StATS: Adjusting for a baseline measurement (February 28, 2005).

Someone asked me today about how to analyze a two group experiment with a baseline value. This is common research design. Researchers will assess all patients at the beginning of the study. They then randomly assign half of these patients to receive an intervention and half to be in a control group. Then they take a second measurement of the same outcome. The measurement at the beginning of the study, the baseline value, helps improve the research design by removing some of the variation in the data.

There are four common approaches for analyzing this data, two good and two bad. The first approach, and the one I like best, is to compute a change score and use that change score as the unit of analysis. The change score is simply the difference between the second measurement and the first. Change scores are very easy to interpret, because they represent how much someone changed or improved over time.

A second approach and one that I dislike is to ignore the baseline value. This throws away precision and should only be used if you can show that there is little or no correlation between baseline measurement and the subsequent measurement. If you collected the baseline data, it almost seems almost criminal to ignore it.

A third approach that I like well is to use the baseline value as a covariate in an analysis of covariance (ANCOVA) model. The ANCOVA model has greater flexibility than the change score approach, because it incorporates the change score as a special case. You can show without too much difficulty that if the slope for the baseline covariate is exactly equal to one, then the ANCOVA model is identical to the change score. You can also show that if the slope for the covariate is exactly equal to zero, that this is identical to ignoring the baseline value. Advocate for the ANCOVA model point out that this model makes the optimal adjustment unlike the change score model. I find the ANCOVA model a bit more difficult to interpret, but I still think it is a very good choice.

A fourth approach, and probably the worst approach, is to treat the baseline and subsequent measurements as repeated measures in a repeated measures analysis of variance ANOVA). This repeated measures ANOVA would show evidence of a intervention effect only if the treatment by time interaction is statistically significant. The model for the repeated measures ANOVA is difficult to set up and tricky to interpret.

Further reading

  1. Change scores as dependent variables in regression analysis. Allison P. Sociological methodology 1990: 20; 93-114.
  2. Case studies, single-subject research, and N of 1 randomized trials: comparisons and contrasts. Backman CL, Harris SR. Am J Phys Med Rehabil 1999: 78(2); 170-6. [Medline]
  3. Contrasting Split Plot and Repeated Measures Experiments and Analyses. Monlezun C, Blouin D, Malone L. The American Statistician 1984: 38(1); 21-27.
  4. Assessing change with longitudinal and clustered binary data. Neuhaus JM. Annu Rev Public Health 2001: 22; 115-28.
  5. Planning gorup sizes in clinical trials with a continuous outcome and repeated measures. Schouten H. Stats in Medicine 1999: 18(3); 255-64.
  6. Repeated measures in clinical trials: simple strategies for analysis using summary measures. Senn S. Statistics in Medicine 2000: 19; 861-877.
  7. The use of percentage change from baseline as an outcome in a controlled trial is statistically inefficient: a simulation study. Vickers AJ. BMC Med Res Methodol 2001: 1(1); 6. [Medline] [Abstract] [Full text] [PDF]
  8. Statistics notes: Analysing controlled trials with baseline and follow up measurements. Vickers AJ, Altman DG. Bmj 2001: 323(7321); 1123-4. [Medline] [Full text] [PDF]

Broken link (Reported August 30, 2007. I will try to fix this when I have time)

This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Covariate adjustment.