Sampled on outcome, still predictable: a weighted gradient boosting machine matches Cox on uranium miner cancer data
In outcome-dependent sampling, covariates are collected for only part of the cohort, so standard survival models trained on the sampled data target a distribution that differs from the cohort. A gradient boosting machine carries the sampling weights into training and tuning, selecting iterations by a weighted integrated Brier score, and the weighted empirical risk is shown to converge to the corresponding integrated Brier risk. In simulations it outperformed the Cox model in high-dimensional and nonlinear settings, and on uranium miner cancer data the test C-index was 0.803 versus 0.801 for Cox.