Optimal Enrollment in Late-Stage New Drug Development with Learning of Drug’s Efficacy for Group-Sequential Clinical Trials

Problem definition: The cost for developing a new drug ranged from $1 billion to more than $2 billion between 2010 and 2019. In addition to high development costs, the efficacy of the candidate drug, patient enrollment, the market exclusivity period (MEP), and the planning horizon are uncertain. Moreover, slow enrollment leads to increased costs, canceled clinical trials, and lost potential revenue. Many firms, hoping to detect efficacy versus futility of the candidate drug early to save development costs, plan interim analyses of patient-response data in their clinical trials. Academic/practical relevance: The problem for optimizing patient-enrollment rates has an uncertain planning horizon. We developed a continuous-time dynamic programming (DP) model with learning of a drug’s efficacy and MEP to assist firms in developing optimal enrollment policies in their clinical trials. We also established the optimality equation for this DP model. Through a clinical trial for testing a cancer drug developed by a leading pharmaceutical firm, we demonstrate that our DP model can help firms effectively manage their trials with a sizable profit gain (as large as $270 million per drug). Firms can also use our model in simulation to select their trial design parameters (e.g., the sample sizes of interim analyses). Methodology: We update a drug’s efficacy by Bayes’ rules. Using the stochastic order and the likelihood-ratio order of distribution functions, we prove the monotonic properties of the value function and an optimal policy. Results: We established that the value of the drug-development project increases as the average response from patients using the candidate drug increases. For drugs having low annual revenue or a strong market brand or treating rare diseases, we also established that the optimal enrollment policy is monotonic in the average patient response. Moreover, the optimal enrollment rate increases as the variance of the MEP decreases. Managerial implications: Firms can use the properties of the value function to select late-stage clinical trials for their drug-development project portfolios. Firms can also use our optimal policy to guide patient recruitment in their clinical trials considering competition from other drugs in the marketplace. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.1162 .