Miscellanea. Semiparametric two-sample tests in clinical trials with a post-randomisation response indicator

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Abstract
In many clinical trials involving survival endpoints, one has additional data on some binary indicator of ‘response’, such as initial tumour shrinkage in cancer trials. This paper studies the case of randomised clinical trials where the response indicator is available shortly after randomisation, and where one can assume that, within each stratum defined by the response indicator, a two treatment-group proportional-hazards model holds. The same model may also describe some incompletely randomised or observational studies. Asymptotic relative efficiencies for Kaplan-Meier-based estimators versus maximum partial likelihood estimators are examined under this model for estimating either the difference in survival probabilities at a specified time or the parameter estimated by the logrank numerator. It is shown that the efficiency gains using the model are more promising when estimating the difference in survival probabilities. An example is given comparing the long-term survival experience of two groups of patients with advanced Hodgkin's disease

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