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.