O.R. Applications
Models and software for improving the profitability of pharmaceutical research

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Abstract

The pharmaceutical industry is highly competitive, and the discovery and development of new drugs is extremely expensive and time consuming. This paper is a contribution to the task of improving the effectiveness of pre-clinical research. Our model investigates for any given project the number of lead series which should if necessary be optimised in the search for a development compound which is sufficiently promising to proceed to clinical trials. The numbers of scientists which should be allocated to each research stage are also investigated. Two widely-applied profitability criteria are considered. Computer software designed to implement the optimisation calculations is described and shown to produce reasonable results, leading to a potentially dramatic improvement in profitability.

Introduction

Pharmaceutical companies require great patience and enormous capital. It typically takes 12–15 years to successfully complete the research and development (R&D) process of a new drug, with probability of success less than 20%, while the combined cost of R&D and market introduction for a significant product today exceeds £700 million (Chen, 2004). For these reasons, bringing research projects to an early successful conclusion gives an important competitive advantage.

There is a substantial literature, some of it specific to the pharmaceutical industry, on criteria for project selection and resource allocation in R&D. These range from simple check-lists to sophisticated pharmacoeconomic analysis. The journals R&D Management and Pharmacoeconomics are good general sources, see for example the review papers by Miller, 2005, Poh et al., 2001. The earlier literature is reviewed by Bergman and Gittins (1985).

The model discussed in this paper is a stochastic economic model. There are three important themes with a bearing on models of this type, as follows:

  • The methodology of decision analysis. This has been around since the 1960s. Key ingredients are personal probabilities, utility functions, sequential decisions expressed as a decision tree, and solution by a dynamic programming algorithm. McNamee and Celona (1990) have written a useful handbook, and Lindley (1991) gives a good introduction to the main ideas.

  • Real options. Black and Scholes (1973) provided a methodology for valuing financial options. Others, notably Dixit and Pindyck (1994), have pointed out that a similar analysis is possible for options to invest in specific projects.

  • Pharmacoeconomics. This is the science of relating the costs and benefits, both to individuals and to society, of therapeutic regimes, including drugs. Analysis along these lines is becoming routine in the planning of clinical trials. The journal Pharmacoeconomics started in 1983.

The insight from financial options theory that the ability to postpone, and possibly eventually not take up, an investment opportunity can strongly influence its value has been important, see for example Burman and Senn, 2003, Chen, 2004, Perlitz et al., 1999. However, the match between financial and real options is far from exact, and current economic approaches to pharmaceutical project planning tend to owe more to decision analysis than to real options theory. The papers by Stonebraker, 2002, Ding and Eliashberg, 2002, Loch and Bode-Greuel, 2001 are good examples.

All these papers focus at least as much on development as on pre-clinical research, and so far as the authors are aware we have modelled the pre-clinical stages of research, in discussion with people working in the industry, in a much more detailed fashion than is to be found elsewhere. This is borne out by the comment in Miller (2005) that there is currently very little pharmacoeconomic planning in the early stages of research. Islei et al. (1991) have written an important paper describing a planning system for those early stages. However, it does not include an economic model.

Section 2 describes what happens in pre-clinical pharmaceutical research. Section 3 describes our model and the OPRRA (Optimal Pharmaceutical Research Resource Allocation) software. Section 4 sets out the details of some of the optimality calculations, with further details in an appendix. Section 5 discusses some numerical examples which show that large increases in profitability may well be possible. Brief concluding comments including plans for further work are given in Section 6.

Section snippets

The setting

Until the mid 1990s most pharmaceutical research projects proceeded in the following sequence. Bioscientists first work out an hypothesis for the way in which a chemical intervention in the body’s processes might achieve the desired result. Then bioscientists and chemists devise tests using animal tissue or live animals in order to screen compounds for relevant activity. Afterwards, chemists synthesise compounds designed in the hope of finding relevant activity. These are then subject to a

Project stages

The purpose of this paper is to extend the model so as to include the possibility, which very frequently occurs in practice, of looking for two or more lead compounds with distinct characteristics, each of which serves as the starting point for a lead series (LS) from which development compounds (DCs) may be chosen. To avoid a more complicated discussion we restrict attention in this paper to cases for which DCs are selected from at most two LSs. We consider a five-stage model for a discovery

Total expected reward, total expected cost, and optimisation calculations

This section gives an account of some of the calculations carried out by OPRRA. To calculate the total expected reward we need to add the expected values of successive development compounds, taking account of discounting and obsolescence. For total expected cost we need to add the expected numbers of discounted scientist-years for each stage These calculations are quite complex. In this section we give details for (m, l) = (m, 0). Expressions for (m, l) = (m, 1) and (m, l) = (m, 2) are listed in an

Examples

The parameter values and initial allocations mentioned in this section are based on discussion with colleagues in the pharmaceutical industry. They are realistic, but do not correspond to specific current projects.

The input variables (see Section 3) were set as follows:

  • (p1, p2, p4) = (0.3, 0.3, 0.5), (0.3, 0.5, 0.7), (0.5, 0.5, 0.5), and (0.5, 0.7, 0.7). In the output listings these 4 cases are identified by the short-hand notation p124 = 335, 357, 555, and 577.

  • γ = 0.09, corresponding to an annual cost of

Conclusion

In this paper, a mathematical model and corresponding software for improving the profitability of a pharmaceutical research project are described using both the profitability index and the internal rate of return criteria. It improves upon previous versions of the model by incorporating the possibility of following more than one lead series of active compounds. The optimal numbers of scientists to be allocated to each research stage and the optimal number of backup compounds to be identified

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