The joint survival super learner: A super learner for right‐censored data

Risk prediction models are widely used to guide real‐world decision‐making in areas such as healthcare and economics, and they also play a key role in estimating nuisance parameters in semiparametric inference. The super learner is a machine learning framework that combines a library of prediction algorithms into a meta‐learner using cross‐validated loss. In the context of right‐censored data, careful consideration must be given to both the choice of the loss function and the estimation of expected loss. Moreover, estimators such as the inverse probability of censoring weighting requires accurate modeling and an estimator of the censoring distribution. We propose a novel approach to super learning for survival analysis that jointly evaluates the candidate learners for both the event‐time distribution and the censoring distribution. Our method imposes no restrictions on the algorithms included in the library, accommodates competing risks, and does not rely on a single prespecified estimator of the censoring distribution. We establish a finite‐sample bound on the average price we pay for using cross‐validation, and show that this price vanishes asymptotically, up to poly‐logarithmic terms, provided that the size of the library does not grow faster than at a polynomial rate in the sample size. We demonstrate the practical utility of our method using prostate cancer data and compare it to existing super learner algorithms for survival analysis using synthesized data.