Arsenic in Drinking Water (1999) / Chapter Skim
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10 Statistical Issues
10 Statistical Issues
Pages 264-298
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From page 264... ...
It also discusses the kind of measurement error that arises in this context and its implication for risk assessment in general, as well as specifically for the analysis of the Tseng data. The fourth section presents some empirical analysis based on cancer mortality data from Taiwan.
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. Q k are elements of the unknown parameter vector q , which needs to be estimated using maximum likelihood.
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From page 266... ...
For animal studies, the 1996 guidelines suggest that the 10% excess risk level will typically provide an appropriate point of departure that can be estimated without significant extrapolation. For epidemiological studies, however, a lower level (1% or 5%)
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The step after model fitting is calculating the exposure concentration that corresponds to a specified excess risk above background. This step is more complicated when an age-adjusted model has been used.
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male drinking water contaminated with arsenic at x µg/L would have the same age-specific cancer risk as a Taiwanese male exposed to 0.45x µg/L. Using this approach, EPA estimated the U.S.
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Ecological studies are most problematic when the groups being analyzed are very heterogeneous. That would be the case, for example, if one were to measure arsenic concentrations for every county in the United States and then try to correlate those concentrations with county-specific cancer rates.
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Besides the potential for confounding, a second concern with ecological studies is the lack of individual exposure assessment. Instead of assigning individual-level exposures, an ecological study assigns individuals to exposure categories based on aggregate exposure concentrations measured for the group to which the individuals belong.
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The error here would correspond to individual departures from the village mean exposure concentrations, due to variations among wells within a village, individual drinking habits, and so forth. If the Berkson measurement-error model applies and the outcome of interest follows a linear model involving the true exposure concentration, then it is well known that fitting the model naively with x i replaced by w i will lead to valid estimates of the regression parameters from this true model, although variances might be incorrectly estimated.
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From page 272... ...
As was the case with the representative exposure concentrations, varying those values is likely to have only a moderate effect on estimated risk levels. The measurement error theory described in this section and the results presented in Table 10-3 suggest a certain robustness of the risk assessment conducted by EPA using the Tseng data.
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From page 273... ...
Although we will also present some dose-response analysis of these data, it is important to emphasize again that the results are not to be interpreted as a formal risk assessment, or as an endorsement of these data for the use of risk assessment for arsenic in drinking water. Rather, we present selected results to illustrate some of the issues that arise in the context of trying to characterize the dose-response relationship of arsenic exposure based on ecological data.
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From page 274... ...
Table 10-5 does not show that, in some cases, arsenic concentrations varied considerably in different wells within the same village (see Addendum)
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From page 275... ...
When the data come in the form of prevalence (the number of subjects alive at various ages and exposure concentrations and the number of those with skin cancer) , then a model, such as the multistage Weibull defined in Equation 3, can be fitted by maximizing the likelihood given in Equation 1.
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From page 276... ...
of dying of cancer at age t for someone exposed to arsenic concentration x. The cause-specific hazard function based on the multistage Weibull model is To simplify calculations, and facilitate use of life tables and death records, age is grouped into 5-year time intervals.
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. The excess lifetime risk of cancer from exposure to concentration x of arsenic in the drinking water can be written as (6)
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Page 278 FIGURE 10-1 Predicted age-specific bladder-cancer incidence rates for males based on the multistage Weibull model.
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Figure 10-2 shows the estimated excess lifetime risks for males of dying from bladder cancer as a function of arsenic concentration in the drinking water. The solid line shows the fitted curve, and the dotted line shows the upper 95% confidence limit, calculated using the nonparametric bootstrap.
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Page 280 FIGURE 10-2 Male bladder-cancer rates per 1,000 people. Estimated excess lifetime risks, based on 1994 U.S. Life Tables (NCHS 1998) for males and females, along with upper 95% confidence limits.
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Page 281 FIGURE 10-3 Male bladder-cancer rates per 1,000 people. Estimated excess lifetime risks, based on 1994 U.S. Life Tables (NCHS 1998) for males and females, along with upper 95% confidence limits; x axis drawn only to 100 ppm (estimated U.S. equivalent for arsenic concentrations)
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From page 282... ...
Excess Lifetime Risk of Male Bladder Cancer (per 1,000) by Arsenic Concentration Village Exclusion Criteria 10 ppb 25 ppb 50 ppb Single well 0.0024 0.0153 0.0612 Multiple wells 0.0037 0.0229 0.0914 Highest five villages 0.0021 0.0130 0.0519 Lowest five villages 0.3244 0.8142 1.6386
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Page 283 Figure 10-4 Dose response for bladder cancer in males. Excess lifetime risks per 1,000 people estimated under different degrees of grouping of arsenic concentrations.
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From page 284... ...
Thus, the fact that grouping does have a strong effect provides evidence of additional measurement error in the arsenic concentrations being assigned at the village level. Other Issues To address the possibility that some of the model sensitivity to grouping and village deletions might be due to the multistage Weibull model, we explored alternatives based on Poisson regression modeling techniques.
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From page 285... ...
Thus, the fact that grouping does have a strong effect provides evidence of additional measurement error in the arsenic concentrations being assigned at the village level. Other Issues To address the possibility that some of the model sensitivity to grouping and village deletions might be due to the multistage Weibull model, we explored alternatives based on Poisson regression modeling techniques.
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From page 286... ...
Under the model that was quadratic in age and linear in dose, the estimated lifetime risks per 1,000 people at 10, 25, and 50 ppb were 0.206, 0.518, and 1.049, respectively. The corresponding upper confidence limits were 0.264, 0.665, and 1.347, respectively.
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Page 287 FIGURE 10-6 Estimated excess lifetime risks of bladder-cancer per 1,000 males based on Poisson regression models.
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. The basic idea in an SMR analysis is to use a large population based on a comparison group to calculate the expected numbers of cancer deaths within different age categories of the study population.
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Once a model has been fitted in this way, then lifetime risks can be calculated using the formulas given in Equations 5 and 6, except that p q (x, t) is now estimated by using the baseline cancer risks taken from the U.S.
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For risk assessments based on epidemiological data, however, a lower point of departure is often warranted because the observable range of effects can go lower in epidemiological studies than animal studies where the numbers are often small. In the case of the bladder-cancer data, a 10% excess lifetime risk is about the level seen at the very highest concentrations of exposure.
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From page 291... ...
The estimated excess lifetime risk at 50 ppb was found to range from about 1 to 5 per 1,000 people, with corresponding upper confidence limits of 3.2 to 7.1. Those results suggest that, although problems exist in using the Tseng data, the conclusions to be drawn about estimated exposure effects are not likely to change too drastically, although the level of uncertainty increases quite a lot because of the issues of grouping and measurement error.
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From page 292... ...
The Poisson modeling yielded estimated risks that were higher than those based on the multistage Weibull model. For example, the estimated risk at 50 ppb was 1.049 per 1,000, with an upper confidence limit of 1.347 per 1,000, or almost 1 excess cancer per 1,000 population.
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From page 293... ...
As presented in Chapter 4, in both the high-exposure regions in Chile and Argentina, the excess numbers of male lung-cancer deaths was in a range of 4 to 5 times that of the excess number of bladder-cancer deaths. Risk estimates for Taiwan have also been reported to be greater for lung cancer than bladder cancer (Smith et al.
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From page 294... ...
Our findings also suggest that additional caution might be needed when exposure concentrations are grouped into broad exposure categories. It is important to keep in mind that the considerable variability in the arsenic concentrations detected in multiple wells within some of the villages leads to considerable uncertainty about exposure concentrations in the Taiwanese data.
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In the case of bladder cancer in males, the Poisson regression analyses yielded fairly consistent results, regardless of whether baseline data were incorporated into the analysis. As an alternative to model-based estimates of risk at low doses, the subcommittee explored methods based on the point-of-departure methods discussed in the 1996 draft EPA guidelines for carcinogen risk assessment.
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Although such data can provide a basis for risk assessment, it is important to keep in mind the potential for bias due to confounding and measurement error. Therefore, the subcommittee recommends that several analyses be conducted to assess the sensitivity of the results to model choice, particular subsets of data, and the way that exposure concentrations are grouped together.
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1992. Cancer potential in liver, lung, bladder and kidney due to ingested inorganic arsenic in drinking water.
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1996. Bladder cancer mortality associated with arsenic in drinking water in Argentina.
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