Baseline adjustment and ANCOVA
What question does this help answer?
Whether groups differ at follow-up, having accounted for where each participant started.
Three ways to analyse the same trial
Comparing follow-up values alone ignores baseline information. Comparing change scores uses it, but imposes a coefficient of exactly 1 on baseline, which is rarely the best fit. ANCOVA estimates that coefficient from the data and is at least as precise as either, usually more so. In a randomized trial with a baseline correlation of 0.5, the gain in precision is substantial and free.
Regression to the mean is why change scores mislead
If people are selected or grouped by an extreme baseline value, their next measurement will tend to be less extreme for purely statistical reasons. A change score analysis in that setting attributes the movement to the intervention. ANCOVA is not immune to this either, which is why the selection matters as much as the model.
Key requirements
- Baseline is measured before assignment, so it cannot have been affected by it.
- The relationship between baseline and outcome is approximately linear, or is modelled flexibly if not.
- The adjustment is prespecified, since choosing covariates after seeing the result is a form of multiplicity.
- Percentage change from baseline is avoided: it is unstable when baseline values are near zero and its distribution is awkward.
- In a nonrandomized comparison, the causal role of the baseline value is thought through rather than assumed benign.
Why Mallard may recommend it
Mallard may name ANCOVA whenever a continuous outcome is measured both before and after, which covers most trials of a symptom score, a physiological measure or a quality-of-life instrument.
What to watch out for
Analysing the CHANGE from baseline is the intuitive approach and the weaker one: it is less precise than adjusting for baseline, and in a nonrandomized comparison it does not remove the bias people expect it to remove. Adjusting for baseline is legitimate in a randomized trial precisely because randomization makes baseline independent of assignment; in an observational study, adjusting for a baseline value that lies on the causal path can create bias rather than remove it.
Clinical example
Question: Does a rehabilitation programme improve six-minute walk distance? Analysis: Regress the 12-week distance on treatment group and baseline distance, reporting the adjusted mean difference rather than the difference in change scores.
- Statistics notes: Analysing controlled trials with baseline and follow up measurements (opens in a new tab) · BMJ · doi 10.1136/bmj.323.7321.1123
- T test as a parametric statistic (opens in a new tab) · Korean J Anesthesiol · doi 10.4097/kjae.2015.68.6.540