Quantitative Models in Life Science Business

The chapter describes value creation and valuation under structural uncertainty in the healthcare and pharma industries. These risks and uncertainties can significantly influence organizational performance, value creation and long-term sustainability. The discussion continues by comparing traditional valuation concepts used in finance with the requirements posed by the current situation of healthcare business. In particular, patent valuation is a critical business issue, and the value of pharma patents and licensing deals has risen markedly in recent years. Existing evaluation approaches do not consider a patent’s life cycle, an important and unique characteristic of pharma and biotech patents. For this reason, the inherent uncertainty in a patent’s value is modelled as a stochastic process.

We sketch a dynamic model of limited commercial licensing, also known as “compulsory licensing”, making use of the framework of piecewise-deterministic differential games. The framework features key ingredients, such as (i) The risk that a compulsory licensing will be issued; (ii) The lack of information available to player in terms of when and even whether the compulsory license will be issued. The setup can be used to tackle the important question about the beneficial and detrimental aspects of compulsory licensing.

Over the last decades the complexity of R &D processes in the pharmaceutical industry have resulted in a decline in the efficiency of those processes. Despite financial resources used in R &D have increased over time the number of drugs developed has remained almost constant. The phenomenon is known as “Eroom’s Law”. In order to start growing R &D efficiency again, the business models of companies were reviewed by mainly implementing open innovation models that can simplify and shorten the drug development process. Pharmaceutical companies are increasingly outsourcing activities from the external environment. The R &D tasks that firms choose to outsource include a wide spectrum of activities from basic research to late-stage development: genetic engineering, target validation, assay development, hit exploration and lead optimization (hit candidates-as-a-service), safety and efficacy tests in animal models, and clinical trials involving humans. Terms such as crowdsourcing, innovation centers, R &D collaboration, and open source are becoming more and more common in the sector. Almost all the Big Pharma are striving to create collaborative networks that might allow them to be more efficient. Pharmaceutical companies are called upon to make a “make or buy” decision to determine whether it is more convenient to outsource these activities rather than exploiting internal resources for generating innovation. In a global context in which the stochastic view has become more suitable for interpreting phenomena the aim of this kind of decision is mainly related to decrease uncertainty. The aim of the chapter is to explore this topic by also providing data and examples.

This chapter summarizes the overall tendering and contracting process in the pharmaceutical industry by providing an overview of the first-sealed price auction theory, auction rules, and drug pricing mechanism of different countries. Comparing procurement systems across Asia, Africa, Europe, and Latin America, the review casts light on various pharmaceutical bidding systems across the world and their impact on drug prices. Then, this review focuses on the empirical estimation of first-price auction models. In terms of model specification, we compare the two most commonly used empirical methods for bidding price estimation: structural models and reduced form approaches to test the auction theory. Maximum likelihood estimation is the most frequently used method for structural estimation in literature and selection bias correction is widely adopted using reduced form models. In addition to parametric model construction, we also provide an extensive introduction of non-parametric testing methodologies, including non-parametric estimation and quantile-based estimation to reduce the computation complexity and further illustrate how auction theory could be validated by real-world applications. Additional thoughts and adjustments on non-parametric testing are brought up based on a real-world tendering use case from a large multi-national pharmaceutical company.

In this chapter, we provide an overview of inventory management within the pharmaceutical industry and how to model and optimize it. Inventory management is a highly relevant topic, as it causes high costs such as holding, shortage, and reordering costs. Especially the event of a stock-out can cause damage that goes beyond monetary damage in the form of lost sales. To minimize those costs is the task of an optimized reorder policy. A reorder policy is optimal when it minimizes the accumulated cost in every situation. However, finding an optimal policy is not trivial. First, the problem is highly stochastic as we need to consider variable demands and lead times. Second, the supply chain consists of several warehouses incl. the factory, global distribution warehouses, and local affiliate warehouses, whereby the reorder policy of each warehouse has an impact on the optimal reorder policy of related warehouses. In this context, we discuss the concept of multi-echelon inventory optimization and a methodology that is capable of capturing both, the stochastic behavior of the environment and how it is impacted by the reorder policy: Markov decision processes (MDPs). On this basis, we introduce the concept, its related benefits and weaknesses of a methodology named Reinforcement Learning (RL). RL is capable of finding (near-) optimal (reorder) policies for MDPs. Furthermore, some simulation-based results and current research directions are presented.

An important problem in finance is the evaluation of the value in the future of assets (e.g., shares in company, currencies, derivatives, patents). The change of the values can be modeled with differential equations. Roughly speaking, a typical differential equation in finance has two components, one deterministic (e.g., rate of interest of bank accounts) and one stochastic (e.g., values of stocks) that is often related to the notion of Brownian motions. The solution of such a differential equation needs the evaluation of Riemann–Stieltjes’s integrals for the deterministic part and Ito’s integrals for the stochastic part. For A few types of such differential equations, it is possible to determine an exact solution, e.g., a geometric Brownian motion. On the other side for almost all stochastic differential equations we can only provide approximations of a solution. We present some numerical methods for solving stochastic differential equations.

A problem frequently encountered in point process modeling is that event times are usually not known. The only available information is the number of events over a given interval. Calculus and regularization present a convenient framework to perform inference in these circumstances through explicit formulas for this class of mixed doubly point processes. As an application, we present a novel way of dealing with uncertainties in the computation of disability-adjusted life year, which is a measure of overall disease burden in populations.