Mathematical Modeling and Pharmaceutical Pricing: Analyses Used to

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Abstract. In the face of significant real healthcare cost inflation, pressured budgets, and ongoing launches of myriad technology of uncertain value, payers have formalized new valuation techniques that represent a barrier to entry for drugs. Cost-effectiveness analysis predominates among these methods, which involves differencing a new technological intervention’s marginal costs and benefits with a comparator’s, and comparing the resulting ratio to a payer’s willingness-to-pay threshold. In this paper we describe how firms are able to model the feasible range of future product prices when making in-licensing and developmental Go/No-Go decisions by considering payers’ use of the costeffectiveness method. We illustrate this analytic method with a simple deterministic example and then incorporate stochastic assumptions using both analytic and simulation methods. Using this strategic approach, firms may reduce product development and in-licensing risk. Keywords: pharmaceutical pricing, R&D investment decision-making, cost-effectiveness analysis, mathematical modeling 1. Introduction

Developmental and in-licensing decision-making in the pharmaceutical, biotechnology, and medical device industries is
fraught with uncertainty and complexity, arguably unparalleled in modern corporate experience. The costs and rewards
balanced upon these decisions, including make-buy determinations about potential compounds that are likely years away
from reaching the marketplace, if ever launched, are enormous. Previous analyses of drug development decisions have
sought to decompose the uncertainty in predicting net present value (NPV) [1]. Not surprisingly, the future price a product will support is a primary driver of variability in its expected NPV. Because of the important role pricing plays, firm research efforts to reduce price-related uncertainty increase as

the product moves through the developmental pipeline. This
process often exceeds a decade, beginning with drug discovery in pre-clinical trials, moving through phases I, II, and III, and ending with regulatory and payer approval and product
launch. As a drug advances in development, the information
stock available to the firm regarding its potential therapeutic and economic benefits builds, allowing the firm to better model its future price.
Moreover, the value to the firm of conducting prospective
pricing analyses has been enhanced considerably in recent
years by the proliferation of explicit reimbursement regulations throughout an increasingly cost-minimizing set of payers. As these payers attempt to limit new medical technology’s contribution to inflation of their healthcare spending, they have developed a set of valuation mechanisms used for product review

after the drug has been determined to be safe and at least minimally efficacious by appropriate regulatory authorities.1 For
example, the National Institute for Clinical Excellence (NICE), a department created by the United Kingdom’s National Health Service in 1999, conducts rigorous economic studies of new
drugs and other medical technologies to determine if they warrant government coverage and reimbursement [2]. In this paper,
we review the payers’ valuation methods and demonstrate the value to the manufacturer of incorporating them into the firm’s decision-making. This process can inform manufacturer decisions regarding developmental and in-licensing products by

forecasting the price ranges payers will be willing to pay.
In competitive markets, price is set based on the elasticity of demand and the marginal cost of production; however, pharmaceutical payers behave as monopsonists, singly negotiating access
and price with manufacturers. International payers such as
government health ministries consider price and willingnessto- pay in social terms, theoretically determining these monetary values based on an objective function that maximizes
societal well-being. Manufacturers consider these values to
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