A semiparametric estimate of treatment effects with censored data

A semiparametric estimate of an average regression effect with right-censor ed failure time data has recently been proposed under the Cox-type model wh ere the regression effect beta (t) is allowed to vary with time. In this ar ticle, we derive a simple algebraic relationship between this average regre ssion effect and a measurement of group differences in k-sample transformat ion models when the random error belongs to the GP family of Harrington and Fleming (1982, Biometrika 69, 553 566), the latter being equivalent to the conditional regression effect in a gamma frailty model. The models conside red here are suitable for the attenuating hazard ratios that often arise in practice. The results reveal ail interesting connection among the above th ree classes of models as alternatives to the proportional hazards assumptio n and add to our understanding of the behavior of the partial likelihood es timate under nonproportional hazards. The algebraic relationship provides a simple estimator under the transformation model. We develop a variance est imator based on the empirical influence function that is much easier to com pute than the previously suggested resampling methods. When there is trunca tion in the right tail of the failure times, we propose a method of bias co rrection to improve the coverage properties of the confidence intervals. Th e estimate, its estimated variance, and the bias correction term call all b e calculated with minor modifications to standard software for proportional hazards regression.