Recovery of Information and Adjustment for Dependent Censoring Using Surrogate Markers
A class of tests and estimators for the parameters of the Cox proportional hazards model, the accelerated failure time model, and a model for the effect of treatment on the mean of a response variable of interest are proposed that use surrogate marker data to recover information lost due to independent censoring and to adjust for bias due to dependent censoring in randomized clinical trials. We construct an adaptive test that (i) is asymptotically distribution free under the null hypothesis of no treatment effect on survival, (ii) incorporates surrogate marker data, and (iii) is guaranteed to be locally more powerful than the ordinary log-rank test against proportional hazards alternatives when the baseline failure time distribution is Weibull. The proposed test is shown to outperform the log-rank test in a series of simulation experiments. We also prove the optimal estimator within our class is semiparametric efficient by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model with data missing at random, and then deriving a representation for the efficient score in this more general problem.
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