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### UNCERTAINTY AND VALUE OF INFORMATION WHEN ALLOCATING RESOURCES WITHIN AND BETWEEN MULTIPLE HEALTHCARE PROGRAMMES WITH A BUDGET CONSTRAINT

Zaid Chalabi, PhD1, Karl Claxton, PhD, MSc, BA2, and David Epstein, MSc2. (1) London School of Hygiene and Tropical Medicine, London, United Kingdom, (2) University of York, York, United Kingdom

Purpose

Decision makers must determine the optimal allocation of resources within and between multiple healthcare programmes to maximise population health given a fixed budget. Furthermore, costs and benefits may not be known with certainty. The purpose of this paper is to address these challenges, and to calculate the expected value of perfect information (EVPI) for the whole system.

Methods

Costs and benefits of healthcare programmes will be imperfectly known because of irreducible or natural variability (different outcomes between patients) and uncertainty (in mean outcomes) which is reducible with additional information. It is irrelevant to the allocation problem where randomness arises from. Risk neutral decision makers will aim to allocate resources to maximise expected health benefits subject to expected costs meeting the budget constraint. Since costs are random variables, for some realisations of costs for a given allocation of resources the budget may be exceeded. In these cases there will be an opportunity loss of health as cheaper programmes are substituted for more expensive ones.

To allocate resources optimally, decision makers must consider all potential realisations of costs and health benefits, and identify which programmes will be adjusted in order to minimise the expected loss of health.

We demonstrate a two stage stochastic mathematical programming solution, using a numerical example. The first stage maximises the expectation of the overall health benefit whilst ensuring that the expected cost is below the budget constraint. The second stage re-allocates resources such that the budget is now satisfied strictly for every possible permutation of the uncertain parameters in the model and deviation of the expected health benefit from that obtained in the first stage is minimised.

Further information will reduce uncertainty, and hence lead to better decisions, but will not reduce variability. Because we distinguish clearly between variability and uncertainty using a hierarchical model, we can calculate EVPI for the whole system.

Results

We demonstrate the mathematical programme and calculate EVPI for the whole system using a numerical example.

Conclusions

A conventional stochastic mathematical programming solution maximises expected health under the constraint that the probability that total costs will exceed the budget is less than a given arbitrary value. Our two-stage stochastic formulation does not require arbitrary parameters and allows calculation of EVPI for the whole system.