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

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

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

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

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

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

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

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

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

10. Opportunity Loss of budget rules Budget rule Health gain (QALY) Opp Loss (QALY) Budget spent No constraint 73170£180m

11. Opportunity Loss of budget rules Budget rule Health gain (QALY) Opp Loss (QALY) Budget spent No constraint 73170£180m Equal phasing 35863731£103m

12. Opportunity Loss of budget rules Budget rule Health gain (QALY) Opp Loss (QALY) Budget spent No constraint 73170£180m Equal phasing 35863731£103m All in 1 st 5 years 48792438£75m

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

14. Indivisibility and horizontal equity Health gain (QALY) Opp. Loss (QALY) No equity constraint 35860 Equity popn. 1 (type 1 diabetes) 3066520 Equity popn. 2 (age<60, lymphoma) 354719 Equity popn 1 and popn 2 3066520

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

16. Equity between populations Health gain (QALY) Opp. Loss No equity constraint35860 Equity: programme 1 (lymphoma: older = younger) 35797 Equity: programme 2 (diabetes: type 1 = type 2) 3126460 Equity prog 1 and prog 23122464

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

18. End of presentation