In this paper, we measure the extent to which a biological marker is a
surrogate endpoint for a clinical event by the proportional reduction
in the regression coefficient for the treatment indicator due to the
inclusion of the marker in the Cox regression model. We estimate this
proportion by applying the partial likelihood function to two Cox mode
ls postulated on the same failure time variable. We show that the resu
ltant estimator is asymptotically normal with a simple variance estima
tor. One can construct confidence intervals for the proportion by usin
g the direct normal approximation to the point estimator or by using F
ieller's theorem. Extensive simulation studies demonstrate that the pr
oposed methods are appropriate for practical use. We provide applicati
ons to HIV/AIDS clinical trials. (C) 1997 by John Wiley & Sons, Ltd.