Abstract
Clinical trial planning of candidate drugs is an important task for pharmaceutical companies. In this paper, we propose two new multistage stochastic programming formulations (CM1 and CM2) to determine the optimal clinical trial plan under uncertainty. Decisions of a clinical trial plan include which clinical trials to start and their start times. Its objective is to maximize expected net present value of the entire clinical trial plan. Outcome of a clinical trial is uncertain, i.e., whether a potential drug successfully completes a clinical trial is not known until the clinical trial is completed. This uncertainty is modeled using an endogenous uncertain parameter in CM1 and CM2. The main difference between CM1 and CM2 is an additional binary variable, which tracks both start and end time points of clinical trials in CM2. We compare the sizes and solution times of CM1 and CM2 with each other and with a previously developed formulation (CM3) using different instances of clinical trial planning problem. The results reveal that the solution times of CM1 and CM2 are similar to each other and are up to two orders of magnitude shorter compared to CM3 for all instances considered. In general, the root relaxation problems of CM1 and CM2 took shorter to solve, CM1 and CM2 yielded tight initial gaps, and the solver required fewer branches for convergence to the optimum for CM1 and CM2.
Highlights
Pharmaceutical industry is a global business with over one trillion U.S dollars per year market with extensive supply chains throughout the world [1]
The proposed binary variables in CM1 and CM2 contribute to shorter root relaxation solution times and generate tighter initial gaps
For all formulations, we found that the root relaxation solution time and number of branches have stronger impact on solution time than initial gap
Summary
Pharmaceutical industry is a global business with over one trillion U.S dollars per year market with extensive supply chains throughout the world [1]. To avoid making decisions that anticipate the values of uncertain parameters that have not been realized, a set of constraints, called non-anticipativity constraints (NACs), are introduced to MSSPs. Multistage stochastic programming is a scenario-based approach that considers recourse actions in multiple stages after realization of uncertainty. There have been a number of studies that introduced stochastic programing models for solving pharmaceutical clinical trial planning problem. No recent literature studied the impact of different decision variable definitions and corresponding sequencing and non-anticipativity constraints on the size and solution times of the resulting MSSP formulations constructed for clinical trial planning. The second formulation, CM2, introduces an additional binary variable, which tracks both start and end time points of a clinical trial We applied both formulations to solve 42 instances of clinical trial planning problem [16].
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