Extending the simple linear regression model to account for correlated responses: An introduction to generalized estimating equations and multi-level mixed modelling

Abstract

Much of the research in epidemiology and clinical science is based upon longitudinal designs which involve repeated measurements of a variable of interest in each of a series of individuals. Such designs can be very powerful, both statistically and scientifically, because they enable one to study changes within individual subjects over time or under varied conditions. However, this power arises because the repeated measurements tend to be correlated with one another, and this must be taken into proper account at the time of analysis or misleading conclusions may result. Recent advances in statistical theory and in software development mean that studies based upon such designs can now be analysed more easily, in a valid yet flexible manner, using a variety of approaches which include the use of generalized estimating equations, and mixed models which incorporate random effects. This paper provides a particularly simple illustration of the use of these two approaches, taking as a practical example the analysis of a study which examined the response of portable peak expiratory flow meters to changes in true peak expiratory flow in 12 children with asthma. The paper takes the reader through the relevant practicalities of model fitting, interpretation and criticism and demonstrates that, in a simple case such as this, analyses based upon these model-based approaches produce reassuringly similar inferences to standard analyses based upon more conventional methods.

Prescription Patterns and Mineral Metabolism Abnormalities in the Cinacalcet Era

“…Continuous variables were expressed as medians and interquartile ranges, whereas categorical variables were expressed as proportions. The P values were calculated from generalized estimating equations with robust variance estimation, often used to analyze correlated data (29)(30)(31), to determine the difference between two groups based on cinacalcet patterns at the treatment visit.…”

A longitudinal examination of factors related to changes in serum polychlorinated biphenyl levels.

“…Moreover, differences in the analytic approach may offer some explanation as well. Whereas the earlier study evaluated changes in serum PCB levels using a single measure, in which there may have been some loss of information in the summary statistic (Burton et al 1998), we relied on linear mixed modeling that captures all of the information in the measurements that were available for analysis while accounting for the lack of independence among observations from the same individual.…”

Quality of End-of-Life Care Between Medical Oncologists and Other Physician Specialists for Taiwanese Cancer Decedents, 2001–2006

“…The impact of physician specialty on the indicators of poor EOL care was examined by multivariate logistic regression using the generalized estimating equation method [34] with robust standard errors that account for correlation in the error term resulting from clustering of individuals in the same hospital and with adjustment of the aforementioned confounders. (Table 2).…”