Estimation of attributable risk for case-control studies with multiple matching

Kuritz and Landis considered case-control studies with multiple matching and proposed an asymptotic interval estimator of the attributable risk based on Wald's statistic. Using Monte Carlo simulation, Kuritz and Landis demonstrated that their interval estimator could perform well when the number of matched sets was large (>or=100). However, the number of matched sets may often be moderate or small in practice. In this paper, we evaluate the performance of Kuritz and Landis' interval estimator in small or moderate number of matched sets and compare it with four other interval estimators. We note that the coverage probability of Kuritz and Landis' interval estimator tends to be less than the desired confidence level when the probability of exposure among cases is large. In these cases, the interval estimator using the logarithmic transformation and the two interval estimators derived from the quadratic equations developed here can generally improve the coverage probability of Kuritz and Landis' interval estimator, especially for the case of a small number of matched sets. Furthermore, we find that an interval estimator derived from a quadratic equation is consistently more efficient than Kuritz and Landis' interval estimator. The interval estimator using the logit transformation, although which performs poorly when the underlying odds ratio (OR) is close to 1, can be useful when both the probability of exposure among cases and the underlying OR are moderate or large.