FAST COMPUTATION OF EXACT CONFIDENCE-LIMITS FOR THE COMMON ODDS RATIO IN A SERIES OF 2 X-2 TABLES

The odds ratio is widely used as a measure of association in epidemiologic studies and clinical trials. We consider calculation of exact confidence limits for the common odds ratio in a series of indenpendent 2 x 2 tables and propose three modifications of the network algorithm of Mehta, Patel and Gray: (1) formulating and dealing with the problem in algebraic instead of graph theoretic terms, (2) performing convolutions on the natural scale instead of the logarithmic scale, and (3) using the secant method instead of binary search to compute roots of polynomial equations. Enhancement of computational efficiency, exceeding an order of magnitude, afforded by these modifications is empirically demonstrated. We also compare the modified method with one based on the fast Fourier transform (FFT). Further, we show that the FFT method can also result in considerable loss of numerical accuracy. The modifications proposed in this article yield an algorithm that is not only fast and accurate but that combines conceptual simplicity with ease of implementation. Anyone with a rudimentary knowledge of computer programming can implement it and quickly compute exact confidence intervals for relatively large data sets even on microcomputers. Thus it should help make exact analysis of the common odds ratio more common.