THE POWER OF THE MANTEL-HAENSZEL TEST FOR GROUPED FAILURE TIME DATA

The Mantel-Haenszel test for grouped failure time data (MHF test) comp ares 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 cens oring. The approximations are appropriate for both equal and nonequal odds ratios in the constituent tables, and can be used for arbitrary s ubdivisions of time. Four approximations are proposed. They differ fro m each other according to whether the parameter measuring treatment ef fect is an odds ratio or a difference in proportions, and whether the survival distributions are calculated under the null or alternative hy pothesis. In addition, we demonstrate that when the hazards are consta nt, increasing the number of subintervals often produces only a neglig ible increase in the power of the MHF test. On the other hand, for arb itrary hazards and nonconstant hazard ratios, the choice of frequency and actual times of measurement can have important effects on power. F inally, the paper presents simple expressions for power under exponent ial failure and censoring models.