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Abstract In this paper, we develop an inferential method based on conformal prediction, which can wrap around any survival prediction algorithm to produce calibrated, covariate-dependent lower predictive bounds on survival times. In the Type I right-censoring setting, when the censoring times are completely exogenous, the lower predictive bounds have guaranteed coverage in finite samples without any assumptions other than that of operating on independent and identically distributed data points. Under a more general conditionally independent censoring assumption, the bounds satisfy a doubly robust property which states the following: marginal coverage is approximately guaranteed if either the censoring mechanism or the conditional survival function is estimated well. The validity and efficiency of our procedure are demonstrated on synthetic data and real COVID-19 data from the UK Biobank.
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Conformalized survival analysis with adaptive cut-offs
Summary 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 data-adaptive 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.
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- Award ID(s):
- 2023109
- PAR ID:
- 10506752
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrika
- Volume:
- 111
- Issue:
- 2
- ISSN:
- 0006-3444
- Format(s):
- Medium: X Size: p. 459-477
- Size(s):
- p. 459-477
- Sponsoring Org:
- National Science Foundation
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