Estimating conditional survival benefit for the allocation of scarce resources

Whenever treatment is scarce, the question of how to allocate resources arises. One option is to allocate based on conditional survival benefit, defined as the contrast between an individual's expected survival with and without treatment. Estimating conditional survival benefit from observational data may present the following three challenges: (i) time-dependent confounding, arising when treatments are assigned based on longitudinal health markers which are in turn affected by past assignments; (ii) multiple time scales, namely time since becoming eligible for treatment, relevant for comparability of patients, and calendar time, representing when treatment decisions are made; and (iii) multiple versions of treatment, leading to multiple counterfactual outcomes with treatment. Building on previous work where cross-sections and inverse probability of treatment weighting were combined to estimate survival benefit on the treated population, we propose a strategy to dynamically estimate conditional survival benefit for all patients awaiting scarce treatment at any time treatment becomes available, accounting for multiple versions of treatment. After delineating identifiability assumptions, we show in a simulation study that our proposed method improves the estimation of conditional survival benefit compared to simpler methods. The proposed method is then applied to liver transplant data from the Eurotransplant region.