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