Aligning Data-Driven Predictors with Allocation: A Decision-Focused Approach to Survival Analysis

Machine learning predictors have become essential tools for guiding automated decision making. However, a major misalignment persists: predictive models are typically optimized in terms of standard statistical metrics in isolation from the algorithmic tasks they inform. We highlight this incongruity in both theory and practice in the high-stakes domain of organ allocation. We demonstrate that any algorithm relying on (even near-perfect) survival predictors optimized for standard metrics—such as the Concordance index (C-index)—can yield arbitrarily poor outcomes when used for allocation, failing to guarantee utility better than a uniform random selection. To bridge the gap between survival analysis and policy optimization, we introduce a decision-focused learning approach based on optimizing normalized discounted cumulative gain (NDCG), a mainstay metric in information retrieval. We establish the utility of NDCG in survival analysis by proving that it translates to guarantees on the performance of allocation. Empirically, we develop a bootstrapping approach to optimize the NDCG of existing survival models. Unlike prior work, we also address the challenge of right censoring when evaluating NDCG. We show the aforementioned misalignment persists in historical heart transplant data from the US, and our method dramatically boosts the NDCG across a suite of survival models by 40-100%. We anticipate that our framework will find broader applications in decision making with predictions.