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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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