Text S2: The algebra of flexible cost functions Supporting information for HIV Treatment as Prevention: Modelling the Cost of Antiretroviral Treatment- State of the Art and Future Directions

A “cost function” is a mathematical function that defines the relationship between an output produced, here defined as patient-years (or -months) of antiretroviral therapy (ART), and the cost of the resources consumed in that production. A cost function, either explicit or implicit, is a necessary component of any estimate of the costs and benefits of ART service delivery. This appendix gives supporting details on the mathematical distinction between two classes of cost functions, which we refer to as “accounting identity” cost functions and “flexible” cost functions. Our purpose is not to elevate one of these types of cost functions over the other in all situations, but to distinguish them as distinct approaches to projecting costs, each of which has its strengths and weaknesses. In modelling practice, the most useful cost function might be one or the other or, in some cases, a hybrid of the two.