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 …
[1]
Robert L. Jones,et al.
The effect of chelation therapy with succimer on neuropsychological development in children exposed to lead.
,
2001,
The New England journal of medicine.
[2]
Toon W. Taris,et al.
A Primer in Longitudinal Data Analysis
,
2000
.
[3]
George G. Rhoads,et al.
Safety and Efficacy of Succimer in Toddlers with Blood Lead Levels of 20–44 μg/dL
,
2000,
Pediatric Research.
[4]
P. Quanjer,et al.
Decreases in VC and FEV1 with time: indicators for effects of smoking and air pollution.
,
1981,
Bulletin europeen de physiopathologie respiratoire.
[5]
G. Molenberghs.
Applied Longitudinal Analysis
,
2005
.
[6]
Sophia Rabe-Hesketh,et al.
Multilevel and longitudinal modeling using Stata. 2nd edition
,
2008
.
[7]
J. Singer,et al.
Applied Longitudinal Data Analysis
,
2003
.
[8]
S J Pocock,et al.
Repeated measures in clinical trials: analysis using mean summary statistics and its implications for design.
,
1992,
Statistics in medicine.
[9]
G. Fitzmaurice,et al.
A caveat concerning independence estimating equations with multivariate binary data.
,
1995,
Biometrics.
[10]
Dibyen Majumdar,et al.
Conditional Second-Order Generalized Estimating Equations for Generalized Linear and Nonlinear Mixed-Effects Models
,
2002
.
[11]
F. Speizer,et al.
The relationship of nonspecific bronchial responsiveness to respiratory symptoms in a random population sample.
,
1987,
The American review of respiratory disease.
[12]
Helen Brown,et al.
Applied Mixed Models in Medicine
,
2000,
Technometrics.
[13]
Sophia Rabe-Hesketh,et al.
Multilevel and Longitudinal Modeling Using Stata
,
2005
.
[14]
Jos Twisk,et al.
Attrition in longitudinal studies. How to deal with missing data.
,
2002,
Journal of clinical epidemiology.
[15]
P. Albert,et al.
Models for longitudinal data: a generalized estimating equation approach.
,
1988,
Biometrics.