Comparative analysis of two rates

In this paper, we examine comparative analysis of rates with a view to each of the usual comparative parameters-rate difference (RD), rate ratio (RR) and odds ratio (OR)-and with particular reference to first principles. For RD and RR we show the prevailing statistical practices to be rather poor. We stress the need for restricted estimation of variance in the chi-square function underlying interval estimation (and also point estimation and hypothesis testing). For RR analysis we propose a chi-square formulation analogous to that for RD and, thus, one which obviates the present practice of log transformation and its associated use of Taylor series approximation of the variance. As for OR analysis, we emphasize that the chi-square function, introduced by Cornfield for unstratified data, and extended by Gart to the case of stratified analysis, is based on the efficient score and thus embodies its optimality properties. We provide simulation results to evince the better performance of the proposed (parameter-constrained) procedures over the traditional ones.