Exploratory assessment of treatment-dependent random-effects distribution using gradient functions.

In analyzing repeated measurements from randomized controlled trials with mixed-effects models, it is important to carefully examine the conventional normality assumption regarding the random-effects distribution and its dependence on treatment allocation in order to avoid biased estimation and correctly interpret the estimated random-effects distribution. In this article, we propose the use of a gradient function method in modeling with the different random-effects distributions depending on the treatment allocation. This method can be effective for considering in advance whether a proper fit requires a model that allows dependence of the random-effects distribution on covariates, or for finding the subpopulations in the random effects.