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

The attributable risk (AR) is probably the most useful and commonly used ep idemiologic index to measure the importance of a risk factor in public heal th 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 n otes 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 a s the sample size is reasonably large (greater than or equal to 100) and th e probability of exposure is moderate (greater than or equal to0.20), the i nterval estimator suggested by Fleiss can consistently perform well with re spect to the coverage probability in a variety of situations considered her e. However, using this interval estimator tends to generally lose efficienc y. 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 prevalenc e rate ratio (RR) between the exposure and the non-exposure groups is great er than or equal to2. Finally, this paper notes that if we know that the un derlying parameter RR is large (greater than or equal to4) and the probabil ity of exposure is not small (greater than or equal to0.05), the interval e stimator suggested by Leung and Kupper will probably be preferable to all t he other estimators considered here. Copyright (C) 2001 John Wiley & Sons, Ltd.