title: Sigmoidal mixed models for longitudinal data.
abstract: Linear mixed models are widely used to analyze longitudinal cognitive data. Often, however, the trajectory of cognitive function is nonlinear. For example, some participants may experience cognitive decline that accelerates as death approaches. Polynomial regression and piecewise linear models are common approaches used to characterize nonlinear trajectories, although both have assumptions that may not correspond with the actual trajectories. An alternative is to use a flexible sigmoidal mixed model based on the logistic family of curves. We describe a general class of such a model, which has up to five parameters, representing (1) final level, (2) rate of decline, (3) midpoint of decline, (4) initial level before decline, and (5) asymmetry. Focusing on a four-parameter symmetric sub-class of the model, with random effects on two of the parameters, we demonstrate that a likelihood approach to fitting this model produces accurate estimates of mean levels across time, even in the case of model misspecification. We also illustrate the method on deceased participants who had completed at least 5 years of annual cognitive testing and annual assessment of body mass. We show that departures from a stable body can modify the trajectory curves and anticipate cognitive decline.
authors.affiliation: 1 Rush Alzheimer's Disease Center, Rush University Medical Center, Chicago, IL, USA.
authors.forename: Ana W
authors.initials: AW
authors.lastname: Capuano
authors.affiliation: 1 Rush Alzheimer's Disease Center, Rush University Medical Center, Chicago, IL, USA.
authors.forename: Robert S
authors.initials: RS
authors.lastname: Wilson
authors.affiliation: 1 Rush Alzheimer's Disease Center, Rush University Medical Center, Chicago, IL, USA.
authors.forename: Sue E
authors.initials: SE
authors.lastname: Leurgans
authors.affiliation: 2 Department of Biostatistics, University of Iowa, Iowa City, IA, USA.
authors.forename: Jeffrey D
authors.initials: JD
authors.lastname: Dawson
authors.affiliation: 1 Rush Alzheimer's Disease Center, Rush University Medical Center, Chicago, IL, USA.
authors.forename: David A
authors.initials: DA
authors.lastname: Bennett
authors.affiliation: 3 Department of Public Health Sciences, Biostatistics, The University of Chicago, Chicago, IL, USA.
authors.forename: Donald
authors.initials: D
authors.lastname: Hedeker
mesh_terms: D056808:Biostatistics / Q000379:methods*; D015992:Body Mass Index; D060825:Cognitive Dysfunction / Q000175:diagnosis / Q000473:pathology; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D016014:Linear Models; D016015:Logistic Models; D008137:Longitudinal Studies; D008297:Male; D015233:Models, Statistical
keywords: Alzheimer’s disease; Nonlinear models; cognitive decline; longitudinal data; mixed models; terminal decline