An Estimate of the Odds Ratio That Always Exists

This article proposes an estimate of the odds ratio in a (2 £ 2) table obtained from studies in which the row totals are Ž xed by design, such as a phase II clinical trial. Our estimate,basedon themedianunbiasedestimateof the probabilitiesof success in the (2£2) table, will always be in the interval (0;1): Another estimate of the odds ratio which has such properties is obtained when adding .5 to each cell of the table. Using simulations, we compared our proposed estimate to that obtained by adding .5 to every cell, and found that our estimate had smaller Ž nite sample bias, and larger mean square error. We also propose the use of the bootstrap to form a conŽ dence interval for the odds ratio based on our proposed estimate. Instead of a Monte Carlo bootstrap, one can easily calculate the “exact” bootstrap distribution of our estimate of the odds ratio, and use this distribution to calculate conŽ dence intervals.