Linear mixed-effects models for analysis of longitudinal repeated measures: a conceptual framework for clinical researchers

In this paper, we provide a conceptual introduction to linear mixed-effects models (LMMs), statistical approaches that are used for analysis of longitudinal repeated-measure data, for clinical researchers with a limited statistical background. We begin by contrasting LMMs with repeated-measures analysis of variance, and highlight the limitations of the latter approach, including its restrictive assumption of sphericity and its sensitivity to dropout. We show that LMMs overcome these limitations by providing valid inferences under the missing-at-random assumption, accommodating unbalanced designs, and offering flexible options for modeling covariance structures. Beyond addressing the core assumptions of LMMs, we evaluate the implications of modeling time as a numerical versus as a categorical factor. We discuss approaches for handling baseline values, including longitudinal data analysis, constrained longitudinal data analysis, and analysis of covariance, and describe their relative strengths and limitations in both randomized and observational studies. We explain the roles of random effects and residual covariance structures and provide practical guidance for selecting candidate models by using exploratory plots and information criteria, such as the Akaike and Bayesian information criteria. Overall, by providing a clear and accessible conceptual framework, we hope to enable clinical researchers to understand, evaluate, and apply LMMs effectively.