Some Notes on Adjustment for Covariates

Abstract

In randomized clinical trials, continuous outcome measures are often used as end-points. For qualitative covariates associated with the primary endpoint, stratified randomization is frequently used in order to ensure balance between treatment groups. Quantitative covariates associated with the primary endpoint are also frequently pre-specified. "Points to Consider on Adjustment for Baseline Covariates" (2003) strongly recommends analysis of covariance (ANCOVA) as a primary analysis for such trials to improve the precision and compensate for imbalance. This paper also recommends ANCOVA, but also accepts the two sample t-test under a small loss of precision and unlikely imbalances of covariates. Interactions between treatment group and covariates will not be generally included in the primary analysis model. Even if they exist, differences between least square means estimated by the ANCOVA model without interactions and differences between arithmetic means of treatment groups are equal in expectation under several assumptions. Therefore, it can be said the ANCOVA without interactions is better than the usual t-test in precision. An example of the preferred way to show ANCOVA results is given. Also the interpretation of least square mean is briefly discussed.