GENERALIZED ADDITIVE MODELS FOR DATA WITH CONCURVITY: STATISTICAL ISSUES AND A NOVEL MODEL FITTING APPROACH

The Generalized Additive model (GAM) has been used as a standard tool for epidemiologic analysis exploring the effect of air pollution on population health during the last decade as it allows nonparametric relationships between the independent predictors and response. One major concern to the use of the GAM is the presence of concurvity in the data. The standard statistical software, such as S-plus, can seriously overestimate the GAM model parameters and underestimate their variances in the presence of concurvity. We explore an alternate class of models, generalized linear models with natural cubic splines (GLM+NS), that may not be affected as much by concurvity. We make systematic comparisons between GLM+NS and GAMs with smoothing splines (GAM+S) in the presence of varying degrees of concurvity using simulated data. Our results suggest that GLM+NS perform better than GAM+S when medium-to-high concurvity exists in the data. Since GLM+NS result in loss in flexibility, we also investigate an alternative approach to fit a GAM. This approach, which is based on partial residuals, gives regression coefficients and variance estimates with less bias in the presence of concurvity, compared to the estimates obtained by the standard approach. It can accommodate asymmetric smoothers and is more robust with respect to the choice of smoothing parameters. Illustrative examples are provided. The public health significance of this study is that the proposed approach improves the estimate of adverse health effect of air pollution, which is important for public and governmental agencies to revise health-based regulatory standards for ambient air pollution.