Conformalized survival analysis with adaptive cutoffs

This paper introduces a method that constructs valid and efficient lower predictive bounds (LPBs) for survival times with censored data. Traditional methods for survival analysis often assume a parametric model for the distribution of survival time as a function of the measured covariates, or assume that this conditional distribution is captured well with a non-parametric method such as random forests; however, these methods may lead to undercoverage if their assumptions are not satisfied. In this paper, we build on recent work by Cand\`es et al. (2021), which offers a more assumption-lean approach to the problem. Their approach first subsets the data to discard any data points with early censoring times and then uses a reweighting technique (namely, weighted conformal inference (Tibshirani et al., 2019)) to correct for the distribution shift introduced by this subsetting procedure. For our new method, instead of constraining to a fixed threshold for the censoring time when subsetting the data, we allow for a covariate-dependent and data-adaptive subsetting step, which is better able to capture the heterogeneity of the censoring mechanism. As a result, our method can lead to LPBs that are less conservative and give more accurate information. We show that in the Type I right-censoring setting, if either of the censoring mechanism or the conditional quantile of survival time is well estimated, our proposed procedure achieves approximately exact marginal coverage, where in the latter case we additionally have approximate conditional coverage. We evaluate the validity and efficiency of our proposed algorithm in numerical experiments, illustrating its advantage when compared with other competing methods. Finally, our method is applied to a real dataset to generate LPBs for users' active times on a mobile app.