Conformalized survival analysis with adaptive cut-offs

Yu Gui, Rohan Hore, Zhimei Ren, Rina Foygel Barber

Abstract:

This paper introduces an assumption-lean method that constructs valid and efficient
lower predictive bounds for survival times with censored data. We build on recent work
by Candès et al. (2023), whose 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 dataadaptive subsetting step, which is better able to capture the heterogeneity of the censoring
mechanism. As a result, our method can lead to lower predictive bounds that are less conservative and give more accurate information. We show that in the Type-I right-censoring
setting, if either the censoring mechanism or the conditional quantile of the survival time
is well estimated, our proposed procedure achieves nearly 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 lower predictive bounds for users’ active times on a mobile app.