Longitudinal incremental propensity score interventions for limited resource settings.

Many real-life treatments are of limited supply and cannot be provided to all individuals in the population. For example, patients on the liver transplant waiting list usually cannot be assigned a liver transplant immediately at the time they reach highest priority because a suitable organ is not immediately available. In settings with limited supply, investigators are often interested in the effects of treatment strategies in which a limited proportion of patients receive an organ at a given time, that is, treatment regimes satisfying resource constraints. Here, we describe an estimand that allows us to define causal effects of treatment strategies that satisfy resource constraints: incremental propensity score interventions (IPSIs) for limited resources. IPSIs flexibly constrain time-varying resource utilization through proportional scaling of patients' natural propensities for treatment, thereby preserving existing propensity rank ordering compared to the status quo. We derive a simple class of inverse-probability-weighted estimators, and we apply one such estimator to evaluate the effect of restricting or expanding utilization of "increased risk" liver organs to treat patients with end-stage liver disease.