Longitudinal studies are helpful in understanding how subtle associations between factors of interest change over time. Our goal is to apply statistical methods which are appropriate for analyzing longitudinal data to a repeated measures epidemiological study as a tutorial in the appropriate use and interpretation of random effects models. To motivate their use, we study the association of alcohol consumption on markers of HIV disease progression in an observational cohort. To make valid inferences, the association among measurements correlated within a subject must be taken into account.

We describe a linear mixed effects regression framework that accounts for the clustering of longitudinal data and that can be fit using standard statistical software. We apply the linear mixed effects model to a previously published dataset of HIV infected individuals with a history of alcohol problems who are receiving HAART (n = 197). The researchers were interested in determining the effect of alcohol use on HIV disease progression over time. Fitting a linear mixed effects multiple regression model with a random intercept and random slope for each subject accounts for the association of observations within subjects and yields parameters interpretable as in ordinary multiple regression. A significant interaction between alcohol use and adherence to HAART is found: subjects who use alcohol and are not fully adherent to their HIV medications had higher log RNA (ribonucleic acid) viral load levels than fully adherent non-drinkers, fully adherent alcohol users, and non-drinkers who were not fully adherent.

Longitudinal studies are increasingly common in epidemiological research. Software routines that account for correlation between repeated measures using linear mixed effects methods are now generally available and straightforward to utilize. These models allow the relaxation of assumptions needed for approaches such as repeated measures ANOVA, and should be routinely incorporated into the analysis of cohort studies.