Minimum risk weights for comparing treatments in stratified binomial trials

When comparing two treatments in a stratified trial with a binary endpoint, data are commonly analysed using a weighted averaging of the stratum-specific differences between proportions. Two popular sets of weights are the harmonic means of the stratum-specific sample sizes (SSIZE) and the reciprocals of the variances of the stratum-specific differences (INVAR). Either the SSIZE or INVAR weights are chosen and prespecified in the data analysis plan. We show that the 'wrong' choice between SSIZE and INVAR can result in a significantly inefficient analysis. To circumvent this potential problem, we propose a 'minimum risk' (MR) weighting strategy. The easy-to-compute MR weights are designed to yield more precise and less biased estimates of the overall treatment difference relative to the SSIZE and INVAR weights, respectively. We show, via a simulation study, that the proposed weights are an attractive compromise between the SSIZE and INVAR weights in terms of statistical power. Numerical examples are presented to illustrate the utility of the MR weights.