A mathematical model for maximizing the value of phase 3 drug development portfolios incorporating budget constraints and risk

Abstract

We describe a value-driven approach to optimizing pharmaceutical portfolios. Our approach incorporates inputs from research and development and commercial functions by simultaneously addressing internal and external factors. This approach differentiates itself from current practices in that it recognizes the impact of study design parameters, sample size in particular, on the portfolio value. We develop an integer programming (IP) model as the basis for Bayesian decision analysis to optimize phase 3 development portfolios using expected net present value as the criterion. We show how this framework can be used to determine optimal sample sizes and trial schedules to maximize the value of a portfolio under budget constraints. We then illustrate the remarkable flexibility of the IP model to answer a variety of 'what-if' questions that reflect situations that arise in practice. We extend the IP model to a stochastic IP model to incorporate uncertainty in the availability of drugs from earlier development phases for phase 3 development in the future. We show how to use stochastic IP to re-optimize the portfolio development strategy over time as new information accumulates and budget changes occur.

Utility‐based optimization of phase II/III programs

“…One way of determining an optimal design is by maximizing the expected value of a pre‐specified utility function, which includes both costs and future revenue (gain) usually expressed in the same unit like a monetary one . This corresponds to considering the expected net present value (NPV), which is the NPV weighted by development risks . Thus, three key components for assessing the value of pharmaceutical products, namely, expected costs, expected revenue, and probability of success of the drug development process , are combined in the expected utility.…”

Decision-theoretic designs for small trials and pilot studies: A review

“…Twenty-seven articles 18 – 44 specifically described methods in pilot or phase II settings. The others 14 , 45 – 83 did not describe methods specific to small clinical trials or pilot studies, but would nevertheless be appropriate in this setting.…”

“…Some articles extend the multi-stage designs for single-arm trials or two-arm comparative trials to seek optimal multi-arm designs. Such a problem is considered by Chen and Beckman, 20 Lai et al., 26 Palmer, 29 Patel and Ankolekar, 71 Patel et al., 72 Stallard et al. 35 and Thall et al.…”

“…The objective of the designs considered by Patel and Ankolekar 71 and Patel et al. 72 is to maximize the expected profit from a portfolio of treatments while incurring the costs of running the trials within the given budget. An optimal size is obtained for each treatment (each trial) and the trials may run concurrently.…”

Decision-making in product portfolios of pharmaceutical research and development – managing streams of innovation in highly regulated markets

“… 25 A mathematical framework with a value-driven approach to optimizing pharmaceutical portfolios should be used to determine optimum sample sizes and trial schedules to maximize the value of a portfolio under budgetary constraints. 26 The same model can be used to answer a variety of “what if” questions that reflect situations that arise in practice. This is extremely important, not least because financial issues pose one of the biggest challenges to drug development.…”