Sample-Size Formula for the Proportional-Hazards Regression Model

A formula is derived for determining the number of observations necessary to test the equality of two survival distributions when concomitant information is incorporated. This formula should be useful in designing clinical trials with a heterogeneous patient population. Schoenfeld (1981, Biometrika 68, 316-319) derived the asymptotic power of a class of statistics used to test the equality of two survival distributions. That result is extended to the case where concomitant information is available for each individual and where the proportional-hazards model holds. The loss of efficiency caused by ignoring concomitant variables is also computed.