Stratifying Subjects for Treatment Selection with Censored Event Time Data from a Comparative Study

The conventional approach to comparing a new treatment with a standard therapy is often based on a summary measure for the treatment difference over the entire study population. A positive trial with respect to such a global measure, however, does not mean that all individual future patients would benefit from the new treatment. On the other hand, a negative finding may not be sufficiently conclusive to claim that the new treatment is entirely futile. In this article, we propose a systematic approach to identify future patients who would benefit from the new treatment with respect to an event time outcome via a two-stage inference procedure. We first develop a scoring index to stratify study patients based on parametric or semiparametric survival models with the observed event times and covariates. We then use a nonparametric method to estimate the average treatment difference for each stratum defined by the score. Sampling variation of the resulting estimator is also provided across the entire spectrum of the score by controlling certain local and global error rates. With a numerical study, we show that the new proposal performs well under various practical settings. Our method is illustrated with the data from a recent clinical trial to evaluate whether a specific anti-hypertensive drug would prolong the lives for patients with stable coronary artery disease and normal or slightly reduced left ventricular function.