‘Covariate adjustment’ is a statistical analysis that uses baseline measurements about trial participants in a statistical model to give us a more accurate estimate of the treatment effect. Our work focuses on when, why and how to do covariate adjustment in randomised controlled trials.

What is covariate adjustment about and why is it relevant?

The simplest way to estimate the effect of a treatment in a randomised clinical trial (RCT) is to compare the average outcomes between groups or arms. This is valid if the RCT used simple randomisation. However, ‘valid’ does not mean ‘best’ for two reasons:

  1. It ignores the differences between patients, such as age, stage of disease, or baseline prognosis. Adjusting these ‘baseline covariates’ can help us to estimate a treatment effect more precisely by accounting for these differences between patients. This increases the statistical power of the analysis.
  2. In practice, clinical trials often use stratified block randomisation or minimisation to ensure that all arms have the same distribution of patient characteristics, such as age. These methods actively promote balance across arms. However, this makes the simple analysis that compares average outcomes statistically inaccurate. It is necessary to adjust our analysis for the covariates that were balanced across different arms.

What have we done?

Our work on covariate adjustment has:

  • Shown that covariate adjustment can increase power by over 15% in real trials, and shown that there is very little loss when we adjust for non-prognostic covariates
  • Explained why adjustment is necessary after stratified randomisation or minimisation
  • Identified how best to adjust for continuous covariates and covariates that are misclassified at randomisation
  • Reviewed the conduct and reporting of covariate adjustment, finding much room for improvement.

Trial statisticians need to be able to plan the analysis in detail before getting data. There is more than one way to adjust for covariates. Our work guides trial statisticians in how to choose an adjustment method and what to consider, starting with the estimand.

We have also:

  • Shown the remarkable robustness of analysis of covariance (ANCOVA) to choosing an imperfect statistical model
  • Explained that ‘canonical links’ are special
  • Contributed to understanding the properties of covariate adjustment in cluster-randomised trials.

Ongoing work includes a study of which methods of adjustment are robust and efficient when we group a continuous variable for randomisation, and accurate small-sample inference for estimators based on weighting.

How will this make a difference?

Our work shows that trialists can and should use covariate adjustment routinely to obtain more informative estimates of treatment effect. It also provides practical guidance on how covariate adjustment can be done in practice.