The correlation between baseline score and post-intervention score, and its implications for statistical analysis

Background When using a continuous outcome measure in a randomised controlled trial (RCT), the baseline score should be measured in addition to the post-intervention score, and it should be analysed using the appropriate statistical analysis. Methods We derive the correlation between the change score and baseline score and show that there is always a correlation (usually negative) between the change score and baseline score. We discuss the following correlations and provide the mathematical derivations in the Appendix: Correlation between change score and baseline score Correlation between change score and post score Correlation between change score and average score. The setting here is a parallel, two-arm RCT, but the method discussed in this paper is applicable for any studies or trials that have a continuous outcome measure; it is not restricted to RCTs. Results We show that using the change score as the outcome measure does not address the problem of regression to the mean, nor does it take account of the baseline imbalance. Whether the outcome is change score or post score, one should always adjust for baseline using analysis of covariance (ANCOVA); otherwise, the estimated treat effect may be biased. We show that these correlations also apply when comparing two measurement methods using Bland-Altman plots. Conclusions The correlation between baseline and post-intervention scores can be derived using the variance sum law. We can then use the derived correlation to calculate the required sample size in the design stage. Baseline imbalance may occur in RCTs, and ANCOVA should be used to adjust for baseline in the analysis stage.