Pooling controls from different studies

Abstract

This paper develops a method for estimating the odds ratio in a case-control study that 'borrows' strength from the controls in similar previous studies. We assume that the observations within each stratum in the current study are generated from a pair of independent binomial distributions. We assume that the observations on the controls, again within each stratum and from the previous studies, are independent binomial random variables. We use these controls to construct a prior distribution for the stratum specific log-odds for the controls in the current study which we then combine with the likelihood from the current study to arrive at the posterior distribution of the target quantities of interest, the adjusted or stratum specific log-odds ratios. We assume a diffuse prior distribution for the stratum specific log-odds ratio. A simulation study investigates the frequency or repeated sampling properties of the inference based upon the posterior distribution of the log-odds ratio so constructed.