Optimal Design of a Pharmaceutical Price-Volume Agreement in the Presence of Random Demand and Unobservable Marketing Effort

Presenter: Hui Zhang, Lakehead University

Abstract

Third-party payers for drugs often make use of formularies, which are lists of drugs that they will reimburse. It is common for drug manufacturers to submit formulary applications that include arguments about a drug’s clinical effectiveness, cost effectiveness, and total budget impact. Once a drug is on a formulary, the payer may face unlimited liability for that drug because demand is determined by physicians and patients but not by the payer. If sales are higher than stated in the budget impact analysis included with the formulary application it is difficult for payers to determine whether this was due to random variation or aggressive marketing. A number of risk sharing mechanisms, such as price-volume agreements, have been developed to allow payers to manage some of the risk associated with unlimited liability. However, regulation of marketing is difficult because the level of marketing effort and the resulting effect on demand are unobservable to the payer, resulting in a moral hazard problem. In this paper we consider the optimal design of a price-volume agreement from the payer’s perspective in the presence of random demand and unobservable marketing. One form of the price-volume agreement specifies a volume threshold value. The manufacturer has to give a rebate to the payer if the actual sales exceed this threshold.

We formulate the problem as a principal-agent model. The payer, acting as the principal, seeks to design a price-volume agreement for a new drug. We assume that the payer seeks to maximize the total health benefit of all drugs purchased subject to constraints on budget and cost effectiveness, that the manufacturer seeks to maximize profits, and that both parties are risk neutral.

There is debate about whether pharmaceutical marketing is informative, providing patients and physicians with information to enable them to make better decisions, or persuasive, inducing patients or physicians to request unnecessary or ineffective medications. We consider both effects by modeling the drug’s average benefit per person as a quadratic function of the marketing effort.

We developed 3 sets of models to explore the marketing and the threshold decisions in this setting. These models differ regarding which decision-maker chooses the threshold decision and which constraints are included. We identify how unobservable marketing effort changes both parties’ decisions and their performance, how different constraints affect the optimal results, and how the party that sets the threshold changes the optimal decisions.

Our models lead to a number of interesting observations. First, persuasive marketing effort is often permitted by the payer. Second, informative marketing is not always encouraged. Third, the influence of moral hazard on marketing effort varies with the decision maker of the threshold. Fourth, the optimal threshold value deviates from the expected demand as for most cases. Fifth, it is possible that the payer induces the manufacturer to act in her best interest. Sixth, the authority over the threshold makes no difference without moral hazard; however, it does make difference with moral hazard. Finally, in the presence of moral hazard the first-best results can be achieved.