In a typical single-payer setting that uses an explicit cost-effectiveness (CE) threshold in its decision-making, the payer aims to maximize the net-monetary-benefit (NMB) given the CE threshold, whilst the manufacturer aims to maximize the expected discounted-cash-flow (DCF) resulting from the sales of that technology. Managed entry agreements (MEAs) are tools that are used to improve access to expensive technologies that would otherwise not be deemed to be cost-effective to payers. While simple discount on the list price is the most commonly applied MEA type, there are different forms, each having a different impact on the cost-effectiveness of the technology, on the lifetime DCF-per-patient and on the decision uncertainty. We aim to analyze the sequential decision-making (SDM) of different MEAs (i.e. simple discount, free treatment initiation, lifetime treatment acquisition cost-capping [LTTACC], performance-based money-back guarantee [MBG]) at the manufacturer and at the payer level, respectively. We first model the SDM of the manufacturer and the payer as a sequential game and explain the challenges to find an equilibrium analytically. Then we propose a heuristic computational method to follow for each of the MEA types, based on practice. To demonstrate this SDM on a case study, a UK-based cost-utility analysis using a three-state, partitioned-survival-model was constructed to determine the cost-effectiveness of regorafenib versus best-supportive-care for the second-line treatment of hepatocellular carcinoma. The optimal agreement terms that would maximise the lifetime DCF-per-patient for each MEA, whilst remaining below the CE-threshold (£50,000/QALY gained) were obtained in the deterministic base-case. Robustness for each optimized MEA was then assessed using probabilistic sensitivity and scenario analyses, the value of information (VoI), and HTA-risk analyses. As expected, the introduction of all MEAs improved the probabilistic ICER and NMB values to (almost) acceptable levels, compared to the "no-MEA" case (ICER ~ £78,000/QALY-gained). The expected DCFs across the explored MEAs were all similar, whilst the payer strategy & uncertainty burden (PSUB) for regorafenib decreased in all MEAs explored. VoI analyses revealed that regorafenib mean-dose-intensity and time-on-treatment (ToT) parameters attributed most to the decision uncertainty. LTTACC provided the smallest PSUB and the most robust NMB estimates under parametric uncertainty. For scenarios assuming increased regorafenib ToT or mean-dose-intensity, LTACC again provided acceptable cost-effectiveness outcomes, whereas for scenarios assuming decreased regorafenib progression-free/overall survival effectiveness, only MBG resulted in plausible ICER values. In scenarios, where the source of uncertainty was not targeted by MEA parameters (e.g. the scenario assuming higher progressed disease resource utilization), all investigated MEA types resulted in unacceptable cost-effectiveness outcomes. Each MEA type has a different implication. The impact of different MEAs on the NMB is more noteworthy than on the DCF, in relative terms, hence payers will benefit from the early participation of the MEA design rather than leaving this up to the prerogative of the manufacturer. While simple discount might be practical for implementation purposes, other MEAs can provide additional benefits to the payer in terms of increased NMB, reduced decision risk and reduced uncertainty. MEA performance should be investigated not only under parametric uncertainty, but also under-identified structural uncertainty, and the barriers of implementation should be considered thoroughly before choosing the most appropriate MEA type.
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