Model Choice Can Obscure Results in Longitudinal Studies

EPIDEMIOLOGICAL studies that involve repeated observations from the same individuals over a period of years have provided important information on the etiology, pathophysiology, and consequences of chronic diseases (1). Longitudinal studies are the best method to study individual change (longitudinal differences) and to identify factors associated with that change (2) while still allowing comparison between individuals of different ages (cross-sectional differences). Modeling the average response as a function of age without considering differences in age at study entry assumes that cross-sectional and longitudinal effects of aging are equivalent. On the contrary, it is known that the cross-sectional effects of age at study entry and changes over time are quite different thus requiring special attention in the modeling and interpretation of results. Schaie (3) discusses how the longitudinal design better separates age, time, and cohort effects. Analyses of repeated measures are often accomplished using hierarchical or multilevel models where age is a Level 1 variable and time is a Level 2 variable. However, in unbalanced longitudinal studies with participants over wide age range, a model should be used that can simultaneously describe cross-sectional and longitudinal patterns. These models will typically require careful parameterization of interactions and higher order terms to adequately fit the data and perhaps handle cohort effects. Mixed-effects and random-effects models have contributed greatly to the study of longitudinal patterns of change (4–7). In mixed-effects models both individual patterns of change (individual random effects) and population averages (fixed effects) can be estimated. The correlation between the repeated measures is accounted for through the variance-covariance structure of the random effects. Unlike traditional repeated measures analyses (8) mixed-effects models use all available data, provided data are missing at random (9). Different approaches have been used to model longitudinally the relationship of age and follow-up time with a response variable. Alfaro-Acha and colleagues (10) in a 7-year prospective study of handgrip strength and cognitive decline in Mexican Americans aged 65 and older used a mixed-effects model including baseline age and time. However, no interaction terms involving baseline age and time were reported, assuming that the longitudinal changes in cognitive decline are not influenced by the individual's starting age. To study hip fracture in female patients aged 65 and older participating in the Baltimore Hip Studies followed up for 12 months, Miller and colleagues (11,12) used baseline age in their generalized estimating equations (GEE) analyses and treated time as a categorical variable. Blaum and colleagues (13) examined the metabolic syndrome in Mexican Americans aged 60–98 years over a 3-year follow-up and modeled their longitudinal data using GEE with both age as a covariate as well as a Time × Age interaction. Park and Lee (14) considered only age in modeling the occurrence of urinary incontinence during a 2-year period in community-dwelling elderly. In an analysis of data from HIV patients, Edwards and colleagues (15) evaluated longitudinal changes in viral load according to time from infection regardless of age at study entry. A major issue in modeling age and time in observational longitudinal data is selection or recruitment bias (16–19), that is, participants recruited at an older age may be different from participants who were recruited at a younger age and remained in the study to become older persons. For example, participants who begin at age 60 may be systematically different from participants who started at age 40 and remain in the study for 20 years. For example, in the Baltimore Longitudinal Study of Aging (BLSA) (20), all volunteers are healthy at recruitment, whereas the health of participants who have been in the study for some time may have deteriorated over time. Repeated measures analyses must account for these differences. In this article, we examine how different parameterizations of age and time in modeling observational longitudinal data can affect the results.