Pitfalls of linear regression for estimating slopes over time and how to avoid them by using linear mixed-effects models

Abstract

Clinical epidemiological studies often focus on investigating the underlying causes of disease. For instance, a nephrologist may be interested in the association between blood pressure and the development of chronic kidney disease (CKD). However, instead of focusing on the mere occurrence of CKD, the decline of kidney function over time might be the outcome of interest. For examining this kidney function trajectory, patients are typically followed over time with their kidney function estimated at several time points. During follow-up, some patients may drop out earlier than others and for different reasons. Furthermore, some patients may have greater kidney function at study entry or faster kidney function decline than others. Also, a substantial heterogeneity may exist in the number of kidney function estimates available for each patient. This heterogeneity with respect to kidney function, dropout and number of kidney function estimates is important to take into account when estimating kidney function trajectories. In general, two methods are used in the literature to estimate kidney function trajectories over time: linear regression to estimate individual slopes and the linear mixed-effects model (LMM), i.e. repeated measures analysis. Importantly, the linear regression method does not properly take into account the above-mentioned heterogeneity, whereas the LMM is able to retain all information and variability in the data. However, the underlying concepts, use and interpretation of LMMs are not always straightforward. Therefore we illustrate this using a clinical example and offer a framework of how to model and interpret the LMM.

Keywords: GFR trajectory; dropout; kidney function trajectory; linear mixed-effects model; linear regression.