|
Abstract:
|
We consider estimating the single-stage quantile-optimal treatment regime (QOTR) for survival data, where responses are randomly censored. Such data is prevalent in many biomedical applications, where optimizing the marginal quantile of the outcome has attractive properties: First, if a lower quantile is employed, this criterion would prioritize the benefits of patients at the bottom of the response scale, so the selected regime is consistent with the principle of nonmaleficence in medical ethics; Second, when the censoring rate is high, the unrestricted mean survival time is hard to be accurately estimated, but often the median and lower quantiles could still be reliably estimated. To that end, we propose a new model-free estimator of the coefficients indexing the QOTR for a given class of treatment regimes. We studied its nonstandard asymptotics by applying a new theoretical result on non-smooth semiparametric M-estimation problems in the literature (Delsol et al. 2015). We also constructed the m-out-of-n bootstrap confidence interval of the parameters indexing the QOTR. Furthermore, through a sequence of simulation examples, we examined the performance of the proposed estimator.
|
