Environmental and Health Risk Assessment and Management: Principles and Practices

ion and Deduction Inference and Induction Modeled Natural and Artificial Events Model Performance and Evaluation The modeled state of the physical process and its environment: variables, relations and feedbacks, observations on inputs and outputs, time scales, Environmental and Health Risk Assessment and Management 118 Although this process is straightforward, it can often result in incomplete models and conflicting conclusions. Tables 4.1 and 4.2, which contain descriptions of some of the literature on exposure to air pollution and adverse health response, depict the fact that there are different plausible relationships between exposure to air pollution and adverse response. Given these results, increasing the confidence in the results obtained from estimation requires that: 1. The estimated coefficients of the models have the sign that theory demands, provided that theory provides that information a priori (by being based on sound scientific knowledge), 2. The theoretically-relevant independent variables (e.g., age and sex) be included in the relationship, 3. The interval of time (if time is included in the model) separating the values of dependent or independent variables (using lagged values of exposure, for instance: Et-1, rather than Et) must be empirically consistent with biological or other theoretical considerations. The interpretation of the parameter estimates is important for risk assessment and management. If a parameter is positive, then it measures the adverse effect on the dependent variable mortality rate (a is a positive number) per unit increase in the concentration of the pollutant. If it is negative (a is a negative number), the estimate measures the decrease in the value of the dependent variable per unit increase in the concentration. The coefficient can also measure the lack of impact, if it is zero. If the variables in the model are added (additive model), each variable influences the independent variable (response) independently from any of the other variables included in the model. The next example describes a data set that can be used to estimate the parameters of a regression equation. Example 4.3. The risk assessor wants to determine the relationship between exposure to air pollution and lung cancer mortality. She develops a sample of data from 80 major cities from government databases, which provide summaries for a period of one year. This type of data is cross-sectional and the corresponding exposure-response model is also cross-sectional. The sample consists of a yearly average of observations taken for the same periods of time for different cities (same time periods for all the cities in the hypothetical example): City Average daily lung cancer mortality rates (per 100,000) Average daily PM2.5 (μg/m) Average daily SO2 (ppm) . San Miguel 3.5 2.4 5.2 . Civita’ 4.1 3.2 3.4 . This sample is said to be cross-sectional because the measurements are assumed to be unaffected by time. The study is not experimental because the research has no control on the data. Statistical estimation methods, exemplified in Chapter 3, yield numerical values of the coefficients of the exposure-response model, for instance: DR = 120+4.5*SO2+0.02*PM2.5+ . 4 There are doubts about the potential of complex statistical models correctly to obtain forecasts, because relatively simple models can be as good or even superior, to complex models. Chapter 4. Exposure-Response Models for Risk Assessment 119