A Primer in Longitudinal Data Analysis

Longitudinal data, comprising repeated measurements of the same individuals over time, arise frequently in cardiology and the biomedical sciences in general. For example, Frison and Pocock1 used repeated measurements of the liver enzyme creatine kinase in serum of cardiac patients to study changes in liver function over a 12-month study period. The main goal, indeed the raison d’etre , of a longitudinal study is characterization of changes in the response of interest over time. Ordinarily, changes in the response are also related to selected covariates. For example, Frison and Pocock1 compared changes in creatine kinase between patients randomized to active drug and placebo. The past 25 years have witnessed remarkable developments in statistical methods for the analysis of longitudinal data. Despite these important advances, researchers in the biomedical sciences have been somewhat slow to adopt these methods and often rely on statistical techniques that fail to adequately account for longitudinal study designs. The goal of the present report is to provide an overview of some recently developed methods for longitudinal analyses that are more appropriate, with a focus on 2 methods for continuous responses: the analysis of response profiles and linear mixed-effects models. The analysis of response profiles is better suited to settings with a relatively small number of repeated measurements, obtained on a common set of occasions, whereas linear mixed-effects models are suitable in more general settings. Before describing these methods, we review some of the defining features of longitudinal studies and highlight the main aspects of longitudinal data that complicate their analysis. ### Covariance Structure A common feature of repeated measurements on an individual is correlation; that is, knowledge of the value of the response on one occasion provides information about the likely value of the response on a future occasion. Another common feature of longitudinal data is heterogeneous …