When are time-to-event models a waste of time? Bridging mixture cure models and positive-unlabeled learning for binary classification under right-censoring

RESUMO

In clinical settings, predicting binary outcomes is often complicated by right-censoring, which prevents us from distinguishing individuals in whom the event never occurs (i.e., negative, or non-susceptible) from those where it occurs after the censoring time (i.e., positive, or susceptible). To discriminate between these subpopulations, we can use mixture cure models (MCMs), which model both the outcome probability over an infinite horizon and its time-to-event (TTE) distribution when observed. However, the TTE approach requires event timestamps, which can be unreliable, costly to obtain, or biased due to disparities in clinical care. Alternatively, the task can be formulated as positive-unlabeled (PU) learning, in which individuals without an observed event are grouped as "unlabeled" rather than negative, recognizing that this group includes positives whose event occurred after censoring. Here we analyze the relationship between these frameworks and provide evidence-based recommendations for choosing between them. We begin by showing that both families optimize a shared likelihood but differ in how they constrain the probability of event occurrence prior to censoring among susceptible patients, which in PU learning is known as the labeling propensity; and that an MCM may be viewed as a PU model whose labeling propensity is parameterized as a TTE distribution, which makes the model identifiable. In systematic simulations and two real-world clinical cohorts, we examine whether and when including the TTE component benefits binary classification. We show that MCMs are preferred in only one specific regime: under selective censoring where the exact features governing censoring cannot be identified. Otherwise, PU learning achieves equivalent performance while avoiding challenges and potential biases associated with the TTE approach.