Using Appropriate Functional Forms for Continuous Variables and Improving Predictive Accuracy in Developing the Risk Model of Clostridium Difficile Infection

10.6339/JDS.2012.10(1).1020

Yan Yan；Kimberly A. Reske；Victoria J. Fraser；Graham A. Colditz；Erik R. Dubberke

Clinical prediction model ； functional form ； predictive accuracy

Journal of Data Science

10卷1期（2012 / 01 / 01）

37 - 49

英文

Simple parametric functional forms, if appropriate, are preferred over more complicated functional forms in clinical prediction models. In this paper, we illustrate our practical approach to obtaining the appropriate functional forms for continuous variables in developing a clinical prediction model for risk of Clostridium difficile infection. First, we used a nonparametric regression smoother to establish the reference curve. Then, we used regression spline function-restricted cubic spline (RCS) and simple parametric forms to approximate the reference curve. Based on the shape of the reference curve, the model fit information (AIC), and the formal statistical test (Vuong test), we selected the simple parametric forms to replace the more elaborated RCS functions. Finally, we refined the simple parametric forms in the multiple variable regression model using the Wald test and the likelihood-ratio test. In addition, we compared the calibration and discrimination aspects between the model with appropriate functional forms and the model with simple linear terms. The calibration χ^2 (8.4 versus 10) and calibration plot, the area under ROC curve (0.88 vs 0.84, p ＜ 0.05), and integrated discrimination improvement (0.0072, p ＜ 0.001) indicated the model with appropriate forms was better calibrated and had higher discrimination ability.