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It is challenging to deal with censored data, where we only have access tothe incomplete information of survival time instead of its exact value.Fortunately, under linear predictor assumption, people can obtain guaranteedcoverage for the confidence band of survival time using methods like CoxRegression. However, when relaxing the linear assumption with neural networks(e.g., Cox-MLP (Katzman et al., 2018; Kvamme et al., 2019)), we lose theguaranteed coverage. To recover the guaranteed coverage without linearassumption, we propose two algorithms based on conformal inference. In thefirst algorithm WCCI, we revisit weighted conformal inference and introduce anew non-conformity score based on partial likelihood. We then propose atwo-stage algorithm T-SCI, where we run WCCI in the first stage and applyquantile conformal inference to calibrate the results in the second stage.Theoretical analysis shows that T-SCI returns guaranteed coverage under milderassumptions than WCCI. We conduct extensive experiments on synthetic data andreal data using different methods, which validate our analysis.

T-SCI: A Two-Stage Conformal Inference Algorithm with Guaranteed Coverage for Cox-MLP