Mathematical programming for the optimal allocation of health care resources

The standard decision rules of cost-effectiveness analysis either require the decision maker to set a threshold willingness to pay for additional health care or to set an overall fixed budget. In practice, neither are generally taken, but instead an arbitrary decision rule is followed which may not be consistent with the overall budget, lead to an allocation of resources which is less than optimal, and is unable to identify the programme which should be displaced at the margin. We show, using a policy-relevant example, how mathematical programming can be used as a generalisation of the standard decision rules. This approach allows us to incorporate important aspects of the decision into our framework that are not available if decision making is made using threshold values of the incremental cost-effectiveness ratio alone. We are able to examine alternative budgetary rules about when expenditure can be incurred, and show the opportunity loss, in terms of health benefit forgone, of each budgetary rule. We show that indivisibility in a patient population and other equity concerns can be represented as constraints in the programme and we estimate the opportunity loss if these concerns are held for some patient populations, and for all patient populations.