American Journal of Epidemiology Advance Access originally published online on November 5, 2008
American Journal of Epidemiology 2009 169(1):113-121; doi:10.1093/aje/kwn292
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PRACTICE OF EPIDEMIOLOGY |
Fractional Polynomials and Model Selection in Generalized Estimating Equations Analysis, With an Application to a Longitudinal Epidemiologic Study in Australia
Correspondence to Dr. Jisheng Cui, World Health Organization Collaborating Centre for Obesity Prevention, Deakin University, 221 Burwood Highway, Melbourne, VIC 3125, Australia (e-mail: jisheng.cui{at}deakin.edu.au).
Received for publication January 28, 2008. Accepted for publication August 18, 2008.
In epidemiologic studies, researchers often need to establish a nonlinear exposure-response relation between a continuous risk factor and a health outcome. Furthermore, periodic interviews are often conducted to take repeated measurements from an individual. The authors proposed to use fractional polynomial models to jointly analyze the effects of 2 continuous risk factors on a health outcome. This method was applied to an analysis of the effects of age and cumulative fluoride exposure on forced vital capacity in a longitudinal study of lung function carried out among aluminum workers in Australia (1995–2003). Generalized estimating equations and the quasi-likelihood under the independence model criterion were used. The authors found that the second-degree fractional polynomial models for age and fluoride fitted the data best. The best model for age was robust across different models for fluoride, and the best model for fluoride was also robust. No evidence was found to suggest that the effects of smoking and cumulative fluoride exposure on change in forced vital capacity over time were significant. The trend 1 model, which included the unexposed persons in the analysis of trend in forced vital capacity over tertiles of fluoride exposure, did not fit the data well, and caution should be exercised when this method is used.
fractional polynomial; generalized estimating equation; longitudinal studies; model selection; occupational exposure
Abbreviations: AIC, Akaike's Information Criterion; BIC, Bayesian Information Criterion; FVC, forced vital capacity; GEE, generalized estimating equations; QIC, quasi-likelihood under the independence model criterion