Optimal Scale-Up of HIV Treatment Programs in Resource-Limited Settings Under Supply Uncertainty

HIV clinics in sub-Saharan Africa face an important challenge of allocating scarce and unreliable supply of antiretroviral drugs (ARVs) among new patients (treatment initiation) and patients already on treatment (treatment continuation). The key trade-off underlying this allocation is between the marginal health benefit obtained by initiating an untreated patient on treatment and that obtained by avoiding treatment interruption of a treated patient. Existing national level policies on ARV allocation, based on socioeconomic and demographic criteria, are qualitative and of limited utility in providing quantitative guidance on scaling up of treatment programs at individual clinics. Moreover, the trade-off involved in clinic level allocation decisions has not been studied in the clinical literature, which focuses either on the incremental value obtained from initiating treatment (over no treatment) or on the value of providing continuous treatment (over interrupted treatment) but not on the difference of the two. We cast the clinic’s problem as a stochastic dynamic program, derive the optimal policy structure for some special cases and use it to derive a practically relevant Two-Period heuristic. We conduct extensive numerical analysis to compare the performance of this heuristic with Safety-Stock heuristic widely used in practice. Not serving higher value patients (those already on treatment), to avoid interrupting their treatment in the future, might be optimal under some conditions. Performance of the Two-Period heuristic (within 5% of the upper bound) is significantly better than that of the Safety-Stock heuristic (as much as 20% lower than the upper bound) and is robust to misspecification of key problem parameters, which might be difficult to estimate. Our model can serve as a basis for developing a decision-support tool for clinics to design their ARV treatment program scale-up plans.