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Purpose
To develop a mathematical programming framework to optimise the allocation of resources across healthcare technologies subject to inter-temporal budgetary and other constraints and apply it to policy relevant decisions.
Methods
Healthcare decisions based on the incremental cost-effectiveness ratio (ICER) cannot identify the true opportunity cost (the technologies which should be displaced) of implementing a new, more costly technology.
A mathematical programming framework was developed to optimise the allocation of resources across health technologies subject to inter-temporal budgetary and other constraints. This is applied to a policy problem using examples relevant to the National Institute for Clinical Excellence (NICE) for England and Wales. To determine the optimal level of implementation of each health technology across patient groups, the optimisation problem is characterised in two ways: (i) as a 0-1 Mixed Integer Linear Program (0-1 MILP) or (ii) as a 0-1 Mixed Integer Non-Linear Program (0-1 MINLP). Annual budgets for pharmaceuticals and other healthcare costs are defined for each time period. Horizontal equity concerns are incorporated as indivisibility constraints by restricting the decision variables to be 0-1 integer values. Non-linearity arises where fixed costs or other non-constant returns to scale are identified. Shadow prices are generated for each constraint. In addition, the value gained by trading budgets over time can be explored.
Results
The data required to implement the model was extracted from the 6th and 7th wave of appraisals considered by NICE, showing that the analysis is feasible. The optimal level of implementation across patient groups for each health technology was obtained. The shadow price of each budget for each year was estimated and can be interpreted as the value, in terms of health benefits of relaxing (or trading) these constraints. The opportunity costs of a range of possible horizontal equity concerns were expressed in terms of health benefit foregone. Alternative budgetary rules were also evaluated and showed that gains in population health can be made by allowing budgets to be traded over time.
Conclusion
The mathematical programming framework which has been developed to optimise the allocation of resources across health technologies can be applied to policy-relevant situations. The framework is shown to provide a robust and transparent process for social decision making in public health.
See more of Oral Concurrent Session A - Cost Effective Analysis: Methods
See more of The 26th Annual Meeting of the Society for Medical Decision Making (October 17-20, 2004)