The uniformly minimum variance unbiased estimator of odds ratio in case–control studies under inverse sampling

Abstract

The stated goal of this paper is to propose the uniformly minimum variance unbiased estimator of odds ratio in case–control studies under inverse sampling design. The problem of estimating odds ratio plays a central role in case–control studies. However, the traditional sampling schemes appear inadequate when the expected frequencies of not exposed cases and exposed controls can be very low. In such a case, it is convenient to use the inverse sampling design, which requires that random drawings shall be continued until a given number of relevant events has emerged. In this paper we prove that a uniformly minimum variance unbiased estimator of odds ratio does not exist under usual binomial sampling, while the standard odds ratio estimator is uniformly minimum variance unbiased under inverse sampling. In addition, we compare these two sampling schemes by means of large-sample theory and small-sample simulation.