Uncertainty and Value of Information When Allocating Resources Within and between Healthcare Programmes

Background: The objective of a decision maker is to determine the optimal allocation of treatments across population groups and healthcare programmes given a fixed budget. If costs and benefits are known precisely, deterministic mathematical programming (MP) methods can be used to allocate resources. However, costs and benefits are uncertain and variable. Allocating resources to maximise expected benefits subject to expected costs being below the budget will lead to a probability that the budget is exceeded. Stochastic MP methods have been proposed, but most require specification of an arbitrary probability level that the budget is exceeded. In addition, methods have not distinguished between parameter uncertainty and variability and therefore value of information for the allocation problem has not been considered. Methods: We propose a two-stage stochastic MP method that does not contain any arbitrary parameters. The first stage determines the optimal allocation that maximises expected benefits subject to expected costs being below the budget with respect to the uncertain and variable parameters. When the realisation that the budget cannot be met is determined, the second stage re-allocates remaining resources such that the budget is satisfied strictly for every random permutation while minimising the deviation of the benefits from those obtained in the first stage. Further information can reduce uncertainty but cannot reduce variability. Distinguishing between types of randomness enables us to calculate the expected value of perfect information (EVPI). We apply our framework to a stylised but relevant allocation problem and we calculate the EVPI for the whole system. Results: The results demonstrate that it is possible to evaluate actual budgetary policies, such as a strict constraint where the budget cannot be exceeded. For example, by comparing the costs of a strict budgetary policy with one based on expectation where additional public funds are required to indemnify any deficit, we obtain an estimate of the opportunity costs incurred from exceeding the budget. This can be compared to the transactions cost of policing such a policy when there is information asymmetry. EVPI is the difference between expected benefits with perfect information (no uncertainty) and expected benefits with current information. The monetary value is the additional budget required under current uncertainty to generate the same expected benefits as with perfect information. The traditional EVPI approach overestimates the true EVPI. This is because not only is information valuable in so far as it reduces uncertainty in the choice between treatments (given a particular population and healthcare programme), but also because other unrelated treatments can become possible within the strict constraint. EVPI for parameters directly relevant to a programme depends on the other competing but unrelated programmes. Furthermore, EVPI is a function of the budgetary rules imposed on the system and depends on any other constraints (e.g. equity). Conclusions: In a budget constrained healthcare system, decisions regarding allocation of resources within a programme must be made simultaneously with those of competing programmes. We present a unified framework that examines a strict budgetary rule and the value of acquiring further information to inform the allocation problem