CCTimeBoost: Learning Time-Varying Relative Risk with Case-Control Boosted Trees

Many survival problems are inherently time-dependent: a biomarker may be predictive soon after diagnosis but irrelevant years later, or a treatment effect may diminish, reverse, or interact with follow-up duration. However, tree-based survival models commonly used in practice typically assign each individual a fixed, time-independent risk score. Neural non-proportional-hazards models can capture dynamic effects, but are often more challenging to tune, scale, and interpret than boosted trees. We present CCTimeBoost, a gradient-boosted tree framework for learning continuous-time, time-varying relative risk. The method augments covariates with time features, trains boosted trees on sampled risk sets using a group-softmax objective, and estimates a full-risk-set baseline hazard to generate survival curves. We show that this objective has a likelihood interpretation: for finite sampled risk sets, it matches a nested case-control likelihood, and in the full-risk-set limit, it converges to the Cox partial likelihood. Across eight right-censored survival benchmarks, CCTimeBoost delivers state-of-the-art discrimination performance relative to tree and neural baselines and is competitive in calibration. In controlled simulations, it accurately recovers diminishing effects, crossing hazards, and rule-based temporal interactions, also behaving as a proportional model when proportional hazards are present. These results indicate that non-proportional survival modeling can be incorporated into standard boosted-tree methods.