On efficiency of constrained longitudinal data analysis versus longitudinal analysis of covariance

In randomized clinical trials, measurements are often collected on each subject at a baseline visit and several post-randomization time points. The longitudinal analysis of covariance in which the postbaseline values form the response vector and the baseline value is treated as a covariate can be used to evaluate the treatment differences at the postbaseline time points. Liang and Zeger (2000, Sankhyā: The Indian Journal of Statistics, Series B 62, 134-148) propose a constrained longitudinal data analysis in which the baseline value is included in the response vector together with the postbaseline values and a constraint of a common baseline mean across treatment groups is imposed on the model as a result of randomization. If the baseline value is subject to missingness, the constrained longitudinal data analysis is shown to be more efficient for estimating the treatment differences at postbaseline time points than the longitudinal analysis of covariance. The efficiency gain increases with the number of subjects missing baseline and the number of subjects missing all postbaseline values, and, for the pre-post design, decreases with the absolute correlation between baseline and postbaseline values.