Using ecological data to estimate a regression model for individual data: the association between arsenic in drinking water and incidence of skin cancer.

In ecologic studies, participants are studied by groups, and the exposure status of each group is usually represented by a single indicator, mostly the mean exposure. In this paper, we propose using multiple variables derived from dummy variables at the individual level to describe the exposure. An analysis of the association between arsenic in drinking water and skin cancer was used as an example. Well water arsenic levels and skin cancer incidence from 1980 to 1987 were assessed for 243 townships in Taiwan. We first analyzed the data using the mean arsenic concentration in each township as the only exposure variable. The second analysis used multiple variables to describe arsenic exposure; each variable denoted the percentage of wells with arsenic levels within a specific range in each township. Although the first approach did not identify associations between arsenic levels and skin cancer, the multiple-variable approach identifies a positive association at the highest arsenic exposure category (>0.64 mg/L) in both men and women. Therefore, using multiple variables to describe an exposure in ecologic studies may facilitate a better description of the exposure status and thereby lead to more accurate risk assessment, especially when the dose-response relationship is not linear.