Radon Epidemiology: Continuous and Categorical Trend Estimators When the Exposure Distribution is Skewed and Outliers May Be Present

Abstract

As other epidemiological exposure variables, indoor radon levels have a right-skewed, approximately lognormal distribution. The continuous linear trend estimator is then known to be sensitive to outlying observations. We consider trend estimators based on replacing the exposure x by a transformed variable z: (1) trimmed estimators, that is, extreme values are deleted in z; (2) winsorized estimators, that is, extreme values are replaced by a lower value; (3) categorical estimators, that is, x is categorized and the continuous variable z takes on scores such as the mean or median within categories. The latter approach is often used in meta-analyses of published odds ratios. Statistically optimal categories can be defined. The corresponding scores are the expected values within the categories, based on the assumption of a lognormal distribution. In a simulation study, it turned out that procedures with different cutpoints for cases and controls, winsorized estimators, and categorical estimators based on category medians can be badly biased upward. Categorical estimators using category means are not always robust against outlying observations. However, categorical estimators employing optimal categories with expected values are nearly unbiased, even in the presence of outliers. Cutpoints should be determined according to the overall distribution of cases and controls combined. Trimmed estimators based on this distribution are unbiased, but highly variable. For right-skewed exposure variables, we therefore suggest sensitivity analyses based on the categorical estimator with optimal cutpoints and expected value scores. In the West German case-control study on indoor radon and lung cancer, these sensitivity analyses lead to increased risk estimates.

We thank all colleagues at the GSF and outside who have helped to collect and prepare the data for the German radon studies, especially Dr. Michael Gerken. Thanks also to the reviewers for their valuable comments. Financial support by BMU (Federal Ministry for the Environment, Nature Conservation and Nuclear Safety), grant StSch 4237.

Notes

We thank all colleagues at the GSF and outside who have helped to collect and prepare the data for the German radon studies, especially Dr. Michael Gerken. Thanks also to the reviewers for their valuable comments. Financial support by BMU (Federal Ministry for the Environment, Nature Conservation and Nuclear Safety), grant StSch 4237.