I have been following Frank’s discussions on the use of change as a dependent variable in regression models.
I have come across trialists using change from baseline as a dependent variable in mixed models, specifically mixed models for repeat measurements (MMRM). Considering the complexity of this model – even for modeling actual Y_ijk responses as dependent variables-- I have been wondering the implications of performing analysis with change-from-baseline as dependent variables and whether inferences obtained can be valid. Are there some insights into this issue, specifically on the impact of this practice in MMRMs?
mine will not be the best answer but i would just say that Senn (statistical issues in drug development) says if you adjust for baseline it makes no difference whether you use change or not. For MMRM it seems to me you induce a treatment x time interaction if baseline is included in the time variable, rather than as a covariate …
Senn’s comment pertains to linear models only. Nonlinear models (ordinal regression and others) don’t share this property. And many dependent variables don’t have the property that subtraction works as it should. For example, if Y is ordinal but not interval scaled (e.g., pain severity 5-point Likert scale), Y minus its baseline value Y0 is no longer ordinal. In addition, even for interval-scaled Y, the relationship between Y and Y0 may not be linear. In that case change scores can’t work. The general solution is to use raw Y as the repeated outcomes, adjusting for raw Y0 (using a spline function for protection against nonlinear effects). Details are in BBR Section 14.4. I personally don’t even compute Y-Y0 much less analyze it.
For the current discussion it matter little whether Y is multivariate (longitudinal) or univariate.
Best answer that I know of. Also, if you’re looking for a plain-language description, Frank’s paragraph in this article is my favorite and has been very helpful when trying to explain this to others: https://www.fharrell.com/post/errmed/#change
“The purpose of a parallel-group randomized clinical trial is to compare the parallel groups, not to compare a patient with herself at baseline. The central question is for two patients with the same pre measurement value of x, one given treatment A and the other treatment B, will the patients tend to have different post-treatment values? This is exactly what analysis of covariance assesses. Within-patient change is affected strongly by regression to the mean and measurement error. When the baseline value is one of the patient inclusion/exclusion criteria, the only meaningful change score requires one to have a second baseline measurement post patient qualification to cancel out much of the regression to the mean effect. It is he second baseline that would be subtracted from the follow-up measurement.”