Super learner for survival prediction in case-cohort and generalized case-cohort studies

The case-cohort study design is often used in modern epidemiological studies of rare diseases, as it can achieve similar efficiency as a much larger cohort study with a fraction of the cost. Previous work focused on parameter estimation for case-cohort studies based on a particular statistical model, but few discussed the survival prediction problem under such type of design. In this article, we propose a super learner algorithm for survival prediction in case-cohort studies. We further extend our proposed algorithm to generalized case-cohort studies. The proposed super learner algorithm is shown to have asymptotic model selection consistency as well as uniform consistency. We also demonstrate our algorithm has satisfactory finite sample performances. Simulation studies suggest that the proposed super learners trained by data from case-cohort and generalized case-cohort studies have better prediction accuracy than the ones trained by data from the simple random sampling design with the same sample sizes. Finally, we apply the proposed method to analyze a generalized case-cohort study conducted as part of the Atherosclerosis Risk in Communities Study.