Conformalized Survival Analysis
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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 exogeneous, 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: marginal coverage is approximately guaranteed if either the censoring mechanism or the conditional survival function is estimated well.
- $(X_i, C_i, T_i)$ are i.i.d. copies of the random vector $(X, C, T)$
- consider the Type I right-censoring setting, $\tilde T_i = \min(T_i, C_i)$
two assumptions on the dependence structure between $T$ and $C$
- Assumption 1 (conditionally indepedent censoring): $T\ind C\mid X$
- Assumption 2 (completely independent censoring): $(T, X)\ind C$
the ultimate goal is to generate a covariate-dependent LPB as a conservative assessment of the uncensored survival time $T$.
denote by $\hat L(\cdot)$ a generic LPB estimated from the observed data $(X_i, C_i, T_i)_{i=1}^n$. We say an LPB is calibrated if it satisifies the following coverage criterion
\[P(T\ge \hat L(X)) \ge 1-\alpha\,.\]the coverage of LPBs is evaluated as
\[\frac{1}{n_{test}}\sum_{i=1}^{n_{test}}1\{T_i\ge \hat L(X_i)\}\]