Notes on interval estimation of the attributable risk in cross-sectional sampling

The attributable risk (AR) is probably the most useful and commonly used epidemiologic index to measure the importance of a risk factor in public health issues. This paper focuses the discussion on interval estimation of the AR in cross-sectional studies and compares the finite-sample performance of five asymptotic interval estimators of the AR by calculating the coverage probability and the average length in a variety of situations. This paper notes that the coverage probability of the two interval estimators proposed by Leung and Kupper, including the one that combines the interval estimator on the basis of Wald's test statistic, can be substantially less than the desired confidence level when the underlying risk ratio equals 1. As long as the sample size is reasonably large (> or =100) and the probability of exposure is moderate (> or =0.20), the interval estimator suggested by Fleiss can consistently perform well with respect to the coverage probability in a variety of situations considered here. However, using this interval estimator tends to generally lose efficiency. This paper also finds that with respect to the coverage probability, the interval estimator using Fieller's theorem is generally preferable to the interval estimator on the basis of Wald's test statistic when the prevalence rate ratio (RR) between the exposure and the non-exposure groups is > or =2. Finally, this paper notes that if we know that the underlying parameter RR is large (> or =4) and the probability of exposure is not small (> or =0.05), the interval estimator suggested by Leung and Kupper will probably be preferable to all the other estimators considered here.