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Pharmaceutical companies have to face huge risks and enormous costs of production before they can produce a drug. Efficient allocation of resources is essential to help in maximizing profits. Chen [14] and Yu and Gittins [66] describe a stochastic optimisation model (the OPRRAa model) and associated software for determining efficient allocations for a pre-clinical research project. This is the starting point for this thesis. We first look for the nature of optimal policies for the selection of successive candidate drugs using two restricted versions of the OPRRAa model, and investigate how these depend on the model parameters. To some extent these results are likely to be applicable to the OPRRAa model. We then extend the OPRRAa model by introducing further modelling for stages and incorporating feedback from clinical trials to update the success probabilities for the corresponding stages using a hierarchical Bayes setting. Computer software has been written to implement the optimisation calculations. We show that very large improvements in profitability are possible in realistic cases.

Current practice for sample size computations in clinical trials is largely based on frequentist or classical methods. These methods have the drawback of requiring a point estimate of the variance of treatment effect and are based on arbitrary settings of type I and II errors. They also do not directly address the question of achieving the best balance between the costs of the trial and the possible benefits by using a new medical treatment, and fail to consider the important fact that the number of users depends on evidence for improvement compared with the current treatment.A novel Bayesian approach, Behavioral Bayes (or BeBay for short) (Gittins and Pezeshk, 2000a,b, 2002a,b; Pezeshk, 2003), assumes that the number of patients switching to the new treatment depends on the strength of the evidence which is provided by clinical trials, and takes a value between zero and the number of potential patients in the country. The better a new treatment, the more patients switch to it and the more the resulting benefit. The model defines the optimal sample size to be the sample size that maximises the expected net benefit resulting from a clinical trial. Gittins and Pezeshk use a simple form of benefit function for paired comparisons between two medical treatments and assume that the variance of the efficacy is known.The research in this thesis generalises these original conditions by introducing a logistic benefit function to take account of differences in efficacy and safety between two drugs. The model is also extended to the more general cases of unpaired comparisons and unknown variance. The expected net benefit defined by Gittins and Pezeshk is based on the efficacy of the new drug only. It does not consider the incidence of adverse reactions and their effect on patients’ preferences. Here we include the costs of treating adverse reactions and calculate the total benefit in terms of how much the new drug can reduce societal expenditure.We describe how our model may be used for the design of phase III clinical trials, cluster randomised clinical trials and bridging studies. This is done in some detail and using illustrative examples based on published studies. For phase III trials we allow the possibility of unequal treatment group sizes, which often occur in practice. Bridging studies are those carried out to extend the range of applicability of an established drug, for example to new ethnic groups. Throughout the objective of our procedures is to optimise the costbenefit in terms of national health-care. BeBay is the leading methodology for determining sample sizes on this basis. It explicitly takes account of the roles of three decision makers, namely patients and doctors, pharmaceutical companies and the health authority.

Pharmaceutical R&D; is time-consuming, extremely costly and involves great uncertainty. Although there is a broad range of literature on statistical issues in clinical trials, there is not much that focuses directly on the modelling of pre-clinical research.This thesis investigates models and associated software for improving decisionmaking in this area, building on earlier work by the same research group. We introduce a class of adaptive policies called forwards induction policies for candidate drug selection, and show that these are optimal, with a straightforward solution algorithm, within a restricted setting, and are usually close to optimal more generally. We also introduce an adaptive probabilities model that allows the incorporation of learning from a project’s progress into the planning process. Real options analysis in the evaluation of project value is discussed. Specifically, we consider the option value of investing in clinical trials once a candidate drug emerges from pre-clinical research. Simulation algorithms are developed to investigate the probability distributions of the total reward, total cost, profitability index and the required future resource allocations of a pharmaceutical project under a given allocation plan. The ability to simulate outcome distributionsmeans that we can also compare the riskiness of different projects and portfolios of projects.