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Background  South Africa has a large domestically funded HIV programme with highly saturated coverage levels for most prevention and treatment interventions. To further optimise its allocative efficiency, we designed a novel optimisation method and examined whether the optimal package of interventions changes when interaction and non-linear scale-up effects are incorporated into cost-effectiveness analysis.    Methods  The conventional league table method in cost-effectiveness analysis relies on the assumption of independence between interventions. We added methodology that allowed the simultaneous consideration of a large number of HIV interventions and their potentially diminishing marginal returns to scale. We analysed the incremental cost effectiveness ratio (ICER) of 16 HIV interventions based on a well-calibrated epidemiological model that accounted for interaction and non-linear scale-up effects, a custom cost model, and an optimisation routine that iteratively added the most cost-effective intervention onto a rolling baseline before evaluating all remaining options. We compared our results with those based on a league table.    Results  The rank order of interventions did not differ substantially between the two methods- in each, increasing condom availability and male medical circumcision were found to be most cost-effective, followed by anti-retroviral therapy at current guidelines. However, interventions were less cost-effective throughout when evaluated under the optimisation method, indicating substantial diminishing marginal returns, with ICERs being on average 437% higher under our optimisation routine.    Conclusions  Conventional league tables may exaggerate the cost-effectiveness of interventions when programmes are implemented at scale. Accounting for interaction and non-linear scale-up effects provides more realistic estimates in highly saturated real-world settings.    Electronic supplementary material  The online version of this article (doi:10.1186/s12889-017-4023-3) contains supplementary material, which is available to authorized users.

Designing an optimal HIV programme for South Africa: Does the optimal package change when diminishing returns are considered?