Article Text

Interval estimation of the attributable risk in case-control studies with matched pairs
1. K-J Lui
1. Department of Mathematical and Computer Sciences, College of Sciences, San Diego State University, San Diego, CA 92182-7720, USA
1. Dr Lui (kjl{at}rohan.sdsu.edu)

## Abstract

OBJECTIVE The attributable risk (AR), which represents the proportion of cases who can be preventable when we completely eliminate a risk factor in a population, is the most commonly used epidemiological index to assess the impact of controlling a selected risk factor on community health. The goal of this paper is to develop and search for good interval estimators of the AR for case-control studies with matched pairs.

METHODS This paper considers five asymptotic interval estimators of the AR, including the interval estimator using Wald's statistic suggested elsewhere, the two interval estimators using the logarithmic transformations: log(x) and log(1–x), the interval estimator using the logit transformation log(x/(1–x)), and the interval estimator derived from a simple quadratic equation developed in this paper. This paper compares the finite sample performance of these five interval estimators by calculation of their coverage probability and average length in a variety of situations.

RESULTS This paper demonstrates that the interval estimator derived from the quadratic equation proposed here can not only consistently perform well with respect to the coverage probability, but also be more efficient than the interval estimator using Wald's statistic in almost all the situations considered here. This paper notes that although the interval estimator using the logarithmic transformation log(1–x) may also perform well with respect to the coverage probability, using this estimator is likely to be less efficient than the interval estimator using Wald's statistic. Finally, this paper notes that when both the underlying odds ratio (OR) and the prevalence of exposure (PE) in the case group are not large (OR ⩽2 and PE ⩽0.10), the application of the two interval estimators using the transformations log(x) and log(x/(1–x)) can be misleading. However, when both the underlying OR and PE in the case group are large (OR ⩾4 and PE ⩾0.50), the interval estimator using the logit transformation can actually outperform all the other estimators considered here in terms of efficiency.

CONCLUSIONS When there is no prior knowledge of the possible range for the underlying OR and PE, the interval estimator derived from the quadratic equation developed here for general use is recommended. When it is known that both the OR and PE in the case group are large (OR ⩾4 and PE ⩾0.50), it is recommended that the interval estimator using the logit transformation is used.

• case-control studies
• attributable risk
• interval estimation

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