Journal of Biometrics & Biostatistics

A Comparison of Generalized Additive Models to Other Common Modeling Strategies for Continuous Covariates: Implications for Risk Adjustment

Abstract

Lynne Moore, James A Hanley, Alexis F Turgeon and André Lavoie

Common modeling strategies for quantitative covariates include single linear terms, dummy variables on categories, Fractional Polynomials (FP) and cubic smoothing splines in Generalized Additive Models (GAM). The goal of this study was to evaluate the impact of using GAM over other common covariate modeling strategies on risk adjustment. Analyses were based on inter-hospital mortality comparisons in a Canadian provincial trauma system (n=123,732; 59 hospitals). Parameter estimates describing the increase in log odds of mortality for one hospital compared to the reference were adjusted with five quantitative covariates modeled using 1) single linear terms, 2) dummy variables on 2, 3, 4, 5 categories, 3) FP, and 4) GAM. The parameter estimates generated by the first three modeling strategies were compared to that generated by the GAM using mean standardized difference. Mean standardized difference (95% CI) was 71.69 (51.7-91.7) for single linear terms, 21.1 (14.3-28.9); 23.4 (15.6-31.2); 49.6 (28.1-71.1); and 48.5 (28.8-68.2) for dummy variables on 2, 3, 4, and 5 categories, respectively and 12.7 (10.0-15.4) for FP. Results suggest that GAM, FP and at least 4 risk-homogeneous categories provide equivalent risk adjustment to smoothing splines in GAM while single linear terms and less than 4 categories may induce residual confounding.