Using ANCOVA when groups differ on the covariate

I am learning about analysis of covariance and have encountered seemingly conflicting information regarding the assumption that the predictor variable and covariate should be independent. This article says ANCOVA can be used to adjust for baseline imbalance in a randomized controlled trial, however doesn’t this suggest that the predictor variable and covariate are not independent? Is the difference here that the imbalance was not caused by analysing “naturalling occuring groups” but instead by random assignment?

This is actually a very deep subject but a fair simplification is to see that you don’t use ANCOVA for a randomized study to adjust for imbalance. You use it to account for outcome heterogeneity within a treatment group.

maybe youre confusing terminology? you mean outcome?

At first I thought I may have, but after re-reading the article, I don’t think so:

" Some use change scores to take account of chance imbalances at baseline between the treatment groups. However, analysing change does not control for baseline imbalance because of regression to the mean: baseline values are negatively correlated with change because patients with low scores at baseline generally improve more than those with high scores. A better approach is to use analysis of covariance (ANCOVA), which, despite its name, is a regression method."

“If, by chance, baseline scores are worse in the treatment group, the treatment effect will be underestimated by a follow up score analysis and overestimated by looking at change scores (because of regression to the mean). By contrast, analysis of covariance gives the same answer whether or not there is baseline imbalance.”

From these two excerpts it seems that the baseline score is treated as the covariate and the group assignment is the predictor variable?

it seems they dont use “predictor” in that article and, very roughly speaking, with RCT and biostats youll more often hear covariate, and with epidem and risk modelling it will be predictor. It would be quite presumptuous if a drug company referred to treatment assignment as a predictor. I only mention this because what you described sounded like Multicollinearity - Wikipedia. To answer your Q, I’d read the relevant section in stephen senn’s book, i believe a 3rd edition is out soon.