Analyzing Repeated Measurements Using Mixed Models

INTRODUCTION

This JAMA Guide to Statistics and Methods discusses analyzing longitudinal studies that use repeated measurements of each participant's status or outcome to assess differences over time using mixed models.

Longitudinal studies often include multiple, repeated measurements of each patient's status or outcome to assess differences in outcomes or in the rate of recovery or decline over time. Repeated measurements from a particular patient are likely to be more similar to each other than measurements from different patients, and this correlation needs to be considered in the analysis of the resulting data. Many common statistical methods, such as linear regression models, should not be used in this situation because those methods assume measurements to be independent of one another.

It is possible to compare outcomes between treatments using only a final measurement to determine whether there was a difference at the end of the study; however, this approach would not include much of the information captured with repeated measurements and there would be no consideration of the pattern of outcomes each patient experienced in reaching his or her final outcome. When outcomes are measured repeatedly over time, a wide variety of clinically important questions may be addressed.

In the EXACT study, Moseley et al¹ examined activity limitations and quality of life (QOL) among patients with ankle fractures to determine if a supervised exercise program with rehabilitation advice was more beneficial than advice alone. Activity limitations and QOL were measured at baseline and at 1, 3, and 6 months of follow-up. The authors used mixed models² to compare patient outcomes over time between the 2 intervention groups.

USE OF THE METHOD

Why Are Mixed Models Used for Repeated Measures Data?

Mixed models are ideally suited to settings in which the individual trajectory of a particular outcome for a study participant over time is influenced both by factors that can be assumed to be the same for many patients (eg, the effect of an intervention) and by characteristics that are likely to vary substantially from patient to patient (eg, the severity of the ankle fracture, baseline level of function, and QOL). Mixed models explicitly account for the correlations between repeated measurements within each patient.

The factors assumed to have the same effect across many patients are called fixed effects and the factors likely to vary substantially from patient to patient are called random effects. For example, the effect of a new treatment may be assumed to be the same for all patients and modeled as a fixed effect, whereas patients may have markedly different baseline function or inherent rates of recovery and these may be best modeled as random effects. Mixed models are called “mixed” because they generally contain both fixed and random effects. The ability to consider both fixed and random effects in the model gives ...