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Optimizing Healthcare Resource Allocation: A Mathematical Programming Approach

This study builds on an existing decision framework by applying mathematical programming to a relevant policy problem in healthcare resource allocation. The analysis includes cost profiles over time and constraints relating to equity considerations, allowing for examination of trade-offs between equity and efficiency. Data from UK NICE appraisals on various treatments is utilized to maximize discounted health benefits subject to overall budget limitations, with options for mixed or pure interventions. The study explores the impact of budget constraints on opportunity costs and the importance of equity considerations in decision-making. Conclusions highlight the varying shadow prices with budget changes, the significance of cost profiles, and implications of different equity concerns on efficiency. Further work is suggested to address uncertainties and explore resource constraints in future decisions.

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Optimizing Healthcare Resource Allocation: A Mathematical Programming Approach

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  1. The return of the 5 year plan David Epstein, Karl Claxton, Mark Sculpher (CHE) Zaid Chalabi (LSHTM) Mathematical programming for allocation of health care resources Medical Research Council Health Services Research Collaboration

  2. This study • Builds on existing decision framework • Applying mathematical programming to a stylised but relevant policy problem • Profile of costs over time • Equity concerns are constraints • Allowing examination of equity-efficiency trade offs

  3. Data • Data from 6th wave UK NICE appraisals • Flu treatments (adults, elderly, residential elderly, children) • Rituximab (<60 years old, elderly) • Long acting insulin (type 1 diabetics, type 2 diabetics) • Data available for each treatment: • costs for each year 1-15 (compared to ‘current care’) • total QALYs (compared to ‘current care’) • Prevalence and incidence • Assume decision can be reviewed at 5 years

  4. The problem Maximise total (discounted) health benefits • subject to • Total cost<= overall budget • Interventions can be MIXED or PURE

  5. Optimal solution 100 Flu 1 % receiving intervention Flu 2,3 &4 0 Budget (£million)

  6. Optimal solution 100 Flu 1 % receiving intervention Flu 2,3 &4 0 Budget (£million)

  7. Optimal solution 100 Flu 1 Diab 1 % receiving intervention Flu 2,3 &4 Diab 2 0 Budget (£million)

  8. Optimal solution 100 % receiving intervention 0 Budget (£million)

  9. Shadow Price of budget constraint £10500 / QALY Shadow Price (QALYs / £m) £42900 / QALY Budget (£million)

  10. Opportunity Loss of budget rules

  11. Opportunity Loss of budget rules

  12. Opportunity Loss of budget rules

  13. Indivisibility and horizontal equity • Optimum solution allows mixed treatment options for some patient groups • Requirement for horizontal equity is a constraint • Can explore the opportunity loss of this equity concern on one or more programmes or populations

  14. Indivisibility and horizontal equity

  15. Equity between populations • Usually acceptable to differentiate on basis of age • Other more controversial examples might be gender or social class

  16. Equity between populations

  17. Conclusions • What has been done? • Used linear programming to assist a policy-relevant decision • What does it show? • Shadow price varies with overall budget • The profile of cost over time is important • Different equity concerns have different implications for efficiency • Further work • Uncertainty • Fixed costs and other non-linear functions • Repeat decisions • Resource as well as budget constraints

  18. End of presentation

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