An empirical comparison of segmented and stochastic linear mixed effects models to estimate rapid disease progression in longitudinal biomarker studies.

Longitudinal studies of rapid disease progression often rely on noisy biomarkers; the underlying longitudinal process naturally varies between subjects and within an individual subject over time; the process can have substantial memory in the form of within-subject correlation. Cystic fibrosis lung disease progression is measured by changes in a lung function marker (FEV1), such as a prolonged drop in lung function, clinically termed rapid decline. Choosing a longitudinal model that estimates rapid decline can be challenging, requiring covariate specifications to assess drug effect while balancing choices of covariance functions. Two classes of longitudinal models have recently been proposed: segmented and stochastic linear mixed effects (LMEs) models. With segmented LMEs, random changepoints are used to estimate the timing and degree of rapid decline, treating these points as structural breaks in the underlying longitudinal process. In contrast, stochastic LMEs, such as random walks, are locally linear but utilize continuously changing slopes, viewing bouts of rapid decline as localized, sharp changes. We compare commonly utilized variants of these approaches through an application using the Cystic Fibrosis Foundation Patient Registry. Changepoint modeling had the worst fit and predictive accuracy but certain covariance forms in stochastic LMEs produced problematic variance estimates.