Distribution-free inference on contrasts of arbitrary summary measures of survival

We present an approach for inference on contrasts of clinically meaningful functionals of a survivor distribution (e.g., restricted mean, quantiles) that can avoid strong parametric or semiparametric assumptions on the underlying structure of the data. In this multistage approach, we first use an adaptive predictive model to estimate conditional survival distributions based on covariates. We then estimate nonparametrically one or more functionals of survival from the covariate-specific survival curves and evaluated contrasts of those functionals. We find that the use of an adaptive nonparametric tree-based predictive model leads to minimal loss in precision when semiparametric assumptions hold and provides marked improvement in accuracy when those assumptions are invalid. Therefore, this work as a whole supports the use of survival summaries appropriate to a given medical application, whether that be, for example, the median or 75th percentile in some settings or perhaps a restricted mean in others. The approach is also compared with the Mayo R score for primary biliary cirrhosis prognosis.