MODELLING A PAY-FOR-PERFORMANCE RISK SHARING AGREEMENT

Purpose: “Pay for performance” risk sharing schemes between drug manufacturers and third party payers are becoming increasingly common. We investigated the optimal decisions for a drug manufacturer that seeks formulary listing with a third party payer under a pay-for-performance contract.

Method: We modeled a risk sharing scheme where the rebate is a percentage of the total sales until an evaluation time. In particular, those who are responding to the drug at the evaluation time are eligible to continue receiving the drug and a rebate is paid for all other individuals. We assumed that the rebate rate is fixed and the evaluation time is subject to negotiation. We developed a basic disease progression model consisting of three states: “Sick”, “Responding to the drug” and “Progression of disease”. Patients move between these states with fixed transition rates. We modeled this movement with a system of linear differential equations and used this system to estimate the manufacturer’s profit and payer’s costs. We fit the model with data from a clinical trial for bortezomib, which has recently been subjected to a pay-for-performance risk sharing agreement in the UK.   

Result: For every rebate rate, the manufacturer can find an optimal evaluation time to maximize profits. The optimal evaluation time depends on the transition rates between health states. In general, if the rebate rate is greater than a threshold value, then the optimal evaluation time is early, and if the rebate rate is less than a threshold value the optimal evaluation time is late. In both instances, the actual value of the optimal evaluation time is highly dependent on the transition rate between the “Responding to the drug” and “Progression of disease” health states.

Conclusion: This work shows how a drug manufacturer can find an optimal evaluation time for every rebate rate and how the optimal decision is related to the transition rates between health states. It is important for payers to understand how manufacturers make their decisions so that they can optimally design performance-based risk sharing schemes.