![]() 2, with its left-hand side showing the change score as the outcome measure. 1, with its left-hand side showing the post score as the outcome measure. In both of the preceding scenarios, the appropriate statistical analysis is ANCOVA adjusting for baseline scores. the treatment effect of acupuncture will be over-estimated. the treatment effect of acupuncture will be under-estimated.Ĭhange score: Acupuncture will appear to have a positive effect, even though it has no effect i.e. Post score: If post score is positively correlated with the baseline score (which is usually the case in clinical practice), acupuncture will appear to have a negative effect, even though it has no effect i.e. We consider two options of outcome measure: If, by chance, the baseline scores of the intervention group are lower than the scores of the general population, their post scores will still be higher than their baseline scores, due to RTM. Suppose that the baseline scores of the control group reflect the scores of the general population, and that acupuncture has no treatment effect. In the RCT example in, the treatment effect of acupuncture was measured by a 100-point rating score, where lower scores indicate poorer outcomes. If an extreme measure is observed at baseline, then its value is likely to be less extreme in the post-intervention measure, even if the intervention has no effect. In this paper, we consider RTM in the context of baseline measures. RTM has been discussed by a number of authors, e.g. RTM is a well-known statistical phenomenon, first discovered by Galton in. In practice, the estimated b in an ANCOVA is rarely equal to 1 hence, it is only a special case of ANCOVA. Baseline imbalance may occur in RCTs, and ANCOVA should be used to adjust for baseline in the analysis stage.Įquation 3 shows that using change score as outcome without adjusting for baseline is only equivalent to a standard ANCOVA when b = 1. We can then use the derived correlation to calculate the required sample size in the design stage. The correlation between baseline and post-intervention scores can be derived using the variance sum law. We show that these correlations also apply when comparing two measurement methods using Bland-Altman plots. 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 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. 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. ![]() We discuss the following correlations and provide the mathematical derivations in the Appendix:Ĭorrelation between change score and baseline scoreĬorrelation between change score and post scoreĬorrelation between change score and average score. 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. 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. ![]()
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