Selection of Working Correlation Structure and Best Model in GEE Analyses of Longitudinal Data

The Generalized Estimating Equations (GEE) method is one of the most commonly used statistical methods for the analysis of longitudinal data in epidemiological studies. A working correlation structure for the repeated measures of the outcome variable of a subject needs to be specified by this method. However, statistical criteria for selecting the best correlation structure and the best subset of explanatory variables in GEE are only available recently because the GEE method is developed on the basis of quasi-likelihood theory. Maximum likelihood based model selection methods, such as the widely used Akaike Information Criterion (AIC), are not applicable to GEE directly. Pan (2001 Pan , W. ( 2001 ). Akaike's information criterion in generalized estimating equations . Biometrics 57 : 120 – 125 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) proposed a selection method called QIC which can be used to select the best correlation structure and the best subset of explanatory variables. Based on the QIC method, we developed a computing program to calculate the QIC value for a range of different distributions, link functions and correlation structures. This program was written in Stata software. In this article, we introduce this program and demonstrate how to use it to select the most parsimonious model in GEE analyses of longitudinal data through several representative examples.     

Correlation Structure and Model Selection for Negative Binomial Distribution in GEE

A new model selection criterion, termed as the “quasi-likelihood under the independence model criterion” (QIC), was proposed by Pan (2001 Pan , W. ( 2001 ). Akaike's information criterion in generalized estimating equations . Biometrics 57 : 120 – 125 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) for GEE models. Cui (2007 Cui , J. ( 2007 ). QIC program and model selection in GEE analyses . Stata Journal 7 : 209 – 220 .[Web of Science ®] , [Google Scholar]) developed a general computing program to implement the QIC method for a range of statistical distributions. However, only a special case of the negative binomial distribution was considered in Cui (2007 Cui , J. ( 2007 ). QIC program and model selection in GEE analyses . Stata Journal 7 : 209 – 220 .[Web of Science ®] , [Google Scholar]), where the dispersion parameter equals to unity. This article introduces a new computing program that can be applied for the general negative binomial model, where the dispersion parameter can be any fixed value. An example is also given in this article.     

Revealing age-specific past and future unrelated costs of pneumococcal infections by flexible generalized estimating equations

We aimed to study the excess health-care expenditures for persons with a known positive isolate of Streptococcus pneumoniae. The data set was compiled by linking the database of the largest Belgian Sickness Fund with data obtained from laboratories reporting pneumococcal isolates. We analyzed the age-specific per-patient cumulative costs over time, using generalized estimating equations (GEEs). The mean structure was described by fractional polynomials. The quasi-likelihood under the independence model criterion was used to compare different correlation structures. We show for all age groups that the health-care costs incurred by diagnosed pneumococcal patients are significantly larger than those incurred by undiagnosed matched persons. This is not only the case at the time of diagnosis but also long before and after the time of diagnosis. These findings can be informative for the current debate on unrelated costs in health economic evaluation, and GEEs could be used to estimate these costs for other diseases. Finally, these results can be used to inform policy on the expected budget impact of preventing pneumococcal infections.