the population in which the risk assessment is conducted. Biomonitoring and exposome studies, provided they assessed multiple exposures simultaneously in the same participants, allow providing such a joint distribution [97]. Equation (9) assumes that the risk for a given combination ($x_1, x_2$) of exposures $X_1$ and $X_2$ is the product of the relative risks associated with $X_1$ and $X_2$, corresponding to a hypothesis of lack of effect measure modification of $X_1$ by $X_2$.

If now there is evidence of effect measure modification (sometimes termed interaction) between risk factors then in principle $RR_1(x_1)RR_2(x_2)$ in Eq. (9) should be replaced by $RR(x_1,x_2)$, that is the relative risk function describing the joint effect of $x_1$ and $x_2$, which can incorporate a different relative risk associated with $x_1$ at each given value of $x_2$. To our knowledge, there are currently few examples of risk factors and outcomes for which this function is accurately characterized and available.

Another option to handle it is to consider different ERFs in different population strata; again, one needs information on the joint distribution of all relevant factors, as well as stratum-specific relative risks.

Another (non-exclusive) situation is that of mediation effects [98]. Consider the case of a disease D (say, lung

cancer), influenced by several risk factors including active smoking (A) and green space exposure (B), the effect of which being partly mediated by changes in air pollution levels (C). Figure 7 provides a possible model of the assumed relations between A, B, C and D. Let us assume that one is interested in estimating the overall impact of factors A, B, C on D, that is, the number (or the fraction) of cases of disease D that would be avoided if A, B, and C all had “optimal” levels. The estimated impacts of B (improving green space exposure) and C (getting rid of air pollution) cannot be considered as being independent because a part of the effect of B is included in the effect of C (a mediation issue). Estimates of the share of the effect (in the sense of measure of association) of B on D that is not mediated by C (but that may be mediated by other factors not considered here, such as an increase in physical activity), termed the natural direct effect, can be provided by mediation analysis techniques [98]. This natural direct effect of B on the disease risk is by construction independent of the effect of C on disease risk, so that the corresponding attributable fractions can then be estimated and combined using formula (8) above. In the Global Burden Disease methodology, for each pair of risk factors that share an outcome, the fraction of the risk mediated through the other factor is estimated using mediation analysis techniques, if the relevant studies (in which B, C, D are altogether estimated) are available. A concern here (besides the usual assumptions required by mediation analysis [98]) relates to the transposability

<figure><img src="image_9.png" /><figcaption>**Fig. 7** Causal diagram summarizing the causal relations between hypothetical risk factors (A, B and C) and a disease D. Here, A and B are assumed to independently affect the probability of disease, while a part of the effect of B on D is mediated by C</figcaption></figure>
$$ \int_{x_1=0}^{m_1} \int_{x_2=0}^{m_2} RR_1(x_1)RR_2(x_2)P(x_1, x_2)dx_1dx_2 \quad (9) $$

this implies of course that information on the joint (and not only marginal) distribution of all relevant factors is available or collected in the population in which the risk assessment is conducted. Biomonitoring and exposome studies, provided they assessed multiple exposures simultaneously in the same participants, allow providing such a joint distribution [97]. Equation (9) assumes that the risk for a given combination ($x_1, x_2$) of exposures $X_1$ and $X_2$ is the product of the relative risks associated with $X_1$ and $X_2$, corresponding to a hypothesis of lack of effect measure modification of $X_1$ by $X_2$.

If now there is evidence of effect measure modification (sometimes termed interaction) between risk factors then in principle $RR_1(x_1)RR_2(x_2)$ in Eq. (9) should be replaced by $RR(x_1,x_2)$, that is the relative risk function describing the joint effect of $x_1$ and $x_2$, which can incorporate a different relative risk associated with $x_1$ at each given value of $x_2$. To our knowledge, there are currently few examples of risk factors and outcomes for which this function is accurately characterized and available.

Another option to handle it is to consider different ERFs in different population strata; again, one needs information on the joint distribution of all relevant factors, as well as stratum-specific relative risks.

Another (non-exclusive) situation is that of mediation effects [98]. Consider the case of a disease D (say, lung

cancer), influenced by several risk factors including active smoking (A) and green space exposure (B), the effect of which being partly mediated by changes in air pollution levels (C). Figure 7 provides a possible model of the assumed relations between A, B, C and D. Let us assume that one is interested in estimating the overall impact of factors A, B, C on D, that is, the number (or the fraction) of cases of disease D that would be avoided if A, B, and C all had “optimal” levels. The estimated impacts of B (improving green space exposure) and C (getting rid of air pollution) cannot be considered as being independent because a part of the effect of B is included in the effect of C (a mediation issue). Estimates of the share of the effect (in the sense of measure of association) of B on D that is not mediated by C (but that may be mediated by other factors not considered here, such as an increase in physical activity), termed the natural direct effect, can be provided by mediation analysis techniques [98]. This natural direct effect of B on the disease risk is by construction independent of the effect of C on disease risk, so that the corresponding attributable fractions can then be estimated and combined using formula (8) above. In the Global Burden Disease methodology, for each pair of risk factors that share an outcome, the fraction of the risk mediated through the other factor is estimated using mediation analysis techniques, if the relevant studies (in which B, C, D are altogether estimated) are available. A concern here (besides the usual assumptions required by mediation analysis [98]) relates to the transposability

<figure><img src="image_10.png" /><figcaption>**Fig. 7** Causal diagram summarizing the causal relations between hypothetical risk factors (A, B and C) and a disease D. Here, A and B are assumed to independently affect the probability of disease, while a part of the effect of B on D is mediated by C</figcaption></figure>
from one area to the other of such mediation analyses; for example, the change in air pollution level following a change in green space surface may be influenced by the local share of traffic-related air pollution among the total of the emissions of air pollutants from all sources, which may vary across areas.

In the case of a continuous health outcome, one option to estimate the joint impact of several factors, which assumes a lack of synergy (or of departure from additivity) is to sum the average changes in the outcome attributed to each exposure to obtain an estimate of the impact of the combined exposure.

## Cessation lag

The cessation lag can be defined as the time lag between the implementation of the considered intervention and the consequent change in hazard rate. It is meant to take into account the fact that for most (chronic) clinical endpoints, the effect of changes in (external) risk factors does not manifest fully immediately. The COMEAP study of particulate matter impacts on mortality [89] provides an illustration of the impact of various cessation lags (see also Fig. 8). Such a cessation lag can be implemented in studies relying on person-year approaches. Whether a cessation lag needs to be considered depends on the availability of knowledge about when a change in exposure will start influencing the considered health outcomes, as well as on the question asked: if for example one is interested in knowing how health is likely to

vary in the short and mid-term if one managed to implement a given intervention now (or in a near future), then considering a cessation lag is relevant; if the question of interest is the more theoretical one of quantifying how much better the population health would be today if a given exposure or set of exposure was absent (or if a specific intervention had been implemented a long time ago), then cessation lags might be ignored.

## Socio-economic impact of attributable health effects

One may wish to go beyond the health impact estimates. Economic analysis can further inform choices between different project or policy alternatives considering dimensions beyond health. Such an analysis can be limited to quantifying the costs of implementation of the considered scenarios or policies (e.g., those required to induce a reduction of exposure to a specific factor), and relate these costs to the health benefits expressed in non-monetary terms, such as DALYs (corresponding to a cost–benefit analysis). Beyond this, cost–benefit analyses have the advantage of allowing to compare the costs and monetized health and non-health benefits. Such an analysis is more complete and may be more meaningful for decision-makers than one ignoring the costs of implementation of each of the considered alternatives.

The benefits include the monetization of health benefits, which takes into account both tangible and intangible costs. The tangible costs refer both to direct costs, in particular the costs to the health system (costs of specific

<figure><img src="image_10.png" /><figcaption>**Fig. 8** Illustration of possible cessation lags (in years) considered in the estimation of the impact of fine particulate matter exposure on mortality [89]. The first year of the intervention implementation is designated as year one</figcaption></figure>
from one area to the other of such mediation analyses; for example, the change in air pollution level following a change in green space surface may be influenced by the local share of traffic-related air pollution among the total of the emissions of air pollutants from all sources, which may vary across areas.

In the case of a continuous health outcome, one option to estimate the joint impact of several factors, which assumes a lack of synergy (or of departure from additivity) is to sum the average changes in the outcome attributed to each exposure to obtain an estimate of the impact of the combined exposure.

## Cessation lag

The cessation lag can be defined as the time lag between the implementation of the considered intervention and the consequent change in hazard rate. It is meant to take into account the fact that for most (chronic) clinical endpoints, the effect of changes in (external) risk factors does not manifest fully immediately. The COMEAP study of particulate matter impacts on mortality [89] provides an illustration of the impact of various cessation lags (see also Fig. 8). Such a cessation lag can be implemented in studies relying on person-year approaches. Whether a cessation lag needs to be considered depends on the availability of knowledge about when a change in exposure will start influencing the considered health outcomes, as well as on the question asked: if for example one is interested in knowing how health is likely to

vary in the short and mid-term if one managed to implement a given intervention now (or in a near future), then considering a cessation lag is relevant; if the question of interest is the more theoretical one of quantifying how much better the population health would be today if a given exposure or set of exposure was absent (or if a specific intervention had been implemented a long time ago), then cessation lags might be ignored.

## Socio-economic impact of attributable health effects

One may wish to go beyond the health impact estimates. Economic analysis can further inform choices between different project or policy alternatives considering dimensions beyond health. Such an analysis can be limited to quantifying the costs of implementation of the considered scenarios or policies (e.g., those required to induce a reduction of exposure to a specific factor), and relate these costs to the health benefits expressed in non-monetary terms, such as DALYs (corresponding to a cost–benefit analysis). Beyond this, cost–benefit analyses have the advantage of allowing to compare the costs and monetized health and non-health benefits. Such an analysis is more complete and may be more meaningful for decision-makers than one ignoring the costs of implementation of each of the considered alternatives.

The benefits include the monetization of health benefits, which takes into account both tangible and intangible costs. The tangible costs refer both to direct costs, in particular the costs to the health system (costs of specific

<figure><img src="image_11.png" /><figcaption>**Fig. 8** Illustration of possible cessation lags (in years) considered in the estimation of the impact of fine particulate matter exposure on mortality [89]. The first year of the intervention implementation is designated as year one</figcaption></figure>
treatments for each pathology: drugs, consultation, hospitalization, etc.) and indirect costs linked to absenteeism and the resulting loss of productivity. The intangible costs refer to the inclusion in the economic analysis of the loss of well-being due to anxiety, discomfort, sadness or the restriction of leisure or domestic activities due. These are therefore non-market costs for which it is necessary to reveal their value through survey methods or analysis of the behavior implicitly attributed to them. For example, Ready et al. [99] and Chilton et al. [100] valued the willingness to pay to avoid an air pollution-related morbidity episode. Among these intangible costs, the economic valuation of mortality is a delicate step from an ethical point of view in the absence of consensual values. It is generally based on the monetary valuation of a statistical life or a year of life lost. In recent years, the most popular approach in the economic literature to determining the statistical value of a human life is the willingness-to-pay approach. The statistical value of a human life is thus approximated by the amount of money a society is willing to pay to reduce the risk exposure of each of its members. This literature shows that the statistical value of a human life depends on characteristics such as age at death, time between exposure and death (i.e. latency), and nature of the underlying risk [101, 102]. Empirical assessments have provided a range of values generally between €0.7 and €10 million per human life. The other approach used is that of revealed preferences, which is based on observed behavior: for example, the difference in wages between two branches of economic activity with different mortality risks.

The cost-benefit analysis, beyond the health benefits directly generated by the project or policy, can also integrate co-benefits not directly related to health. For example, Bouscasse et al. [29] considered the following co-benefits of measures to reduce fine particle pollution: the reduction of noise, the development of active mobility on health, which lead to health co-benefits, but also the reduction of greenhouse gas emissions, which includes benefits not related to health.

With regard to the evaluation of costs, it is necessary to define the scope: is it the cost of implementing the policy for the public authorities? Should the impact on household expenditure also be taken into account? This may be important, for example, in the case of measures aimed at reducing air pollution through actions on heating or transport, for which individuals carry a part of the cost. The assessment may also seek to quantify the impact on employment, for example, or on imports or exports of goods and equipment.

Finally, the time dimension is important in the implementation of a cost-benefit analysis. While costs usually occur at the beginning of the period (implementation of

actions or policies, investments), benefits tend to occur later. Indeed, health benefits are generated over time depending i) on the speed of implementation of actions and of the progressiveness of the reduction of exposures, and ii) on the fact that health benefits may not be immediate following the reduction of this exposure (cessation lag).

The time lag between costs and benefits has another consequence in a cost-benefit analysis. We do not give the same value to €1 to be paid today or in several years, because of what economists call the preference for the present. This is introduced into cost-benefit analysis through a *discount rate*, which gives a present value to monetary flows in the future. The higher the discount rate used by the public authority or by the stakeholders, the lower the present value of benefits that occur later.

## Sensitivity and uncertainty analyses

### Sources of uncertainty in quantitative risk assessment studies

Uncertainties exist at each step of risk assessment. For example, there may be uncertainties in the health outcomes influenced by the considered factor or policy, in the level of evidence relating the factor or policy with a given health outcome, in the corresponding dose-response function, in exposure distribution... We will here distinguish uncertainties due to the variability of the quantitative parameters considered in a risk assessment study (typically, in the dose-response function, but also possibly in parameters of higher dimension, such as the distribution of an exposure in the population) from more systemic uncertainties related to the model choice (sometimes termed *systemic* or *epistemic uncertainties*, e.g. related to the assumption that the risk factor(s) considered only influences a specific health outcome, possibly disregarding health effects not identified yet or for which a dose-response function is not available) [103]. A typology of sources of uncertainty in burden of diseases studies is presented in Knoll et al. [104]. We will focus here on uncertainty due to the variability in parameters, and touch upon systemic uncertainty in Sect. "Sensitivity and uncertainty analyses" below.

The consideration of the uncertainty related to variability typically implies to obtain an estimate of the uncertainties occurring at each step of the study, in order to combine these uncertainties (uncertainty propagation, or error propagation) and try providing an estimate of the resulting uncertainty on the overall study results.

## Estimating the impact of uncertainties

In the simple case of a single source of uncertainty, the translation of this uncertainty on the overall results is in principle relatively straightforward; for example, if
treatments for each pathology: drugs, consultation, hospitalization, etc.) and indirect costs linked to absenteeism and the resulting loss of productivity. The intangible costs refer to the inclusion in the economic analysis of the loss of well-being due to anxiety, discomfort, sadness or the restriction of leisure or domestic activities due. These are therefore non-market costs for which it is necessary to reveal their value through survey methods or analysis of the behavior implicitly attributed to them. For example, Ready et al. [99] and Chilton et al. [100] valued the willingness to pay to avoid an air pollution-related morbidity episode. Among these intangible costs, the economic valuation of mortality is a delicate step from an ethical point of view in the absence of consensual values. It is generally based on the monetary valuation of a statistical life or a year of life lost. In recent years, the most popular approach in the economic literature to determining the statistical value of a human life is the willingness-to-pay approach. The statistical value of a human life is thus approximated by the amount of money a society is willing to pay to reduce the risk exposure of each of its members. This literature shows that the statistical value of a human life depends on characteristics such as age at death, time between exposure and death (i.e. latency), and nature of the underlying risk [101, 102]. Empirical assessments have provided a range of values generally between €0.7 and €10 million per human life. The other approach used is that of revealed preferences, which is based on observed behavior: for example, the difference in wages between two branches of economic activity with different mortality risks.

The cost-benefit analysis, beyond the health benefits directly generated by the project or policy, can also integrate co-benefits not directly related to health. For example, Bouscasse et al. [29] considered the following co-benefits of measures to reduce fine particle pollution: the reduction of noise, the development of active mobility on health, which lead to health co-benefits, but also the reduction of greenhouse gas emissions, which includes benefits not related to health.

With regard to the evaluation of costs, it is necessary to define the scope: is it the cost of implementing the policy for the public authorities? Should the impact on household expenditure also be taken into account? This may be important, for example, in the case of measures aimed at reducing air pollution through actions on heating or transport, for which individuals carry a part of the cost. The assessment may also seek to quantify the impact on employment, for example, or on imports or exports of goods and equipment.

Finally, the time dimension is important in the implementation of a cost-benefit analysis. While costs usually occur at the beginning of the period (implementation of

actions or policies, investments), benefits tend to occur later. Indeed, health benefits are generated over time depending i) on the speed of implementation of actions and of the progressiveness of the reduction of exposures, and ii) on the fact that health benefits may not be immediate following the reduction of this exposure (cessation lag).

The time lag between costs and benefits has another consequence in a cost-benefit analysis. We do not give the same value to €1 to be paid today or in several years, because of what economists call the preference for the present. This is introduced into cost-benefit analysis through a *discount rate*, which gives a present value to monetary flows in the future. The higher the discount rate used by the public authority or by the stakeholders, the lower the present value of benefits that occur later.

## Sensitivity and uncertainty analyses

### Sources of uncertainty in quantitative risk assessment studies

Uncertainties exist at each step of risk assessment. For example, there may be uncertainties in the health outcomes influenced by the considered factor or policy, in the level of evidence relating the factor or policy with a given health outcome, in the corresponding dose-response function, in exposure distribution... We will here distinguish uncertainties due to the variability of the quantitative parameters considered in a risk assessment study (typically, in the dose-response function, but also possibly in parameters of higher dimension, such as the distribution of an exposure in the population) from more systemic uncertainties related to the model choice (sometimes termed *systemic* or *epistemic uncertainties*, e.g. related to the assumption that the risk factor(s) considered only influences a specific health outcome, possibly disregarding health effects not identified yet or for which a dose-response function is not available) [103]. A typology of sources of uncertainty in burden of diseases studies is presented in Knoll et al. [104]. We will focus here on uncertainty due to the variability in parameters, and touch upon systemic uncertainty in Sect. "Sensitivity and uncertainty analyses" below.

The consideration of the uncertainty related to variability typically implies to obtain an estimate of the uncertainties occurring at each step of the study, in order to combine these uncertainties (uncertainty propagation, or error propagation) and try providing an estimate of the resulting uncertainty on the overall study results.

### Estimating the impact of uncertainties

In the simple case of a single source of uncertainty, the translation of this uncertainty on the overall results is in principle relatively straightforward; for example, if
one only considers uncertainty on a dose response function expressed using a relative risk and (simplistically) assumes that this uncertainty is conveyed by the confidence interval of the relative risk, then the estimation of the health impact can be repeated using the limits of the confidence interval instead of the point estimate of the relative risk (of course, the confidence interval usually only conveys uncertainties related to the population sampling, more specifically to random error related to sampling.

However, there are multiple sources of uncertainty beyond those related to sampling error. Indeed, in the classical view of epidemiology (developed for measures of association), the uncertainty due to variability can be seen as having a random and a systemic component; only the former is easily estimated, while the estimation of bias requires quantitative bias assessment methods [105] that are seldom applied. In particular, sources of uncertainty related to exposure measurement error, to the assessment of disease frequency, possibly confounding bias or uncertainties in the shape of the exposure response function and the existence and shape of cessation lag, are not conveyed by the confidence interval of the relative risk and are worth considering – but rarely taken into account.

If one tries to simultaneously take into account several sources of uncertainty, then more complex approaches are required to propagate the uncertainty down to the impact estimate. Although analytical approaches (such as the delta-method) may be applicable in relatively simple situations, one more general approach corresponds to Monte-Carlo simulations. Monte-Carlo simulations rely on the principle of repeating a large number of times the health impact estimation, letting all underlying parameters (relative risks, exposure distribution, possibly the number of factors influencing the health outcome and the outcomes that they influence, if there are uncertainties at this level...) vary across realistic values [106, 107]. They allow providing an estimate of the distribution of the possible values of the health impact. This requires knowledge or assumptions on the likely distribution of each parameter considered in the study. If such an approach is implemented, then authors will be able to report a distribution of the most likely value of the health impact or cost. The results will for example be conveyed in a way such as: “Taken all identified sources of uncertainty into account, there is a 90% probability that the number of deaths attributable to factor A in the area is above 10, a 50% chance that it is above 30 and a 10% chance that it is above 50 cases” (with of course specific explanations for a non-scientific audience).

Alternative approaches to Monte-Carlo simulations also exist, in particular in the context of Bayesian modeling [108]. Provided relevant data are available, this framework can in principle accommodate both the uncertainty related to variability, but also systemic uncertainty [109].

In the absence of formal consideration of the systemic uncertainty in the uncertainty analysis, it remains essential for the investigators to state their model's assumptions and limitations, including in particular the impacts related to specific risk factors or health outcomes that could not be taken into account in the quantitative assessment (see also 3.3 below).

## Conclusion

Quantitative assessment studies are at the interplay between scientific, policy and legal issues; contrarily to what the deceptively simple epidemiological concept and formula of the “population attributable fraction” may let think [7, 8], their implementation and interpretation is very challenging.

We have reviewed some of the possible approaches and issues at each step of risk assessment studies. We have made the choice not to discuss the steps of problem framing, study reporting, and issues related to population participation, which are presented elsewhere [19, 21]. In the absence of broad methodological studies (e.g., via simulation approaches) in this field, we acknowledge that some of the choices we have done in presenting methods carry some amount of subjectivity and encourage the development of studies to quantitatively assess bias and trade-offs in this area to help investigators make more informed choices with regards to the methodological options. Such simulation studies could e.g., be used to select the most efficient approach to assess exposures in a given context.

To conclude, we will touch upon issues related to the terminology of risk assessment and HIA studies, the distinction between human-derived and animal-derived (toxicological) risk assessment studies, and research needs.

## Issues related to terminology

Studies aiming at characterizing the health and societal impact of policies or environmental factors are riddled with many different terminologies and acronyms. This diversity of acronyms encompasses some real differences in aims or methodology, but is also due to the convergence of various research and application streams. Indeed, as already mentioned, these studies originate from the epidemiological research stream related to the concept of population attributable fraction, which dates back to the 1950s [7], from the development of
one only considers uncertainty on a dose response func-
tion expressed using a relative risk and (simplistically)
assumes that this uncertainty is conveyed by the con-
fidence interval of the relative risk, then the estimation
of the health impact can be repeated using the limits of
the confidence interval instead of the point estimate of
the relative risk (of course, the confidence interval usu-
ally only conveys uncertainties related to the population
sampling, more specifically to random error related to
sampling.

However, there are multiple sources of uncertainty
beyond those related to sampling error. Indeed, in the
classical view of epidemiology (developed for measures
of association), the uncertainty due to variability can
be seen as having a random and a systemic component;
only the former is easily estimated, while the estimation
of bias requires quantitative bias assessment methods
[105] that are seldom applied. In particular, sources of
uncertainty related to exposure measurement error,
to the assessment of disease frequency, possibly con-
founding bias or uncertainties in the shape of the expo-
sure response function and the existence and shape of
cessation lag, are not conveyed by the confidence inter-
val of the relative risk and are worth considering – but
rarely taken into account.

If one tries to simultaneously take into account
several sources of uncertainty, then more complex
approaches are required to propagate the uncertainty
down to the impact estimate. Although analytical
approaches (such as the delta-method) may be appli-
cable in relatively simple situations, one more general
approach corresponds to Monte-Carlo simulations.
Monte-Carlo simulations rely on the principle of
repeating a large number of times the health impact
estimation, letting all underlying parameters (relative
risks, exposure distribution, possibly the number of
factors influencing the health outcome and the out-
comes that they influence, if there are uncertainties
at this level...) vary across realistic values [106, 107].
They allow providing an estimate of the distribution of
the possible values of the health impact. This requires
knowledge or assumptions on the likely distribution
of each parameter considered in the study. If such an
approach is implemented, then authors will be able
to report a distribution of the most likely value of the
health impact or cost. The results will for example be
conveyed in a way such as: "Taken all identified sources
of uncertainty into account, there is a 90% probability
that the number of deaths attributable to factor A in the
area is above 10, a 50% chance that it is above 30 and
a 10% chance that it is above 50 cases" (with of course
specific explanations for a non-scientific audience).

Alternative approaches to Monte-Carlo simulations
also exist, in particular in the context of Bayesian mod-
eling [108]. Provided relevant data are available, this
framework can in principle accommodate both the
uncertainty related to variability, but also systemic
uncertainty [109].

In the absence of formal consideration of the sys-
temic uncertainty in the uncertainty analysis, it remains
essential for the investigators to state their model's
assumptions and limitations, including in particular
the impacts related to specific risk factors or health
outcomes that could not be taken into account in the
quantitative assessment (see also 3.3 below).

Conclusion

Quantitative assessment studies are at the interplay
between scientific, policy and legal issues; contrarily to
what the deceptively simple epidemiological concept and
formula of the “population attributable fraction” may let
think [7, 8], their implementation and interpretation is
very challenging.

We have reviewed some of the possible approaches
and issues at each step of risk assessment studies. We
have made the choice not to discuss the steps of problem
framing, study reporting, and issues related to popula-
tion participation, which are presented elsewhere [19,
21]. In the absence of broad methodological studies (e.g.,
via simulation approaches) in this field, we acknowledge
that some of the choices we have done in presenting
methods carry some amount of subjectivity and encour-
age the development of studies to quantitatively assess
bias and trade-offs in this area to help investigators make
more informed choices with regards to the methodologi-
cal options. Such simulation studies could e.g., be used to
select the most efficient approach to assess exposures in a
given context.

To conclude, we will touch upon issues related to the
terminology of risk assessment and HIA studies, the
distinction between human-derived and animal-derived
toxicological risk assessment studies, and research needs.

Issues related to terminology

Studies aiming at characterizing the health and soci-
etal impact of policies or environmental factors are rid-
dled with many different terminologies and acronyms.
This diversity of acronyms encompasses some real dif-
ferences in aims or methodology, but is also due to the
convergence of various research and application streams.
Indeed, as already mentioned, these studies originate
from the epidemiological research stream related to
the concept of population attributable fraction, which
dates back to the 1950s [7], from the development of
legal requirements for environmental impact assessment before the development of new policies, plans or programs (which progressively also encompassed health issues), and from the applied stream of chemical risk assessment based on "regulatory toxicology" approaches and the risk assessment logic outlined in the USA National Research Council originally published in 1983 and also known as the "red book [1, 2]. Three key expressions are used: 1) burden of disease; 2) risk assessment; 3) health impact assessment.

*Burden of disease studies* generally correspond to an assessment of the risk (e.g., in terms of attributable cases or DALYs) associated with a given disease in human populations, without referring to an exposure possibly causing the disease or to a policy aiming at limiting its impact. However, when used in relation with a factor or family of factors, then only the risk (or disease burden) associated with this factor is considered (e.g., in “environmental burden of disease”), so that there is no essential distinction anymore with what we have discussed here. In practice, health impact assessment is often used in relation with a policy or intervention likely to affect health, while environmental burden of disease is often used in the absence of explicit consideration of a policy or intervention (see below).

Regarding health impact assessment, a difficulty arises from the fact that much of the theory and examples of HIA studies has been published in the grey literature [10]. The term has most often been used to assess the potential impact of a public policy, plan, program or project not yet implemented [3]. HIA is defined by WHO as “a combination of procedures, methods and tools by which a policy, program or project may be judged as to its potential effects on the health of a population, and the distribution of those effects within the population”. In addition, the consideration of inequalities (i.e., considering the distribution of risk within a population rather than only its mean value) has been put forward as an essential part of HIAs, at least in principle [110]. Several distinctions exist within the field of HIAs, which refer to various notions and dimensions [10, 110, 111]. Some of these notions are at different levels and hence not mutually exclusive (for example some distinctions refer to the way health is conceptualized, other to the qualitative or quantitative nature of the study, others to the level of participation of the considered population), making it difficult to suggest a simple and unified terminology. A distinction between “broad focus” HIA studies, in which “a holistic model of health is used, democratic values and community participation are paramount and in which quantification of health impacts is rarely attempted” [10], and “tight focus” HIAs, based on epidemiology and toxicology and tending towards measurement and quantification, is sometimes

done [10]. “Analytical HIA” is sometimes used synonymously to these “tight focus” HIAs. Harris-Roxas and Harris also quote distinctions such as between quantitative and qualitative HIAs, to those relying on “tight” or “broad” definitions of health, to HIAs of projects or policies [111]. What we have reviewed here is close (if not equivalent) to these “analytical”, “tight focus” or “quantitative” HIAs.

Such quantitative HIAs typically aim at answering a question about the future (“how is the planned policy expected to affect the health of the concerned population?”) while many risk assessment studies aim at answering a question about the present, and are sometimes presented as considering a single factor at a time (typically, “how many lung cancer cases would be avoided in this city if WHO air pollution guidelines were respected?”). We come back to these apparent differences in the Sect. "Assessing the impact of policies versus the impact of exposures".

As already stated, in practice, some HIA or “risk assessment” exercises fall short of providing a quantitative estimate of the risk, e.g., because of a lack of relevant dose response functions or support to collect missing information; they may for example stop at the step of hazard identification. It is, in a way, what happens with animal-based risk assessment studies.

## Animal-based risk assessment studies

It is important to recall that in addition to the approach based on human-derived dose-response functions that we described above exists a whole stream of research and applied studies relying on animal-based dose-response functions and so-called toxicological reference values. The core approach of the benchmark dose (BMDL) consists in identifying an exposure level corresponding to an effect considered small in an animal model (say, a 5% decrease in organ weight or 5% increase in the frequency of a disease) [112]. The lower confidence bound of the benchmark dose is then divided by an uncertainty factor (typically, 100), to take into account between-species and within-species differences in sensitivity, and this value is used as a “daily tolerable dose”, or compared to the exposure distribution in a specific human population. Therefore, this approach aims at identifying a range of doses under which, under certain assumptions, there would be no “appreciable adverse health effects” of exposure. The comparison of the estimated daily tolerable dose with the exposure distribution in the considered population allows to identify if a substantial share of the population is above this daily tolerable dose, and thus finds itself at exposure levels that cannot be deemed safe (a qualitative rather than quantitative statement about risk). For this reason, these risk assessment approaches based on
legal requirements for environmental impact assessment before the development of new policies, plans or programs (which progressively also encompassed health issues), and from the applied stream of chemical risk assessment based on “regulatory toxicology” approaches and the risk assessment logic outlined in the USA National Research Council originally published in 1983 and also known as the “red book” [1, 2]. Three key expressions are used: 1) burden of disease; 2) risk assessment; 3) health impact assessment.

*Burden of disease studies* generally correspond to an assessment of the risk (e.g., in terms of attributable cases or DALYs) associated with a given disease in human populations, without referring to an exposure possibly causing the disease or to a policy aiming at limiting its impact. However, when used in relation with a factor or family of factors, then only the risk (or disease burden) associated with this factor is considered (e.g., in “environmental burden of disease”), so that there is no essential distinction anymore with what we have discussed here. In practice, health impact assessment is often used in relation with a policy or intervention likely to affect health, while environmental burden of disease is often used in the absence of explicit consideration of a policy or intervention (see below).

Regarding health impact assessment, a difficulty arises from the fact that much of the theory and examples of HIA studies has been published in the grey literature [10]. The term has most often been used to assess the potential impact of a public policy, plan, program or project not yet implemented [3]. HIA is defined by WHO as “a combination of procedures, methods and tools by which a policy, program or project may be judged as to its potential effects on the health of a population, and the distribution of those effects within the population”. In addition, the consideration of inequalities (i.e., considering the distribution of risk within a population rather than only its mean value) has been put forward as an essential part of HIAs, at least in principle [110]. Several distinctions exist within the field of HIAs, which refer to various notions and dimensions [10, 110, 111]. Some of these notions are at different levels and hence not mutually exclusive (for example some distinctions refer to the way health is conceptualized, other to the qualitative or quantitative nature of the study, others to the level of participation of the considered population), making it difficult to suggest a simple and unified terminology. A distinction between “broad focus” HIA studies, in which “a holistic model of health is used, democratic values and community participation are paramount and in which quantification of health impacts is rarely attempted” [10], and “tight focus” HIAs, based on epidemiology and toxicology and tending towards measurement and quantification, is sometimes

done [10]. “Analytical HIA” is sometimes used synonymously to these “tight focus” HIAs. Harris-Roxas and Harris also quote distinctions such as between quantitative and qualitative HIAs, to those relying on “tight” or “broad” definitions of health, to HIAs of projects or policies [111]. What we have reviewed here is close (if not equivalent) to these “analytical”, “tight focus” or “quantitative” HIAs.

Such quantitative HIAs typically aim at answering a question about the future (“how is the planned policy expected to affect the health of the concerned population?”) while many risk assessment studies aim at answering a question about the present, and are sometimes presented as considering a single factor at a time (typically, “how many lung cancer cases would be avoided in this city if WHO air pollution guidelines were respected?”). We come back to these apparent differences in the Sect. "Assessing the impact of policies versus the impact of exposures".

As already stated, in practice, some HIA or “risk assessment” exercises fall short of providing a quantitative estimate of the risk, e.g., because of a lack of relevant dose response functions or support to collect missing information; they may for example stop at the step of hazard identification. It is, in a way, what happens with animal-based risk assessment studies.

## Animal-based risk assessment studies

It is important to recall that in addition to the approach based on human-derived dose-response functions that we described above exists a whole stream of research and applied studies relying on animal-based dose-response functions and so-called toxicological reference values. The core approach of the benchmark dose (BMDL) consists in identifying an exposure level corresponding to an effect considered small in an animal model (say, a 5% decrease in organ weight or 5% increase in the frequency of a disease) [112]. The lower confidence bound of the benchmark dose is then divided by an uncertainty factor (typically, 100), to take into account between-species and within-species differences in sensitivity, and this value is used as a “daily tolerable dose”, or compared to the exposure distribution in a specific human population. Therefore, this approach aims at identifying a range of doses under which, under certain assumptions, there would be no “appreciable adverse health effects” of exposure. The comparison of the estimated daily tolerable dose with the exposure distribution in the considered population allows to identify if a substantial share of the population is above this daily tolerable dose, and thus finds itself at exposure levels that cannot be deemed safe (a qualitative rather than quantitative statement about risk). For this reason, these risk assessment approaches based on
animal-derived reference values or dose-response func-
tions rather correspond to safety assessment: they can
allow to state that, given its exposure distribution, a given
human population is “safe”, or unlikely to suffer apprecia-
ble adverse health effects, with respect to a specific expo-
sure (or set of exposures if the approach is used in the
context of mixtures of exposures) and do not strictly cor-
respond to risk assessment as we defined it, i.e., the esti-
mation of a number of disease cases (risks) attributable to
an exposure in a population. To limit ambiguity, it might
be relevant either to use the expression “safety assess-
ment” when referring to the so-called risk assessment
studies relying on animal derived toxicological reference
values, or to distinguish “animal-based risk assessment”
(which implies between-species extrapolation) from
“human-based risk assessment” (which does not).

Assessing the impact of policies versus the impact
of exposures

The factors influencing health considered in risk assess-
ment studies range from single behaviors (e.g., smoking,
physical activity), to physical and chemical factors such
as particulate matter [35, 113] or other environmental
exposures including lead or families of factors such as

endocrine disruptors [12, 75]; these can be considered at
various scales, from the neighborhood, region, country
or at the planetary scale (e.g. as done by the Global Bur-
den of Disease Studies, or by a study considering differ-
ent ozone layer depletion scenarios [37]). In addition, as
described above, the formalism of risk assessment studies
used for a single exposure can be extended to the case of
two or more exposures, at least under certain assump-
tions. Consequently, if one is interested in a project (e.g.,
the building of a road infrastructure, a factory) or a pol-
icy (regulating a behavior such as smoking, alcohol con-
sumption, speed limit on highways, frequency of social
contacts or exposure to a chemical or set of chemical
factors, or consisting in taxes aiming at modifying expo-
sures or behaviors), and if it is possible to provide a quan-
titative estimate of the expected changes in the factors
affecting health impacted by this project or policy, then
the methodology of risk assessment as described above
can be used to provide an estimation of the impact of this
project or policy. Symmetrically, evaluating the impact
of a factor, such as an atmospheric pollutant, implies, as
we have seen, to compare a given situation (usually, the
current one or a future of this situation assuming a “busi-
ness as usual” scenario) with a counterfactual situation (a

A) Assessing the impact of an exposure

<figure><img src="image_11.png" /></figure>

B) Assessing the impact of a policy

<figure><img src="image_12.png" /><figcaption>**Fig. 9** Illustration of the similitude of the principles of risk assessment of an exposure (A) and of a policy or program (B). When considering an exposure (A), the fraction of disease cases attributable to a specific exposure (compared to a lower and theoretically achievable level) is estimated for time t (typically assumed to correspond to the current time). When considering a policy (B), the expected health benefit of the project or policy (consisting in changing the level of one or more environmental factors) is estimated, considering the population at the current time or at a later time t, comparing it to the situation without change. Both approaches can be seen as aiming to estimate the impact of a theoretical policy or intervention lowering (or, more generally, changing) the level of one or several environmental factors, compared to a reference situation considered at the same time period</figcaption></figure>
animal-derived reference values or dose-response func-
tions rather correspond to safety assessment: they can
allow to state that, given its exposure distribution, a given
human population is “safe”, or unlikely to suffer apprecia-
ble adverse health effects, with respect to a specific expo-
sure (or set of exposures if the approach is used in the
context of mixtures of exposures) and do not strictly cor-
respond to risk assessment as we defined it, i.e., the esti-
mation of a number of disease cases (risks) attributable to
an exposure in a population. To limit ambiguity, it might
be relevant either to use the expression “safety assess-
ment” when referring to the so-called risk assessment
studies relying on animal derived toxicological reference
values, or to distinguish “animal-based risk assessment”
(which implies between-species extrapolation) from
“human-based risk assessment” (which does not).

Assessing the impact of policies versus the impact
of exposures

The factors influencing health considered in risk assess-
ment studies range from single behaviors (e.g., smoking,
physical activity), to physical and chemical factors such
as particulate matter [35, 113] or other environmental
exposures including lead or families of factors such as

endocrine disruptors [12, 75]; these can be considered at
various scales, from the neighborhood, region, country
or at the planetary scale (e.g. as done by the Global Bur-
den of Disease Studies, or by a study considering differ-
ent ozone layer depletion scenarios [37]). In addition, as
described above, the formalism of risk assessment studies
used for a single exposure can be extended to the case of
two or more exposures, at least under certain assump-
tions. Consequently, if one is interested in a project (e.g.,
the building of a road infrastructure, a factory) or a pol-
icy (regulating a behavior such as smoking, alcohol con-
sumption, speed limit on highways, frequency of social
contacts or exposure to a chemical or set of chemical
factors, or consisting in taxes aiming at modifying expo-
sures or behaviors), and if it is possible to provide a quan-
titative estimate of the expected changes in the factors
affecting health impacted by this project or policy, then
the methodology of risk assessment as described above
can be used to provide an estimation of the impact of this
project or policy. Symmetrically, evaluating the impact
of a factor, such as an atmospheric pollutant, implies, as
we have seen, to compare a given situation (usually, the
current one or a future of this situation assuming a “busi-
ness as usual” scenario) with a counterfactual situation (a

A) Assessing the impact of an exposure

<figure><img src="image_12.png" /><figcaption>**Fig. 9** Illustration of the similitude of the principles of risk assessment of an exposure (A) and of a policy or program (B). When considering an exposure (A), the fraction of disease cases attributable to a specific exposure (compared to a lower and theoretically achievable level) is estimated for time t (typically assumed to correspond to the current time). When considering a policy (B), the expected health benefit of the project or policy (consisting in changing the level of one or more environmental factors) is estimated, considering the population at the current time or at a later time t, comparing it to the situation without change. Both approaches can be seen as aiming to estimate the impact of a theoretical policy or intervention lowering (or, more generally, changing) the level of one or several environmental factors, compared to a reference situation considered at the same time period</figcaption></figure>

B) Assessing the impact of a policy

<figure><img src="image_13.png" /></figure>
hypothetical present in which a behavior or an exposure has been altered at the population level) that can be seen as resulting from a policy or an infrastructure. For example, assessing the risk associated with air pollution exposure implies to consider a counterfactual level (e.g., the WHO air pollution guidelines); the estimated risk is then identical to the health gain expected from a policy that would allow to lower air pollution from the current situation down to this guideline value (see Fig. 9 for an illustration). In other words, assessing ex-ante the impact of a hypothetical policy or infrastructure (what is sometimes termed health impact assessment) boils down to evaluating the health impact of its immediate consequences relevant for health (a set of factors); and assessing the impact of one or several behavioral, social or environmental factors (for which the expression risk assessment is usually reserved) is equivalent to considering the impact of a policy that would alter this or these factor(s). There may be some differences in implementation between the two specific questions (e.g., one may want to assume that it takes a few years for air pollution to reach the target value in the case of the evaluation of a policy, while an estimation of the current impact only requires to compare two “parallel worlds” with distinct air pollution levels), but these are not always considered and can be seen as minor technical differences. For these reasons, there are no essential differences in quantitatively assessing the effect of a single factor, of several factors, or of a policy or project. Recognizing this similarity in design of risk assessment and analytical/quantitative HIAs may allow to bring more clarity in the methodology and terminology; in particular, it may be relevant to adopt a unified terminology allowing to point to the differences that bear strong consequences, such as whether the study relies on human-based dose response functions (as illustrated here) or on dose-response functions derived from animal models.

## The perils of quantification: leaving emerging hazards by the roadside

Risk assessment studies imply many steps requiring a large amount of data; this is all the more true in the case of studies considering simultaneously multiple exposures, exposures with effects on multiple health endpoints (such as tobacco smoke, particulate matter, lead, physical activity...), or policies likely to influence several exposures or behaviors (such as a “zero pollution action plan”, as envisioned by the European Commission, or a set of actions to limit greenhouse gas emissions in multiple sectors). In some (probably not infrequent) cases, only a fraction of the data relevant for the risk assessment will be available or possibly available within a limited

time frame. Researchers are then facing several non-exclusive options:

1) collect additional data (the scientifically rigorous approach); this may take a long time and be very expensive, since in many cases the missing data correspond to dose-response functions, which are typically generated by cohort studies. For example, in an ongoing exposome study conducted as part of ATHLETE project and considering 74 exposure-outcome pairs corresponding to effects with a level of evidence deemed likely or more than likely, a human dose-response function could be identified for only 70% of these possible effects (Rocabois et al., personal communication). Although working with high-quality data, even if this implies to delay the availability of the final results, is often the preferred option in science, such an option is problematic for health impact assessment studies, which often require to be conducted within a constrained time frame so that a decision about the planned policy or a possibly harmful exposure can be quickly taken, to bring potential health benefits to society or inform a legal process;

2) perform the study with the limited data available in the constrained time frame (imperfect but timely approach); in this case, it is possible that only a fraction of the impact of the exposure(s) or policy will be assessed (because several dose response functions corresponding to the effects of the exposure or policy are available) and that the quantified fraction will be estimated with large uncertainties;

3) perform a purely qualitative health impact assessment study (qualitative approach);

4) not to perform the study (“analysis paralysis”).

In many cases, option 2), consisting in moving along with the limited data available, will be preferred. The consequence may be that a fraction, which may be large, of the impact, will be ignored. Thus, because of their relative complexity, health impact assessment studies, which aim to make health impacts visible, may paradoxically leave a large fraction of this impact on the roadside. Impacts left on the road side will often correspond to “emerging” (newly identified factors, newly identified effects) risks. Under this imperfect but timely approach, it is essential not only to try to provide a quantification of the uncertainty around the quantified part (see above, Sect. "Sensitivity and uncertainty analyses"). It would also be relevant to attempt providing some estimate of the magnitude of what has obviously been left out (for example, the impact of a known exposure likely to affect an outcome for which
hypothetical present in which a behavior or an exposure
has been altered at the population level) that can be seen
as resulting from a policy or an infrastructure. For exam-
ple, assessing the risk associated with air pollution expo-
sure implies to consider a counterfactual level (e.g., the
WHO air pollution guidelines); the estimated risk is then
identical to the health gain expected from a policy that
would allow to lower air pollution from the current situ-
ation down to this guideline value (see Fig. 9 for an illus-
tration). In other words, assessing ex-ante the impact of a
hypothetical policy or infrastructure (what is sometimes
termed health impact assessment) boils down to evalu-
ating the health impact of its immediate consequences
relevant for health (a set of factors); and assessing the
impact of one or several behavioral, social or environ-
mental factors (for which the expression risk assess-
ment is usually reserved) is equivalent to considering the
impact of a policy that would alter this or these factor(s).
There may be some differences in implementation
between the two specific questions (e.g., one may want to
assume that it takes a few years for air pollution to reach
the target value in the case of the evaluation of a policy,
while an estimation of the current impact only requires
to compare two “parallel worlds” with distinct air pollu-
tion levels), but these are not always considered and can
be seen as minor technical differences. For these reasons,
there are no essential differences in quantitatively assess-
ing the effect of a single factor, of several factors, or of
a policy or project. Recognizing this similarity in design
of risk assessment and analytical/quantitative HIAs may
allow to bring more clarity in the methodology and ter-
minology; in particular, it may be relevant to adopt a
unified terminology allowing to point to the differences
that bear strong consequences, such as whether the study
relies on human-based dose response functions (as illus-
trated here) or on dose-response functions derived from
animal models.

The perils of quantification: leaving emerging hazards
by the roadside

Risk assessment studies imply many steps requiring a
large amount of data; this is all the more true in the case
of studies considering simultaneously multiple expo-
sures, exposures with effects on multiple health end-
points (such as tobacco smoke, particulate matter, lead,
physical activity...), or policies likely to influence several
exposures or behaviors (such as a “zero pollution action
plan”, as envisioned by the European Commission, or a
set of actions to limit greenhouse gas emissions in mul-
tiple sectors). In some (probably not infrequent) cases,
only a fraction of the data relevant for the risk assessment
will be available or possibly available within a limited

time frame. Researchers are then facing several non-
exclusive options:

1) collect additional data (the scientifically rigorous approach); this may take a long time and be very expensive, since in many cases the missing data correspond to dose-response functions, which are typically generated by cohort studies. For example, in an ongoing exposome study conducted as part of ATHLETE project and considering 74 exposure-outcome pairs corresponding to effects with a level of evidence deemed likely or more than likely, a human dose-response function could be identified for only 70% of these possible effects (Rocabois et al., personal communication). Although working with high-quality data, even if this implies to delay the availability of the final results, is often the preferred option in science, such an option is problematic for health impact assessment studies, which often require to be conducted within a constrained time frame so that a decision about the planned policy or a possibly harmful exposure can be quickly taken, to bring potential health benefits to society or inform a legal process;

2) perform the study with the limited data available in the constrained time frame (imperfect but timely approach); in this case, it is possible that only a fraction of the impact of the exposure(s) or policy will be assessed (because several dose response functions corresponding to the effects of the exposure or policy are available) and that the quantified fraction will be estimated with large uncertainties;

3) perform a purely qualitative health impact assess-
ment study (qualitative approach);

4) not to perform the study ("analysis paralysis").

In many cases, option 2), consisting in moving along
with the limited data available, will be preferred. The con-
sequence may be that a fraction, which may be large, of
the impact, will be ignored. Thus, because of their relative
complexity, health impact assessment studies, which aim
to make health impacts visible, may paradoxically leave
a large fraction of this impact on the roadside. Impacts
left on the road side will often correspond to "emerging"
(newly identified factors, newly identified effects) risks.
Under this imperfect but timely approach, it is essential
not only to try to provide a quantification of the uncer-
tainty around the quantified part (see above, Sect. "Sensi-
tivity and uncertainty analyses"). It would also be relevant
to attempt providing some estimate of the magnitude of
what has obviously been left out (for example, the impact
of a known exposure likely to affect an outcome for which
no dose-response function is available), or at least to
make the missing part (the “known unknown”) visible in
some way.

Identified gaps

This review provided a general methodological frame-
work for risk assessment studies and demonstrated their
relevance to also consider the expected impact of poli-
cies and infrastructures, and therefore their closeness
to health impact assessment studies; it illustrated recent
development related to the diversity of approaches to
assess factors at the individual levels (such as fine-scale
environmental models and personal dosimeters), and the
potentially strong impact of choices regarding exposure
assessment tools, including the consideration of popu-
lation density when environmental models are used. It
also allowed to identify some gaps, challenges or pend-
ing issues in the methodology of risk assessment studies.
These issues include 1) proposing a formal approach to
the quantitative handling of the level of evidence regard-
ing each exposure-health outcome pairs (see Handling of
the strength of evidence about the effect of environmen-
tal factors on health); 2) more generally, develop more
formal and if possible quantitative assessment of the
health impacts not handled by a specific quantitative risk
assessment study (the “know unknowns”); 3) confronting
the approaches of risk assessment based on human dose-
response function reviewed here with that relying on
toxicological data; and 4) other technical issues related to
the simultaneous consideration of several exposures (or
of policies acting on health via changes in several envi-
ronmental factors), in particular when some of these
exposures are causally related.

**Supplementary Information**

The online version contains supplementary material available at https://doi.
org/10.1186/s12940-023-01039-x.

**Additional file 1: Figure S1.** Illustration of the structure of a health impact assessment tool allowing quantification of the number of deaths preventable through compliance with recommendations regarding physical activity, air pollution, noise, heat and access to green space [36].

Authors' contributions

R.S. and M.R. wrote the main manuscript text, with contributions from S.M.,
J. Be. and J. Bu. All authors reviewed the manuscript.

Funding

The manuscript was conducted as part of HERA (Health Environment Research Agenda for Europe) project funded by Horizon Europe research and innovation programme from the DG Research of the European Commission (grant 825417).

Availability of data and materials

Not applicable.

Declarations

Competing interests

The authors declare no competing interests.

Received: 23 June 2023 Accepted: 5 December 2023

Published online: 27 January 2024

**References**

1. National Research Council. Risk assessment in the federal government. Managing the process. Washington, DC: National Academy Press; 1983.

2. National Research Council (U.S.). Committee on Risk Assessment of Hazardous Air Pollutants. Science and judgment in risk assessment. Washington, D.C: National Academy Press; 1994.

3. Cole BL, Fielding JE. Health impact assessment: a tool to help policy makers understand health beyond health care. Annu Rev Public Health. 2007;28:393-412.

4. Bell ML, Davis DL. Reassessment of the lethal London fog of 1952: novel indicators of acute and chronic consequences of acute exposure to air pollution. Environ Health Perspect. 2001;109(Suppl 3):389-94.

5. Clancy L, Goodman P, Sinclair H, Dockery DW. Effect of air-pollution control on death rates in Dublin, Ireland: an intervention study. Lancet. 2002;360(9341):1210-4.

6. Rockhill B, Newman B, Weinberg C. Use and misuse of population attributable fractions. Am J Public Health. 1998;88(1):15-9.

7. Poole C. A history of the population attributable fraction and related measures. Ann Epidemiol. 2015;25(3):147-54.

8. Greenland S, Robins JM. Conceptual problems in the defini-
tion and interpretation of attributable fractions. Am J Epidemiol.
1988;128(6):1185-97.

9. Bobst S. History of risk assessment in toxicology. London, San Diego: Academic Press is an imprint of Elsevier; 2017.

10. Mindell JS, Boltong A, Forde I. A review of health impact assessment frameworks. Public Health. 2008;122(11):1177-87.

11. Slama R. Causes et conditions extérieures des maladies et de la santé. Paris: Collège de France/Fayard; 2022.

12. Trasande L, Zoeller RT, Hass U, Kortenkamp A, Grandjean P, Myers JP, DiGangi J, Hunt PM, Rudel R, Sathyaranayana S, et al. Burden of disease and costs of exposure to endocrine disrupting chemicals in the European Union: an updated analysis. Andrology. 2016;4(4):565-72.

13. Shaffer RM, Sellers SP, Baker MG, de Buen Kalman R, Frostad J, Suter MK, Anenberg SC, Balbus J, Basu N, Bellinger DC, et al. Improving and expanding estimates of the global burden of disease due to environmental health risk factors. Environ Health Perspect. 2019;127(10):105001.

14. G. B. D. Risk Factors Collaborators. Global burden of 87 risk factors in 204 countries and territories, 1990–2019: a systematic analysis for the Global Burden of Disease Study 2019. Lancet. 2020;396(10258):1223–49.

15. OECD. OECD Environmental Outlook to 2050: the consequences of inaction. In: OECD Environmental Outlook. 2012.

16. Fillol C, Oleko A, Saoudi A, Zeghnoun A, Balicco A, Gane J, Rambaud L, Leblanc A, Gaudreau E, Marchand P, et al. Exposure of the French population to bisphenols, phthalates, parabens, glycol ethers, brominated flame retardants, and perfluorinated compounds in 2014–2016: results from the Esteban study. Environ Int. 2021;147:106340.

17. Lobo Vicente J, Ganzleben C, Gasol R, Marnane I, Gilles L, Buekers J, Bessems J, Colles A, Gerofke A, David M, et al. HBM4EU results support the chemicals' strategy for sustainability and the zero-pollution action plan. Int J Hyg Environ Health. 2023;248:114111.

18. Lebret E. Integrated environmental health impact assessment for risk governance purposes; across what do we integrate? (INTARESE HEIMTSA). Int J Environ Res Public Health. 2015;13(1):71.

19. Briggs DJ. A framework for integrated environmental health impact assessment of systemic risks. Environ Health. 2008;7:61.

20. Harris-Roxas B, Viliani F, Bond A, Cave B, Divall M, Furu P, Harris P, Soeberg M, Wernham A, Winkler M. Health impact assessment: the state of the art. Impact Assess Proj Apprais. 2012;30(1):43-52.
no dose-response function is available), or at least to
make the missing part (the “known unknown”) visible in
some way.

Identified gaps

This review provided a general methodological frame-
work for risk assessment studies and demonstrated their
relevance to also consider the expected impact of poli-
cies and infrastructures, and therefore their closeness
to health impact assessment studies; it illustrated recent
development related to the diversity of approaches to
assess factors at the individual levels (such as fine-scale
environmental models and personal dosimeters), and the
potentially strong impact of choices regarding exposure
assessment tools, including the consideration of popu-
lation density when environmental models are used. It
also allowed to identify some gaps, challenges or pend-
ing issues in the methodology of risk assessment studies.
These issues include 1) proposing a formal approach to
the quantitative handling of the level of evidence regard-
ing each exposure-health outcome pairs (see Handling of
the strength of evidence about the effect of environmen-
tal factors on health); 2) more generally, develop more
formal and if possible quantitative assessment of the
health impacts not handled by a specific quantitative risk
assessment study (the “know unknowns”); 3) confronting
the approaches of risk assessment based on human dose-
response function reviewed here with that relying on
toxicological data; and 4) other technical issues related to
the simultaneous consideration of several exposures (or
of policies acting on health via changes in several envi-
ronmental factors), in particular when some of these
exposures are causally related.

**Supplementary Information**

The online version contains supplementary material available at https://doi.org/10.1186/s12940-023-01039-x.

**Additional file 1: Figure S1.**Illustration of the structure of a health impact assessment tool allowing quantification of the number of deaths preventable through compliance with recommendations regarding physical activity, air pollution, noise, heat and access to green space [36].

Authors' contributions

R.S. and M.R. wrote the main manuscript text, with contributions from S.M., J. Be. and J. Bu. All authors reviewed the manuscript.

Funding

The manuscript was conducted as part of HERA (Health Environment Research Agenda for Europe) project funded by Horizon Europe research and innovation programme from the DG Research of the European Commission (grant 825417).

Availability of data and materials

Not applicable.

Declarations

Competing interests

The authors declare no competing interests.

Received: 23 June 2023 Accepted: 5 December 2023

Published online: 27 January 2024

References

1. National Research Council. Risk assessment in the federal government. Managing the process. Washington, DC: National Academy Press; 1983.

2. National Research Council (U.S.). Committee on Risk Assessment of Hazardous Air Pollutants. Science and judgment in risk assessment. Washington, D.C: National Academy Press; 1994.

3. Cole BL, Fielding JE. Health impact assessment: a tool to help policy makers understand health beyond health care. Annu Rev Public Health. 2007;28:393-412.

4. Bell ML, Davis DL. Reassessment of the lethal London fog of 1952: novel indicators of acute and chronic consequences of acute exposure to air pollution. Environ Health Perspect. 2001;109(Suppl 3):389-94.

5. Clancy L, Goodman P, Sinclair H, Dockery DW. Effect of air-pollution control on death rates in Dublin, Ireland: an intervention study. Lancet. 2002;360(9341):1210-4.

6. Rockhill B, Newman B, Weinberg C. Use and misuse of population attributable fractions. Am J Public Health. 1998;88(1):15-9.

7. Poole C. A history of the population attributable fraction and related measures. Ann Epidemiol. 2015;25(3):147-54.

8. Greenland S, Robins JM. Conceptual problems in the defini-
tion and interpretation of attributable fractions. Am J Epidemiol.
1988;128(6):1185-97.

9. Bobst S. History of risk assessment in toxicology. London, San Diego: Academic Press is an imprint of Elsevier; 2017.

10. Mindell JS, Boltong A, Forde I. A review of health impact assessment frameworks. Public Health. 2008;122(11):1177-87.

11. Slama R. Causes et conditions extérieures des maladies et de la santé. Paris: Collège de France/Fayard; 2022.

12. Trasande L, Zoeller RT, Hass U, Kortenkamp A, Grandjean P, Myers JP, DiGangi J, Hunt PM, Rudel R, Sathyaranayana S, et al. Burden of disease and costs of exposure to endocrine disrupting chemicals in the European Union: an updated analysis. Andrology. 2016;4(4):565-72.

13. Shaffer RM, Sellers SP, Baker MG, de Buen Kalman R, Frostad J, Suter MK, Anenberg SC, Balbus J, Basu N, Bellinger DC, et al. Improving and expanding estimates of the global burden of disease due to environmental health risk factors. Environ Health Perspect. 2019;127(10):105001.

14. G. B. D. Risk Factors Collaborators. Global burden of 87 risk factors in 204 countries and territories, 1990–2019: a systematic analysis for the Global Burden of Disease Study 2019. Lancet. 2020;396(10258):1223–49.

15. OECD. OECD Environmental Outlook to 2050: the consequences of inaction. In: OECD Environmental Outlook. 2012.

16. Fillol C, Oleko A, Saoudi A, Zeghnoun A, Balicco A, Gane J, Rambaud L, Leblanc A, Gaudreau E, Marchand P, et al. Exposure of the French population to bisphenols, phthalates, parabens, glycol ethers, brominated flame retardants, and perfluorinated compounds in 2014–2016: results from the Esteban study. Environ Int. 2021;147:106340.

17. Lobo Vicente J, Ganzleben C, Gasol R, Marnane I, Gilles L, Buekers J, Bessems J, Colles A, Gerofke A, David M, et al. HBM4EU results support the chemicals' strategy for sustainability and the zero-pollution action plan. Int J Hyg Environ Health. 2023;248:114111.

18. Lebret E. Integrated environmental health impact assessment for risk governance purposes; across what do we integrate? (INTARESE HEIMTSA). Int J Environ Res Public Health. 2015;13(1):71.

19. Briggs DJ. A framework for integrated environmental health impact assessment of systemic risks. Environ Health. 2008;7:61.

20. Harris-Roxas B, Viliani F, Bond A, Cave B, Divall M, Furu P, Harris P, Soeberg M, Wernham A, Winkler M. Health impact assessment: the state of the art. Impact Assess Proj Apprais. 2012;30(1):43-52.
21. Nieuwenhuijsen MJ, Khreis H, Verlinghieri E, Mueller N, Rojas-Rueda D. Participatory quantitative health impact assessment of urban and transport planning in cities: a review and research needs. Environ Int. 2017;103:61–72.

22. Brown SL. Quantitative risk assessment of environmental hazards. Annu Rev Public Health. 1985;6:247–67.

23. Goldstein BD. Advances in risk assessment and communication. Annu Rev Public Health. 2005;26:141–63.

24. Grant MJ, Booth A. A typology of reviews: an analysis of 14 review types and associated methodologies. Health Info Libr J. 2009;26(2):91–108.

25. Health impact assessment (HIA) tools and methods. https://www.who.int/tools/health-impact-assessments.

26. Kunzli N, Kaiser R, Medina S, Studnicka M, Chanel O, Filliger P,erry M, Horak F Jr, Puybonnieux-Texier V, Quenel P, et al. Public-health impact of outdoor and traffic-related air pollution: a European assessment. Lancet. 2000;356(9232):795–801.

27. Barboza EP, Cirach M, Khomenko S, lungman T, Mueller N, Barrera-Gomez J, Rojas-Rueda D, Kondo M, Nieuwenhuijsen M. Green space and mortality in European cities: a health impact assessment study. Lancet Planet Health. 2021;5(10):e718-730.

28. Lhachimi SK, Nusselder WJ, Smit HA, Baili P, Bennett K, Fernandez E, Kulik MC, Lobstein T, Pomerleau J, Boshuizen HC, et al. Potential health gains and health losses in eleven EU countries attainable through feasible prevalences of the life-style related risk factors alcohol, BMI, and smoking: a quantitative health impact assessment. BMC Public Health. 2016;16:734.

29. Bouscasse H, Gabet S, Kerneis G, Provent A, Rieux C, Ben Salem N, Dupont H, Troude F, Mathy S, Slama R. Designing local air pollution policies focusing on mobility and heating to avoid a targeted number of pollution-related deaths: Forward and backward approaches combining air pollution modeling, health impact assessment and cost-benefit analysis. Environ Int. 2022;159:107030.

30. Zeng Z, Cook AR, Chen JI, van der Eijk Y. Evaluating the public health impact of partial and full Tobacco flavour bans: a simulation study. Lancet Reg Health West Pac. 2022;21:100414.

31. Martínez-Solanas É, Quijal-Zamorano M, Achebak H, Petrova D, Robine JM, Herrmann FR, Rodó X, Ballester J. Projections of temperature-attributable mortality in Europe: a time series analysis of 147 contiguous regions in 16 countries. Lancet Planet Health. 2021;5(7):e446-454.

32. Pearl J, Glymour M, Jewell NP. Causal inference in statistics: a primer. Chichester: John Wiley & Sons Ltd; 2016. p. 1 online resource.

33. Hernan MA, Robins JM. Causal inference: what if. Boca Raton: Chapman & Hall/CRC; 2020.

34. Morelli X, Rieux C, Cyrys J, Forsberg B, Slama R. Air pollution, health and social deprivation: a fine-scale risk assessment. Environ Res. 2016;147:59–70.

35. Pascal M, Corso M, Chanel O, Declercq C, Badaloni C, Cesaroni G, Henschel S, Meister K, Haluza D, Martin-Olmedo P, et al. Aphekom - assessing the public health impacts of urban air pollution in 25 European cities: results of the Aphekom project. Sci Total Environ. 2013;449:390–400.

36. Mueller N, Rojas-Rueda D, Basagana X, Cirach M, Cole-Hunter T, Dadvand P, Donaire-Gonzalez D, Foraster M, Gascon M, Martinez D, et al. Urban and transport planning related exposures and mortality: a health impact assessment for cities. Environ Health Perspect. 2017;125(1):89–96.

37. van Dijk A, Slaper H, den Outer PN, Morgenstern O, Braesicke P, Pyle JA, Garny H, Stenke A, Dameris M, Kazantzidis A, et al. Skin cancer risks avoided by the Montreal protocol–worldwide modeling integrating coupled climate-chemistry models with a risk model for UV. Photochem Photobiol. 2013;89(1):234–46.

38. Dimick JB, Ryan AM. Methods for evaluating changes in health care policy: the difference-in-differences approach. JAMA. 2014;312(22):2401–2.

39. Petkova EP, Gasparrini A, Kinney PL. Heat and mortality in New York City since the beginning of the 20th century. Epidemiology. 2014;25(4):554–60.

40. Morelli X, Gabet S, Rieux C, Bouscasse H, Mathy S, Slama R. Which decreases in air pollution should be targeted to bring health and economic benefits and improve environmental justice? Environ Int. 2019;129:538–50.

41. What are the WHO air quality guidelines? https://www.who.int/newsroom/feature-stories/detail/what-are-the-who-air-quality-guidelines.

42. Rothman KJ, Gallacher JE, Hatch EE. Why representativeness should be avoided. Int J Epidemiol. 2013;42(4):1012–4.

43. Nieuwenhuijsen M, Paustenbach D, Duarte-Davidson R. New developments in exposure assessment: the impact on the practice of health risk assessment and epidemiological studies. Environ Int. 2006;32(8):996–1009.

44. Heinrich J, Gehring U, Cyrys J, Brauer M, Hoek G, Fischer P, Bellander T, Brunekreef B. Exposure to traffic related air pollutants: self reported traffic intensity versus GIS modelled exposure. Occup Environ Med. 2005;62(8):517–23.

45. Traore T, Forhan A, Sirot V, Kadawathagedara M, Heude B, Hulin M, de Lauzon-Guillain B, Botton J, Charles MA, Crepet A. To which mixtures are French pregnant women mainly exposed? A combination of the second French total diet study with the EDEN and ELFE cohort studies. Food Chem Toxicol. 2018;111:310–28.

46. Villanueva CM, Cantor KP, Grimalt JO, Malats N, Silverman D, Tardon A, Garcia-Closas R, Serra C, Carrato A, Castano-Vinyals G, et al. Bladder cancer and exposure to water disinfection by-products through ingestion, bathing, showering, and swimming in pools. Am J Epidemiol. 2007;165(2):148–56.

47. Ouidir M, Giorgis-Allemand L, Lyon-Caen S, Morelli X, Cracowski C, Pontet S, Pin I, Lepeule J, Siroux V, Slama R. Estimation of exposure to atmospheric pollutants during pregnancy integrating space-time activity and indoor air levels: does it make a difference? Environ Int. 2015;84:161–73.

48. Woodward H, Schroeder A, de Nazelle A, Pain CC, Stettler MEJ, ApSimon H, Robins A, Linden PF. Do we need high temporal resolution modelling of exposure in urban areas? A test case. Sci Total Environ. 2023;885:163711.

49. de Hoogh K, Korek M, Vienneau D, Keuken M, Kukkonen J, Nieuwenhuijsen MJ, Badaloni C, Beelen R, Bolignano A, Cesaroni G, et al. Comparing land use regression and dispersion modelling to assess residential exposure to ambient air pollution for epidemiological studies. Environ Int. 2014;73:382–92.

50. Sellier Y, Galineau J, Hulin A, Caini F, Marquis N, Navel V, Bottagisi S, Giorgis-Allemand L, Jacquier C, Slama R, et al. Health effects of ambient air pollution: do different methods for estimating exposure lead to different resifts? Environ Int. 2014;66:165–73.

51. Kulhánová I, Morelli X, Le Tertre A, Loomis D, Charbotel B, Medina S, Ormsby J-N, Lepeule J, Slama R, Soerjomataram I. The fraction of lung cancer incidence attributable to fine particulate air pollution in France: impact of spatial resolution of air pollution models. Environ Int. 2018;121:1079–86.

52. Raaschou-Nielsen O, Andersen ZJ, Beelen R, Samoli E, Stafoggia M, Weinmayr G, Hoffmann B, Fischer P, Nieuwenhuijsen MJ, Brunekreef B, et al. Air pollution and lung cancer incidence in 17 European cohorts: prospective analyses from the European Study of Cohorts for Air Pollution Effects (ESCAPE). Lancet Oncol. 2013;14(9):813–22.

53. Hamra GB, Guha N, Cohen A, Laden F, Raaschou-Nielsen O, Samet JM, Vineis P, Forastiere F, Saldiva P, Yorifuji T, et al. Outdoor particulate matter exposure and lung cancer: a systematic review and meta-analysis. Environ Health Perspect. 2014;122(9):906–11.

54. Nieuwenhuijsen MJ, Donaire-Gonzalez D, Foraster M, Martinez D, Cisneros A. Using personal sensors to assess the exposome and acute health effects. Int J Environ Res Public Health. 2014;11(8):7805–19.

55. Brunekreef B, Noy D, Clausing P. Variability of exposure measurements in environmental epidemiology. Am J Epidemiol. 1987;125(5):892–8.

56. Avery CL, Mills KT, Williams R, McGraw KA, Poole C, Smith RL, Whitsel EA. Estimating error in using ambient PM2.5 concentrations as proxies for personal exposures: a review. Epidemiology. 2010;21(2):215–23.

57. Avery CL, Mills KT, Williams R, McGraw KA, Poole C, Smith RL, Whitsel EA. Estimating error in using residential outdoor PM2.5 concentrations as proxies for personal exposures: a meta-analysis. Environ Health Perspect. 2010;118(5):673–8.

58. Nethery E. From measures to models: predicting exposure to air pollution among pregnant women. MSc. Vancouver: The University of British Columbia; 2007.

59. Ballesta PP, Field RA, Connolly R, Cao N, Baeza Caracena A, De Saeger E. Population exposure to benzene: one day cross-sections in six European cities. Atmospheric Environ. 2006;40(18):3355–66.
21. Nieuwenhuijsen MJ, Khreis H, Verlinghieri E, Mueller N, Rojas-Rueda D. Participatory quantitative health impact assessment of urban and transport planning in cities: a review and research needs. Environ Int. 2017;103:61–72.

22. Brown SL. Quantitative risk assessment of environmental hazards. Annu Rev Public Health. 1985;6:247–67.

23. Goldstein BD. Advances in risk assessment and communication. Annu Rev Public Health. 2005;26:141–63.

24. Grant MJ, Booth A. A typology of reviews: an analysis of 14 review types and associated methodologies. Health Info Libr J. 2009;26(2):91–108.

25. Health impact assessment (HIA) tools and methods. https://www.who.int/tools/health-impact-assessments.

26. Kunzli N, Kaiser R, Medina S, Studnicka M, Chanel O, Filliger P,erry M, Horak F Jr, Puybonnieux-Texier V, Quenel P, et al. Public-health impact of outdoor and traffic-related air pollution: a European assessment. Lancet. 2000;356(9232):795–801.

27. Barboza EP, Cirach M, Khomenko S, lungman T, Mueller N, Barrera-Gomez J, Rojas-Rueda D, Kondo M, Nieuwenhuijsen M. Green space and mortality in European cities: a health impact assessment study. Lancet Planet Health. 2021;5(10):e718-730.

28. Lhachimi SK, Nusselder WJ, Smit HA, Baili P, Bennett K, Fernandez E, Kulik MC, Lobstein T, Pomerleau J, Boshuizen HC, et al. Potential health gains and health losses in eleven EU countries attainable through feasible prevalences of the life-style related risk factors alcohol, BMI, and smoking: a quantitative health impact assessment. BMC Public Health. 2016;16:734.

29. Bouscasse H, Gabet S, Kerneis G, Provent A, Rieux C, Ben Salem N, Dupont H, Troude F, Mathy S, Slama R. Designing local air pollution policies focusing on mobility and heating to avoid a targeted number of pollution-related deaths: Forward and backward approaches combining air pollution modeling, health impact assessment and cost-benefit analysis. Environ Int. 2022;159:107030.

30. Zeng Z, Cook AR, Chen JI, van der Eijk Y. Evaluating the public health impact of partial and full Tobacco flavour bans: a simulation study. Lancet Reg Health West Pac. 2022;21:100414.

31. Martínez-Solanas É, Quijal-Zamorano M, Achebak H, Petrova D, Robine JM, Herrmann FR, Rodó X, Ballester J. Projections of temperature-attributable mortality in Europe: a time series analysis of 147 contiguous regions in 16 countries. Lancet Planet Health. 2021;5(7):e446-454.

32. Pearl J, Glymour M, Jewell NP. Causal inference in statistics: a primer. Chichester: John Wiley & Sons Ltd; 2016. p. 1 online resource.

33. Hernan MA, Robins JM. Causal inference: what if. Boca Raton: Chapman & Hall/CRC; 2020.

34. Morelli X, Rieux C, Cyrys J, Forsberg B, Slama R. Air pollution, health and social deprivation: a fine-scale risk assessment. Environ Res. 2016;147:59–70.

35. Pascal M, Corso M, Chanel O, Declercq C, Badaloni C, Cesaroni G, Henschel S, Meister K, Haluza D, Martin-Olmedo P, et al. Aphekom - assessing the public health impacts of urban air pollution in 25 European cities: results of the Aphekom project. Sci Total Environ. 2013;449:390–400.

36. Mueller N, Rojas-Rueda D, Basagana X, Cirach M, Cole-Hunter T, Dadvand P, Donaire-Gonzalez D, Foraster M, Gascon M, Martinez D, et al. Urban and transport planning related exposures and mortality: a health impact assessment for cities. Environ Health Perspect. 2017;125(1):89–96.

37. van Dijk A, Slaper H, den Outer PN, Morgenstern O, Braesicke P, Pyle JA, Garny H, Stenke A, Dameris M, Kazantzidis A, et al. Skin cancer risks avoided by the Montreal protocol–worldwide modeling integrating coupled climate-chemistry models with a risk model for UV. Photochem Photobiol. 2013;89(1):234–46.

38. Dimick JB, Ryan AM. Methods for evaluating changes in health care policy: the difference-in-differences approach. JAMA. 2014;312(22):2401–2.

39. Petkova EP, Gasparrini A, Kinney PL. Heat and mortality in New York City since the beginning of the 20th century. Epidemiology. 2014;25(4):554–60.

40. Morelli X, Gabet S, Rieux C, Bouscasse H, Mathy S, Slama R. Which decreases in air pollution should be targeted to bring health and economic benefits and improve environmental justice? Environ Int. 2019;129:538–50.

41. What are the WHO air quality guidelines? https://www.who.int/newsroom/feature-stories/detail/what-are-the-who-air-quality-guidelines.

42. Rothman KJ, Gallacher JE, Hatch EE. Why representativeness should be avoided. Int J Epidemiol. 2013;42(4):1012–4.

43. Nieuwenhuijsen M, Paustenbach D, Duarte-Davidson R. New developments in exposure assessment: the impact on the practice of health risk assessment and epidemiological studies. Environ Int. 2006;32(8):996–1009.

44. Heinrich J, Gehring U, Cyrys J, Brauer M, Hoek G, Fischer P, Bellander T, Brunekreef B. Exposure to traffic related air pollutants: self reported traffic intensity versus GIS modelled exposure. Occup Environ Med. 2005;62(8):517–23.

45. Traore T, Forhan A, Sirot V, Kadawathagedara M, Heude B, Hulin M, de Lauzon-Guillain B, Botton J, Charles MA, Crepet A. To which mixtures are French pregnant women mainly exposed? A combination of the second French total diet study with the EDEN and ELFE cohort studies. Food Chem Toxicol. 2018;111:310–28.

46. Villanueva CM, Cantor KP, Grimalt JO, Malats N, Silverman D, Tardon A, Garcia-Closas R, Serra C, Carrato A, Castano-Vinyals G, et al. Bladder cancer and exposure to water disinfection by-products through ingestion, bathing, showering, and swimming in pools. Am J Epidemiol. 2007;165(2):148–56.

47. Ouidir M, Giorgis-Allemand L, Lyon-Caen S, Morelli X, Cracowski C, Pontet S, Pin I, Lepeule J, Siroux V, Slama R. Estimation of exposure to atmospheric pollutants during pregnancy integrating space-time activity and indoor air levels: does it make a difference? Environ Int. 2015;84:161–73.

48. Woodward H, Schroeder A, de Nazelle A, Pain CC, Stettler MEJ, ApSimon H, Robins A, Linden PF. Do we need high temporal resolution modelling of exposure in urban areas? A test case. Sci Total Environ. 2023;885:163711.

49. de Hoogh K, Korek M, Vienneau D, Keuken M, Kukkonen J, Nieuwenhuijsen MJ, Badaloni C, Beelen R, Bolignano A, Cesaroni G, et al. Comparing land use regression and dispersion modelling to assess residential exposure to ambient air pollution for epidemiological studies. Environ Int. 2014;73:382–92.

50. Sellier Y, Galineau J, Hulin A, Caini F, Marquis N, Navel V, Bottagisi S, Giorgis-Allemand L, Jacquier C, Slama R, et al. Health effects of ambient air pollution: do different methods for estimating exposure lead to different resifts? Environ Int. 2014;66:165–73.

51. Kulhánová I, Morelli X, Le Tertre A, Loomis D, Charbotel B, Medina S, Ormsby J-N, Lepeule J, Slama R, Soerjomataram I. The fraction of lung cancer incidence attributable to fine particulate air pollution in France: impact of spatial resolution of air pollution models. Environ Int. 2018;121:1079–86.

52. Raaschou-Nielsen O, Andersen ZJ, Beelen R, Samoli E, Stafoggia M, Weinmayr G, Hoffmann B, Fischer P, Nieuwenhuijsen MJ, Brunekreef B, et al. Air pollution and lung cancer incidence in 17 European cohorts: prospective analyses from the European Study of Cohorts for Air Pollution Effects (ESCAPE). Lancet Oncol. 2013;14(9):813–22.

53. Hamra GB, Guha N, Cohen A, Laden F, Raaschou-Nielsen O, Samet JM, Vineis P, Forastiere F, Saldiva P, Yorifuji T, et al. Outdoor particulate matter exposure and lung cancer: a systematic review and meta-analysis. Environ Health Perspect. 2014;122(9):906–11.

54. Nieuwenhuijsen MJ, Donaire-Gonzalez D, Foraster M, Martinez D, Cisneros A. Using personal sensors to assess the exposome and acute health effects. Int J Environ Res Public Health. 2014;11(8):7805–19.

55. Brunekreef B, Noy D, Clausing P. Variability of exposure measurements in environmental epidemiology. Am J Epidemiol. 1987;125(5):892–8.

56. Avery CL, Mills KT, Williams R, McGraw KA, Poole C, Smith RL, Whitsel EA. Estimating error in using ambient PM2.5 concentrations as proxies for personal exposures: a review. Epidemiology. 2010;21(2):215–23.

57. Avery CL, Mills KT, Williams R, McGraw KA, Poole C, Smith RL, Whitsel EA. Estimating error in using residential outdoor PM2.5 concentrations as proxies for personal exposures: a meta-analysis. Environ Health Perspect. 2010;118(5):673–8.

58. Nethery E. From measures to models: predicting exposure to air pollution among pregnant women. MSc. Vancouver: The University of British Columbia; 2007.

59. Ballesta PP, Field RA, Connolly R, Cao N, Baeza Caracena A, De Saeger E. Population exposure to benzene: one day cross-sections in six European cities. Atmospheric Environ. 2006;40(18):3355–66.
60. Slama R, Thiebaugeorges O, Goua V, Aussel L, Sacco P, Bohet A, Forhan A, Ducot B, Annesi-Maesano I, Heinrich J, et al. Maternal personal exposure to airborne benzene and intrauterine growth. *Environ Health Perspect.* 2009;117(8):1313–21.

61. Li C, Li Q, Tong D, Wang Q, Wu M, Sun B, Su G, Tan L. Environmental impact and health risk assessment of volatile organic compound emissions during different seasons in Beijing. *J Environ Sci (China)*. 2020;93:1–12.

62. Zhang R, Smit AK, Espinoza D, Allen M, Reyes-Marcelino G, Kimlin MG, Lo SN, Sharman AR, Law MH, Kanetsky PA, et al. Validation of self-reported sun exposure against electronic ultraviolet radiation dosimeters. *Int J Epidemiol.* 2022;52(1):324–8.

63. Kreuzer M, Heinrich J, Wolke G, Schaffrath Rosario A, Gerken M, Wellmann J, Keller G, Kreienbrock L, Wichmann HE. Residential radon and risk of lung cancer in Eastern Germany. *Epidemiology*. 2003;14(5):559–68.

64. Jacobs N, Roberts B, Reamer H, Mathis C, Gaffney S, Neitzel R. Noise exposures in different community settings measured by traditional dosimeter and smartphone app. *Appl Acoust.* 2020;167:107408.

65. Woodruff TJ, Zota AR, Schwartz JM. Environmental chemicals in pregnant women in the United States: NHANES 2003–2004. *Environ Health Perspect.* 2011;119(6):878–85.

66. Calafat AM, Ye X, Silva MJ, Kuklenyik Z, Needham LL. Human exposure assessment to environmental chemicals using biomonitoring. *Int J Androl.* 2006;29(1):166–71 discussion 181–165.

67. Dereumeaux C, Fillol C, Charles MA, Denys S. The French human biomonitoring program: first lessons from the perinatal component and future needs. *Int J Hyg Environ Health.* 2017;220(2 Pt A):64–70.

68. Haug LS, Sakhi AK, Cequier E, Casas M, Maitre L, Basagana X, Andrusaityte S, Chalkiadaki G, Chatzi L, Coen M, et al. In-utero and childhood chemical exposome in six European mother-child cohorts. *Environ Int.* 2018;121(Pt 1):751–63.

69. Weisskopf MG, Webster TF. Trade-offs of personal versus more proxy exposure measures in environmental epidemiology. *Epidemiology*. 2017;28(5):635–43.

70. Perrier F, Giorgis-Allemand L, Slama R, Philippat C. Within-subject pooling of biological samples to reduce exposure misclassification in biomarker-based studies. *Epidemiology*. 2016;27(3):378–88.

71. Flora G, Gupta D, Tiwari A. Toxicity of lead: a review with recent updates. *Interdiscip Toxicol.* 2012;5(2):47–58.

72. Hardy A, Benford D, Halddorsson T, Jeger MJ, Knutsen HK, More S, Naegeli H, Noteborn D, Ockleford C, Ricci A, et al. Guidance on the use of the weight of evidence approach in scientific assessments. *EFSA J. 2017;15(8):e04971*.

73. Martin P, Bladier C, Meek B, Bruyere O, Feinblatt E, Touvier M, Watier L, Makowski D. Weight of evidence for hazard identification: a critical review of the literature. *Environ Health Perspect.* 2018;126(7):076001.

74. National Research Council. Review of EPA's Integrated Risk Information System (IRIS) process. Washington, D.C.: National Academies Press; 2014.

75. Trasande L, Zoeller RT, Hass U, Kortenkamp A, Grandjean P, Myers JP, DiGangi J, Bellanger M, Hauser R, Legler J, et al. Estimating burden and disease costs of exposure to endocrine-disrupting chemicals in the European union. *J Clin Endocrinol Metab.* 2015;100(4):1245–55.

76. Hansen SF, von Krayer MP, Tickner JA. Categorizing mistaken false positives in regulation of human and environmental health. *Risk Anal.* 2007;27(1):255–69.

77. Grandjean P. Science for precautionary decision-making. In: Late lessons from early warnings: science, precaution, innovation. Edited by Gee D et al. Copenhagen: Published by European environment agency (EEA); 2013. p. 623–642. https://www.eea.europa.eu/publications/late-lesso ns-2.

78. Pedeli X, Hoek G, Katsouyanni K. Risk assessment of diesel exhaust and lung cancer: combining human and animal studies after adjustment for biases in epidemiological studies. *Environ Health.* 2011;10:30.

79. Malmqvist E, Oudin A, Pascal M, Medina S. Choices behind numbers: a review of the major air pollution health impact assessments in Europe. *Curr Environ Health Rep.* 2018;5(1):34–43.

80. Heid IM, Kuchenhoff H, Miles J, Kreienbrock L, Wichmann HE. Two dimensions of measurement error: classical and Berkson error in residential radon exposure assessment. *J Expo Anal Environ Epidemiol.* 2004;14(5):365–77.

81. Lee IM, Skerrett PJ. Physical activity and all-cause mortality: what is the dose-response relation? *Med Sci Sports Exerc.* 2001;33(Supplement):S459–71.

82. Woodcock J, Franco OH, Orsini N, Roberts I. Non-vigorous physical activity and all-cause mortality: systematic review and meta-analysis of cohort studies. *Int J Epidemiol.* 2011;40(1):121–38.

83. Pope CA 3rd, Cropper M, Coggins J, Cohen A. Health benefits of air pollution abatement policy: role of the shape of the concentration-response function. *J Air Waste Manag Assoc.* 2015;65(5):516–22.

84. Vandenberg LN, Colborn T, Hayes TB, Heindel JJ, Jacobs DR Jr, Lee DH, Shioda T, Soto AM, vom Saal FS, Welshons WV, et al. Hormones and endocrine-disrupting chemicals: low-dose effects and nonmonotonic dose responses. *Endocr Rev.* 2012;33(3):378–455.

85. Burnett R, Chen H, Szyszkowicz M, Fann N, Hubbell B, Pope CA, Apte JS, Brauer M, Cohen A, Weichenthal S, et al. Global estimates of mortality associated with long-term exposure to outdoor fine particulate matter. *Proc Natl Acad Sci. 2018;115(38):9592–7*.

86. Gasparrini A, Guo Y, Hashizume M, Lavigne E, Zanobetti A, Schwartz J, Tobias A, Tong S, Rocklöv J, Forsberg B, et al. Mortality risk attributable to high and low ambient temperature: a multicountry observational study. *Lancet.* 2015;386(9991):369–75.

87. Sattelmair J, Pertman J, Ding EL, Kohl HW 3rd, Haskell W, Lee IM. Dose response between physical activity and risk of coronary heart disease: a meta-analysis. *Circulation.* 2011;124(7):789–95.

88. Slob W. Benchmark dose and the three rs. Part I. getting more information from the same number of animals. *Crit Rev Toxicol.* 2014;44(7):557–67.

89. COMEAP. The mortality effects of long-term exposure to particulate air pollution in the United Kingdom. In: COMEAP (Committee on the medical effects of air pollutants). 2010. p. 98.

90. Mueller N, Anderle R, Brachowicz N, Graziadei H, Lloyd SJ, de Sampaio Morais G, Sironi AP, Gibert K, Tonne C, Nieuwenhuijsen M, et al. Model choice for quantitative health impact assessment and modelling: an expert consultation and narrative literature review. *Int J Health Policy Manag.* 2023;12:7103.

91. Di Domenico L, Pullano G, Sabbatini CE, Boelle PY, Colizza V. Modeling safe protocols for reopening schools during the COVID-19 pandemic in France. *Nat Commun.* 2021;12(1):1073.

92. Pearl J. On the interpretation of do(x). *J Causal Inference.* 2019;7(1):20190202.

93. Berry G. The analysis of mortality by the subject-years method. *Biometrics.* 1983;39(1):173–84.

94. Rothman KJ, Greenland S, Lash TL. Modern epidemiology. 3rd ed. Philadelphia: Lippincott Williams & Wilkins; 2008.

95. Escher B, Braun G, Zarfl C. Exploring the concepts of concentration addition and independent action using a linear low-effect mixture model. *Environ Toxicol Chem.* 2020;39(12):2552–9.

96. Ezzati M, Vander Hoorn S, Rodgers A, Lopez AD, Mathers CD, Murray CJL. Estimates of global and regional potentil health gains from reducing multiple major risk factors. *Lancet.* 2003;362(9380):271–80.

97. Tamayo-Uria I, Maitre L, Thomsen C, Nieuwenhuijsen MJ, Chatzi L, Siroux V, Aasvang GM, Agier L, Andrusaityte S, Casas M, et al. The early-life exposome: description and patterns in six European countries. *Environ Int.* 2019;123:189–200.

98. VanderWeele TJ. Mediation analysis: a practitioner's guide. Annu Rev Public Health. 2016;37(1):17–32.

99. Ready R, Navrud S, Day B, Dubourg R, Machado F, Mourato S, Spanninks F, Vazquez Rodriquez MX. Benefit transfer in Europe: how reliable are transfers between countries? *Environ Resour Econ.* 2004;29:67–82.

100. Chilton S, Covey J, Jones-Lee M, Loomes G, Metcalf H. Valuation of health benefits associated with reductions in air pollution. London: DEFRA; 2004.

101. Cropper M, Hammitt JK, Robinson LA. Valuing mortality risk reductions: progress and challenges. *Annu Rev Resource Econ.* 2011;3(1):313–36.

102. Dekker T, Brouwer R, Hofkes M, Moeltner K. The effect of risk context on the value of a statistical life: a Bayesian meta-model. *Environ Resour Econ.* 2011;49(4):597–624.

103. Aven T. Risk assessment and risk management: review of recent advances on their foundation. *Eur J Oper Res.* 2016;253(1):1–13.
60. Slama R, Thiebaugeorges O, Goua V, Aussel L, Sacco P, Bohet A, Forhan A, Ducot B, Annesi-Maesano I, Heinrich J, et al. Maternal personal exposure to airborne benzene and intrauterine growth. *Environ Health Perspect.* 2009;117(8):1313–21.

61. Li C, Li Q, Tong D, Wang Q, Wu M, Sun B, Su G, Tan L. Environmental impact and health risk assessment of volatile organic compound emissions during different seasons in Beijing. *J Environ Sci (China)*. 2020;93:1–12.

62. Zhang R, Smit AK, Espinoza D, Allen M, Reyes-Marcelino G, Kimlin MG, Lo SN, Sharman AR, Law MH, Kanetsky PA, et al. Validation of self-reported sun exposure against electronic ultraviolet radiation dosimeters. *Int J Epidemiol.* 2022;52(1):324–8.

63. Kreuzer M, Heinrich J, Wolke G, Schaffrath Rosario A, Gerken M, Wellmann J, Keller G, Kreienbrock L, Wichmann HE. Residential radon and risk of lung cancer in Eastern Germany. *Epidemiology*. 2003;14(5):559–68.

64. Jacobs N, Roberts B, Reamer H, Mathis C, Gaffney S, Neitzel R. Noise exposures in different community settings measured by traditional dosimeter and smartphone app. *Appl Acoust.* 2020;167:107408.

65. Woodruff TJ, Zota AR, Schwartz JM. Environmental chemicals in pregnant women in the United States: NHANES 2003–2004. *Environ Health Perspect.* 2011;119(6):878–85.

66. Calafat AM, Ye X, Silva MJ, Kuklenyik Z, Needham LL. Human exposure assessment to environmental chemicals using biomonitoring. *Int J Androl.* 2006;29(1):166–71 discussion 181–165.

67. Dereumeaux C, Fillol C, Charles MA, Denys S. The French human biomonitoring program: first lessons from the perinatal component and future needs. *Int J Hyg Environ Health.* 2017;220(2 Pt A):64–70.

68. Haug LS, Sakhi AK, Cequier E, Casas M, Maitre L, Basagana X, Andrussaitye S, Chalkiadaki G, Chatzi L, Coen M, et al. In-utero and childhood chemical exposome in six European mother-child cohorts. *Environ Int.* 2018;121(Pt 1):751–63.

69. Weisskopf MG, Webster TF. Trade-offs of personal versus more proxy exposure measures in environmental epidemiology. *Epidemiology*. 2017;28(5):635–43.

70. Perrier F, Giorgis-Allemand L, Slama R, Philippat C. Within-subject pooling of biological samples to reduce exposure misclassification in biomarker-based studies. *Epidemiology*. 2016;27(3):378–88.

71. Flora G, Gupta D, Tiwari A. Toxicity of lead: a review with recent updates. *Interdiscip Toxicol.* 2012;5(2):47–58.

72. Hardy A, Benford D, Halddorsson T, Jeger MJ, Knutsen HK, More S, Naegeli H, Noteborn D, Ockleford C, Ricci A, et al. Guidance on the use of the weight of evidence approach in scientific assessments. *EFSA J. 2017;15(8):e04971*.

73. Martin P, Bladier C, Meek B, Bruyere O, Feinblatt E, Touvier M, Watier L, Makowski D. Weight of evidence for hazard identification: a critical review of the literature. *Environ Health Perspect.* 2018;126(7):076001.

74. National Research Council. Review of EPA's Integrated Risk Information System (IRIS) process. Washington, D.C.: National Academies Press; 2014.

75. Trasande L, Zoeller RT, Hass U, Kortenkamp A, Grandjean P, Myers JP, DiGangi J, Bellanger M, Hauser R, Legler J, et al. Estimating burden and disease costs of exposure to endocrine-disrupting chemicals in the European union. *J Clin Endocrinol Metab.* 2015;100(4):1245–55.

76. Hansen SF, von Krayer MP, Tickner JA. Categorizing mistaken false positives in regulation of human and environmental health. *Risk Anal.* 2007;27(1):255–69.

77. Grandjean P. Science for precautionary decision-making. In: Late lessons from early warnings: science, precaution, innovation. Edited by Gee D et al. Copenhagen: Published by European environment agency (EEA); 2013. p. 623–642. https://www.eea.europa.eu/publications/late-lesso ns-2.

78. Pedeli X, Hoek G, Katsouyanni K. Risk assessment of diesel exhaust and lung cancer: combining human and animal studies after adjustment for biases in epidemiological studies. *Environ Health.* 2011;10:30.

79. Malmqvist E, Oudin A, Pascal M, Medina S. Choices behind numbers: a review of the major air pollution health impact assessments in Europe. *Curr Environ Health Rep.* 2018;5(1):34–43.

80. Heid IM, Kuchenhoff H, Miles J, Kreienbrock L, Wichmann HE. Two dimensions of measurement error: classical and Berkson error in residential radon exposure assessment. *J Expo Anal Environ Epidemiol.* 2004;14(5):365–77.

81. Lee IM, Skerrett PJ. Physical activity and all-cause mortality: what is the dose-response relation? *Med Sci Sports Exerc.* 2001;33(Supplement):S459–71.

82. Woodcock J, Franco OH, Orsini N, Roberts I. Non-vigorous physical activity and all-cause mortality: systematic review and meta-analysis of cohort studies. *Int J Epidemiol.* 2011;40(1):121–38.

83. Pope CA 3rd, Cropper M, Coggins J, Cohen A. Health benefits of air pollution abatement policy: role of the shape of the concentration-response function. *J Air Waste Manag Assoc.* 2015;65(5):516–22.

84. Vandenberg LN, Colborn T, Hayes TB, Heindel JJ, Jacobs DR Jr, Lee DH, Shioda T, Soto AM, vom Saal FS, Welshons WV, et al. Hormones and endocrine-disrupting chemicals: low-dose effects and nonmonotonic dose responses. *Endocr Rev.* 2012;33(3):378–455.

85. Burnett R, Chen H, Szyszkowicz M, Fann N, Hubbell B, Pope CA, Apte JS, Brauer M, Cohen A, Weichenthal S, et al. Global estimates of mortality associated with long-term exposure to outdoor fine particulate matter. *Proc Natl Acad Sci. 2018;115(38):9592–7*.

86. Gasparrini A, Guo Y, Hashizume M, Lavigne E, Zanobetti A, Schwartz J, Tobias A, Tong S, Rocklöv J, Forsberg B, et al. Mortality risk attributable to high and low ambient temperature: a multicountry observational study. *Lancet.* 2015;386(9991):369–75.

87. Sattelmair J, Pertman J, Ding EL, Kohl HW 3rd, Haskell W, Lee IM. Dose response between physical activity and risk of coronary heart disease: a meta-analysis. *Circulation.* 2011;124(7):789–95.

88. Slob W. Benchmark dose and the three rs. Part I. getting more information from the same number of animals. *Crit Rev Toxicol.* 2014;44(7):557–67.

89. COMEAP. The mortality effects of long-term exposure to particulate air pollution in the United Kingdom. In: COMEAP (Committee on the medical effects of air pollutants). 2010. p. 98.

90. Mueller N, Anderle R, Brachowicz N, Graziadei H, Lloyd SJ, de Sampaio Morais G, Sironi AP, Gibert K, Tonne C, Nieuwenhuijsen M, et al. Model choice for quantitative health impact assessment and modelling: an expert consultation and narrative literature review. *Int J Health Policy Manag.* 2023;12:7103.

91. Di Domenico L, Pullano G, Sabbatini CE, Boelle PY, Colizza V. Modeling safe protocols for reopening schools during the COVID-19 pandemic in France. *Nat Commun.* 2021;12(1):1073.

92. Pearl J. On the interpretation of do(x). *J Causal Inference.* 2019;7(1):20190202.

93. Berry G. The analysis of mortality by the subject-years method. *Biometrics.* 1983;39(1):173–84.

94. Rothman KJ, Greenland S, Lash TL. Modern epidemiology. 3rd ed. Philadelphia: Lippincott Williams & Wilkins; 2008.

95. Escher B, Braun G, Zarfl C. Exploring the concepts of concentration addition and independent action using a linear low-effect mixture model. *Environ Toxicol Chem.* 2020;39(12):2552–9.

96. Ezzati M, Vander Hoorn S, Rodgers A, Lopez AD, Mathers CD, Murray CJL. Estimates of global and regional potentil health gains from reducing multiple major risk factors. *Lancet.* 2003;362(9380):271–80.

97. Tamayo-Uria I, Maitre L, Thomsen C, Nieuwenhuijsen MJ, Chatzi L, Siroux V, Aasvang GM, Agier L, Andrusaityte S, Casas M, et al. The early-life exposome: description and patterns in six European countries. *Environ Int.* 2019;123:189–200.

98. VanderWeele TJ. Mediation analysis: a practitioner's guide. Annu Rev Public Health. 2016;37(1):17–32.

99. Ready R, Navrud S, Day B, Dubourg R, Machado F, Mourato S, Spanninks F, Vazquez Rodriquez MX. Benefit transfer in Europe: how reliable are transfers between countries? *Environ Resour Econ.* 2004;29:67–82.

100. Chilton S, Covey J, Jones-Lee M, Loomes G, Metcalf H. Valuation of health benefits associated with reductions in air pollution. London: DEFRA; 2004.

101. Cropper M, Hammitt JK, Robinson LA. Valuing mortality risk reductions: progress and challenges. *Annu Rev Resource Econ.* 2011;3(1):313–36.

102. Dekker T, Brouwer R, Hofkes M, Moeltner K. The effect of risk context on the value of a statistical life: a Bayesian meta-model. *Environ Resour Econ.* 2011;49(4):597–624.

103. Aven T. Risk assessment and risk management: review of recent advances on their foundation. *Eur J Oper Res.* 2016;253(1):1–13.
104. Knol AB, Petersen AC, van der Sluijs JP, Lebret E. Dealing with uncertainties in environmental burden of disease assessment. Environ Health. 2009;8:21.

105. Fox MP, Lash TL. Quantitative bias analysis for study and grant planning. Ann Epidemiol. 2020;43:32-6.

106. Baccini M, Grisotto L, Catelan D, Consonni D, Bertazzi PA, Biggeri A. Commuting-adjusted short-term health impact assessment of airborne fine particles with uncertainty quantification via Monte Carlo simulation. Environ Health Perspect. 2015;123(1):27-33.

107. Burmaster DE, Anderson PD. Principles of good practice for the use of Monte Carlo techniques in human health and ecological risk assessments. Risk Anal. 1994;14(4):477-81.

108. Guo X, Ji J, Khan F, Ding L, Tong Q. A novel fuzzy dynamic Bayesian network for dynamic risk assessment and uncertainty propagation quantification in uncertainty environment. Saf Sci. 2021;141:105285.

109. Hu L, Kang R, Pan X, Zuo D. Uncertainty expression and propagation in the risk assessment of uncertain random system. IEEE Syst J. 2021;15(2):1604-15.

110. Cole BL, MacLeod KE, Spriggs R. Health impact assessment of transportation projects and policies: living up to aims of advancing population health and health equity? Annu Rev Public Health. 2019;40:305-18.

111. Harris-Roxas B, Harris E. Differing forms, differing purposes: a typology of health impact assessment. Environ Impact Assess Rev. 2011;31(4):396-403.

112. Hardy A, Benford D, Halldorsson T, Jeger MJ, Knutsen KH, More S, Mortensen A, Naegeli H, Noteborn H, Ockleford C, et al. Update: use of the benchmark dose approach in risk assessment. EFSA J. 2017;15(1):e04658.

113. Smith KR, Bruce N, Balakrishnan K, Adair-Rohani H, Balmes J, Chafe Z, Dherani M, Hosgood HD, Mehta S, Pope D, et al. Millions dead: how do we know and what does it mean? Methods used in the comparative risk assessment of household air pollution. Annu Rev Public Health. 2014;35:185-206.

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<figure><img src="image_13.png" /></figure>
104. Knol AB, Petersen AC, van der Sluijs JP, Lebret E. Dealing with uncertainties in environmental burden of disease assessment. Environ Health. 2009;8:21.

105. Fox MP, Lash TL. Quantitative bias analysis for study and grant planning. Ann Epidemiol. 2020;43:32–6.

106. Baccini M, Grisotto L, Catelan D, Consonni D, Bertazzi PA, Biggeri A. Commuting-adjusted short-term health impact assessment of airborne fine particles with uncertainty quantification via Monte Carlo simulation. Environ Health Perspect. 2015;123(1):27–33.

107. Burmaster DE, Anderson PD. Principles of good practice for the use of Monte Carlo techniques in human health and ecological risk assessments. Risk Anal. 1994;14(4):477–81.

108. Guo X, Ji J, Khan F, Ding L, Tong Q. A novel fuzzy dynamic Bayesian network for dynamic risk assessment and uncertainty propagation quantification in uncertainty environment. Saf Sci. 2021;141:105285.

109. Hu L, Kang R, Pan X, Zuo D. Uncertainty expression and propagation in the risk assessment of uncertain random system. IEEE Syst J. 2021;15(2):1604–15.

110. Cole BL, MacLeod KE, Spriggs R. Health impact assessment of transportation projects and policies: living up to aims of advancing population health and health equity? Annu Rev Public Health. 2019;40:305–18.

111. Harris-Roxas B, Harris E. Differing forms, differing purposes: a typology of health impact assessment. Environ Impact Assess Rev. 2011;31(4):396–403.

112. Hardy A, Benford D, Halldorsson T, Jeger MJ, Knutsen KH, More S, Mortensen A, Naegeli H, Noteborn H, Ockleford C, et al. Update: use of the benchmark dose approach in risk assessment. EFSA J. 2017;15(1):e04658.

113. Smith KR, Bruce N, Balakrishnan K, Adair-Rohani H, Balmes J, Chafe Z, Dherani M, Hosgood HD, Mehta S, Pope D, et al. Millions dead: how do we know and what does it mean? Methods used in the comparative risk assessment of household air pollution. Annu Rev Public Health. 2014;35:185–206.

**Publisher's Note**

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Ready to submit your research? Choose BMC and benefit from:

* fast, convenient online submission

* thorough peer review by experienced researchers in your field

* rapid publication on acceptance

* support for research data, including large and complex data types

* gold Open Access which fosters wider collaboration and increased citations

* maximum visibility for your research: over 100M website views per year

At BMC, research is always in progress.

Learn more biomedcentral.com/submissions

<figure><img src="image_14.png" /></figure>