Efficient Study Design and Analysis of Longitudinal Dose–Response Data Using Fractional Polynomials

Abstract

ABSTRACTCorrectly characterising the dose–response relationship and taking the correct dose forward for further study is a critical part of the drug development process. We use optimal design theory to compare different designs and show that using longitudinal data from all available timepoints in a continuous‐time dose–response model can substantially increase the efficiency of estimation of the dose–response compared to a single timepoint model. We give theoretical results to calculate the efficiency gains for a large class of these models. For example, a linearly growing Emax dose–response in a population with a between/within‐patient variance ratio ranging from 0.1 to 1 measured at six visits can be estimated with between 1.43 and 2.22 times relative efficiency gain, or equivalently, with 30% to a 55% reduced sample size, compared to a single model of the final timepoint. Fractional polynomials are a flexible way to incorporate data from repeated measurements, increasing precision without imposing strong constraints. Longitudinal dose–response models using two fractional polynomial terms are robust to mis‐specification of the true longitudinal process while maintaining, often large, efficiency gains. These models have applications for characterising the dose–response at interim or final analyses.