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

This study is motivated by the challenges faced by clinics in sub-Saharan Africa in allocating scarce and unreliable supply of antiretroviral drugs (ARVs) among a large pool of eligible patients. Existing discussion of ARV allocation is focused on qualitative rules for prioritizing certain socioeconomic and demographic patient segments over others at the national level. However, such prioritization rules are of limited utility in providing quantitative guidance on scaling up of treatment programs at individual clinics. In this study, we take the perspective of a clinic administrator whose objective is to maximize the quality-adjusted survival of the entire patient population in its service area by allocating scarce and unreliable supply of drugs among two activities: initiating treatment for untreated patients and continuing treatment for previously treated patients. The key trade-off underlying this allocation decision 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. This trade-off has not been explicitly 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 and provide a partial characterization of the optimal policy, which consists of dynamic prioritization of patient segments and is characterized by state-dependent thresholds. We use this structure of the optimal policy to design a simpler Two-Period heuristic and show that it substantially outperforms the Safety-Stock heuristic, which is commonly used in practice. In our numerical experiments based on realistic parameter values, the performance of the Two-Period heuristic is within 4% of the optimal policy whereas that of the Safety-Stock heuristic can be as much as 20% lower than that of the optimal policy. Our model can serve as a basis for developing a decision support tool for clinics to design their ARV treatment program scale-up plans.