A flexible framework for treatment effect inference in longitudinal clinical studies with skewed outcomes

Abstract

Longitudinal continuous outcomes in clinical trials are commonly analyzed using mixed models for repeated measures (MMRM) under normality assumptions. However, many clinical outcomes are skewed, making mean-based treatment effects difficult to interpret and potentially reducing statistical efficiency. The Box--Cox MMRM (BCMMRM) approach accommodates skewness by enabling inference on model-based median differences via inverse transformation. However, BCMMRM typically assumes a common transformation parameter across treatment groups and time points. When distributional shapes differ between groups or evolve over time, this assumption may lead to biased treatment effect. Furthermore, when treatment affects not only central tendency but also distributional shape or tail behavior, treatment effects may not be adequately characterized by a single location summary such as the median. We propose the Box--Cox multivariate regression (BCMVR) framework for longitudinal data with skewed outcomes. BCMVR relaxes this restriction by allowing transformation parameters to vary across groups and time points. The framework enables inference based on interpretable summaries, including median differences and a probability-based treatment effect quantifying the probability that a randomly selected patient in one group has a better outcome than one in another group. This measure integrates information over the entire outcome distribution and provides a complementary summary when distributional shapes differ. Simulation studies demonstrate that BCMMRM can produce biased estimates when distributions differ in shape, whereas BCMVR provides nearly unbiased estimation. The probability-based measure achieves a favorable balance between robustness and statistical efficiency. The proposed framework provides a flexible and interpretable approach to treatment effect inference under distributional heterogeneity.