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Suppose we have a naïve single-arm pretest-posttest design without any control group. Every subject has a pretest score and a posttest score. If we want to determine whether there is a significant difference between the means of pretest and posttest and how large the difference (or effect size) is, we can carry out a paired t-test. However, there are other confounding variables, such as gender and age. How can we control them?

I come up with three models:

  1. Transform pretest and posttest into a factor test (with pre and post as its possible values) and a continuous variable score (transform the wide data into long data). Then build the mixed-effects model score ~ test + gender + age + (1 | subject). If we omit the gender and age terms, the result (slope of test) will exactly be the same as the result of a paired t-test (see Paired data comparison: regression or paired t-test?).
  2. Treat posttest as the response variable and pretest as a covariate. Build the model posttest ~ pretest + gender + age (see Repeated measure t test with covariates in R). If we have both a treatment group and a control group, and we want to measure the treatment effect, this (posttest ~ treatment + pretest + gender + age) will be the preferred way to build models (see Best practice when analysing pre-post treatment-control designs). However, what if we have no control group and just want to measure the pretest-posttest difference? And if we indeed use this model, what will be the effect size? (I assume the intercept can be used to calculate the the effect size when the slope of pretest is 1; what if it isn't 1?).
  3. Build the model (posttest − pretest) ~ 1 + I(pretest − mean(pretest)) + gender + age according to this paper. The intercept can be used to calculate the effect size.

Which model is the most suitable one? And why? Thanks!

sAy
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  • See https://stats.stackexchange.com/questions/3466/best-practice-when-analysing-pre-post-treatment-control-designs – kjetil b halvorsen Oct 11 '21 at 01:33
  • @kjetilbhalvorsen My second model is built according to this link. However, my study is single-arm and there is no control group, so I reckon that the advice from the link is not directly relevant. – sAy Oct 11 '21 at 08:30
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    Here https://stats.stackexchange.com/questions/84164/repeated-measure-t-test-with-covariates-in-r there's a mention that because you do within-subject comparison there shouldn't be any need to adjust for covariates. However, I am wondering in case of clustering (i.e. subejcts are recruited in different centres), your first proposition would be preferable for being able to adjust for this in the random effects with some nesting of subejcts and centres. – user3631369 Feb 17 '23 at 08:59

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