Distribution-Free Selection of Low-Risk Oncology Patients for Survival Beyond a Time Horizon

We study the problem of selecting a subset of patients who are unlikely to experience an event within a specified time horizon, by calibrating a screening rule based on the output of a black-box survival model. This statistics problem has many applications in medicine, including identifying candidates for treatment de-escalation and prioritizing the allocation of limited medical resources. In this paper, we compare two families of methods that can provide different types of distribution-free guarantees for this task: (i) high-probability risk control and (ii) expectation-based false discovery rate control using conformal $p$-values. We clarify the relation between these two frameworks, which have important conceptual differences, and explain how each can be adapted to analyze time-to-event data using inverse probability of censoring weighting. Through experiments on semi-synthetic and real oncology data from the Flatiron Health Research Database, we find that both approaches often achieve the desired survival rate among selected patients, but with distinct efficiency profiles. The conformal method tends to be more powerful, whereas high-probability risk control offers stronger guarantees at the cost of some additional conservativeness. Finally, we provide practical guidance on implementation and parameter tuning.