Comparison of Subsidy Schemes for Reducing Waiting Times in Healthcare Systems

We assume that public healthcare service has no user fee but an observable delay, while private healthcare service has a fee but no delay. Patients in the public system are given a subsidy s to use private service if their waiting times exceed a pre-determined threshold t. We call these subsidy schemes (s, t) policies. As two extreme cases, the (s, t) policy is called an unconditional subsidy scheme if t = 0, and a full subsidy scheme if s is equal to the private service fee. There is a fixed budget constraint so that a scheme with larger s has a larger t. We assess policies using two criteria: total patient cost and serviceability (i.e., the probability of meeting a waiting time target for public service). We prove analytically that, if patients are equally sensitive to delay, a scheme with a smaller subsidy outperforms one with a larger subsidy on both criteria. Thus, the unconditional scheme dominates all other policies. Using empirically derived parameter values from the Hong Kong Cataract Surgery Program, we then compare policies numerically when patients differ in delay sensitivity. Total patient cost is now unimodal in subsidy amount: the unconditional scheme still yields the lowest total patient cost, but the full subsidy scheme can outperform some intermediate policies. Serviceability is unimodal too, and the full subsidy scheme can outperform the unconditional scheme in serviceability when the waiting time target is long.