Suppose I am analyzing a randomized controlled trial with a pre-post design, and I want to estimate the effect of a treatment on a continuous outcome variable. According to this paper by Twisk et al. (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5898524/), because of regression to the mean, the group with the highest baseline value will on average be expected to decrease slightly, and conversely, the group with the lowest value will be expected to increase slightly. For this reason, they claim that simply comparing differences in change scores without adjusting for baseline can give biased estimates of the treatment effect.

I understand that adjusting for the baseline value increases the precision of the treatment estimate, and that it is therefore recommended to do so. However, I am a little confused by claim of bias. If we sampled from the underlying population infinitely many times, would not the difference in change scores approach the same value as the adjusted difference? If yes, does this not mean that it is an unbiased (albeit less percise) estimator of the treatment effect?


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