The power of the Mantel-Haenszel test for grouped failure time data

The Mantel-Haenszel test for grouped failure time data (MHF test) compares the distribution of failure times in two cohorts followed for an interval of time when the data are collected in discrete subintervals. This paper derives approximations to the power of the Mantel-Haenszel test for arbitrary failure time distributions in the presence of censoring. The approximations are appropriate for both equal and nonequal odds ratios in the constituent tables, and can be used for arbitrary subdivisions of time. Four approximations are proposed. They differ from each other according to whether the parameter measuring treatment effect is an odds ratio or a difference in proportions, and whether the survival distributions are calculated under the null or alternative hypothesis. In addition, we demonstrate that when the hazards are constant, increasing the number of subintervals often produces only a negligible increase in the power of the MHF test. On the other hand, for arbitrary hazards and nonconstant hazard ratios, the choice of frequency and actual times of measurement can have important effects on power. Finally, the paper presents simple expressions for power under exponential failure and censoring models.