The global HIV response needs to both integrate with the broader health system and tackle the structural drivers of HIV. Cross-sectoral financing arrangements in which different sectors agree to co-finance structural interventions - have been put forward as promising frameworks to address these concerns. However, co-financing arrangements remain rare for HIV, and there is no consensus on how to distribute costs.

We use case studies to investigate how structural interventions can be incorporated within three quantitative decision-making frameworks. First, we consider cost-benefit analyses (CBA) using an opioid substitution therapy (OST) program in Armenia; second, we construct a theoretical example to illustrate the lessons game theory can shed on the co-financing arrangements implied by CBA; and third we consider allocative efficiency analyses using needle-syringe programs (NSPs) in Belarus.

A cross-sectoral cost-benefit analysis of OST in Armenia demonstrates that the share of that should be funded by the HIV sector depends on the willingness to pay (WTP) to avert an HIV-related DALY, the long-term cost-benefit ratio, and the HIV risk reduction from OST. For reasonable parameter values, the HIV sector's share ranges between 0-48%. However, the Shapley value--a game-theoretic solution to cost attribution that ensures each sector gains as much or more as they would from acting independently--implies that the HIV sector's share may be higher. In Belarus, we find that the HIV sector should be willing to co-finance structural interventions that would increase the maximal attainable coverage of NSPs, with the contribution again depending on the WTP to avert an HIV-related DALY.

Many interventions known to have cross-sectoral benefits have historically been funded from HIV budgets, but this may change in the future. The question of how to distribute the costs of structural interventions is critical, and frameworks that decision-makers use to inform resource allocations will need to take this into account.