KNOWLEDGE / Publication / POST
October 26, 2021

Scientific Poster presented on October 2021 at the Annual Meeting of the Royal Statistical Society of Belgium.

The amount of data collected from patients involved in clinical trials is continuouslygrowing. All baseline patient characteristics are potential covariates that could be used to improve clinical trial analysis and power. However, the limited number of patients in phases I and II studies restricts the possible number of covariates included in the analyses. Indeed, regression adjustment is a trade-off between explained variance and loss of degrees of freedom. There are many rules-of-thumb on the number of covariates that can be included in an analysis1. To the best of our knowledge, none of them balances explained variance and degrees of freedom. With this work, we answer the question of the number of covariates (p) while focusing on the precision of the estimated treatment effect in an ANCOVA. Our result for the maximum number of covariates is a simple closed-form formula, p <(n−g−1)νp, combining the number of patients (n) and study groups (g) with the variance explained by the covariates (νp). Assuming data of previous studies to be available, we show how to further improve the study power by fitting the covariates weights a priori. Similarly, a composite covariate is fitted on previous data and replaces the individual covariates in the treatment effect estimation. The composite covariate approach is already used in practice, e.g. through prognostic indexes. Here, we investigate the use composite covariates specifically to optimize the precision of the treatment effect estimation. Using a composite covariate allows to trade some explained variance to avoid the loss in degrees of freedom. The associated gain is particularly relevant when the sample size is small and the number of covariates is large. Considering the recent advances in placebo effect characterization2 , the composite covariate approach could have a major impact on future RCTs by disentangling the placebo response from the actual treatment efficacy. The placebo effect is a complex phenomenon, individual-dependent with components linked to the subject’s demography, psychology, sociology and disease intensity. This highly multivariate aspect of the placebo makes any adjustment difficult. The composite covariate approach is one way to overcome the problem. We demonstrate its applicability and benefits in this context on a phase II study studying the effect of an intra-articular injection on patient suffering from painful osteoarthritis (OA) of the knee.


1 Austin PC and Steyerberg EW. The number of subjects per variable required inlinear regression analyses.Journal of Clinical Epidemiology2015; 68(6): 627–636.DOI:10.1016/j.jclinepi.2014.12.014.

2 Horing B, Weimer K, Muth ER et al. Prediction of placebo responses: a sys-tematic review of the literature.Frontiers in psychology2014; 5(October): 1079.DOI:10.3389/fpsyg.2014.01079.

Scientific Poster
Samuel Branders, Alvaro Pereira, Guillaume Bernard,Marie Ernst, Adelin Albert
October 21, 2021
Royal Statistical Society of Belgium

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