Stratification in Randomised Clinical Trials for Rare Diseases and Analysis of Covariance: Some Simple Theory and Recommendations

TL;DR

This paper discusses how to best incorporate continuous covariates in stratified randomised clinical trials for rare diseases, providing simple theoretical guidance on model choice and recommending including the covariate in the analysis.

Contribution

It offers a straightforward theoretical framework for understanding the effects of including covariates and stratum indicators in treatment effect models, with practical recommendations.

Findings

Including the covariate improves model accuracy.

Adding the stratum indicator can sometimes be justified.

Guidance on variance inflation and model selection.

Abstract

A simple device for balancing for a continuous covariate in clinical trials is to stratify by whether the covariate is above or below some target value, typically the predicted median. This raises an issue as to which model should be used for modelling the effect of treatment on the outcome variable, $Y$. Should one fit, the stratum indicator, $S$, the continuous covariate, $X$, both or neither? When a covariate is added to a linear model there are three consequences for inference: 1) the mean square error effect, 2) the variance inflation factor and 3) second order precision. We consider that it is valuable to consider these three factors separately, even if, ultimately, it is their joint effect that matters. We present some simple theory, concentrating in particular on the variance inflation factor, that may be used to guide trialists in their choice of model. We also consider the case where the precise form of the relationship between the outcome and the covariate is not known. We conclude by recommending that the continuous covariate should always be in the model but that, depending on circumstances, there may be some justification in fitting the stratum indicator also.