Efficient power computation for exact and mid-P tests for the common odds ratio in several 2 x 2 tables

When designing a study that may generate a set of sparse 2 x 2 tables, or when confronted with 'negative' results upon exact analysis of such tables, we need to compute the power of exact tests. In this paper we provide an efficient approach for computing exact unconditional power for four exact tests on the common odds ratio in a series of 2 x 2 tables. These tests are the traditional exact test; a test based on a probability ordering of the sample space; and two tests based on ordering the sample space according to distance from the mean, or median. For each test, we consider both a conservative version and a mid-P adjusted version. We explore three computational options for power determination: exact power computation, calculation of exact upper and lower bounds for power, and Monte Carlo confidence bounds for power. We present an interactive program implementing these options. For study design, the program may be run several times to arrive at a sample configuration with adequate power.