Selection of important variables and determination of functional form for continuous predictors in multivariable model building.
In developing regression models, data analysts are often faced with many predictor variables that may influence an outcome variable. After more than half a century of research, the 'best' way of selecting a multivariable model is still unresolved. It is generally agreed that subject matter knowledge, when available, should guide model building. However, such knowledge is often limited, and data-dependent model building is required. We limit the scope of the modelling exercise to selecting important predictors and choosing interpretable and transportable functions for continuous predictors. Assuming linear functions, stepwise selection and all-subset strategies are discussed; the key tuning parameters are the nominal P-value for testing a variable for inclusion and the penalty for model complexity, respectively. We argue that stepwise procedures perform better than a literature-based assessment would suggest. Concerning selection of functional form for continuous predictors, the principal competitors are fractional polynomial functions and various types of spline techniques. We note that a rigorous selection strategy known as multivariable fractional polynomials (MFP) has been developed. No spline-based procedure for simultaneously selecting variables and functional forms has found wide acceptance. Results of FP and spline modelling are compared in two data sets. It is shown that spline modelling, while extremely flexible, can generate fitted curves with uninterpretable 'wiggles', particularly when automatic methods for choosing the smoothness are employed. We give general recommendations to practitioners for carrying out variable and function selection. While acknowledging that further research is needed, we argue why MFP is our preferred approach for multivariable model building with continuous covariates.
Institute of Medical Biometry and Medical Informatics, University Medical Center Freiburg, Stefan-Meier-Strasse 26, 79104 Freiburg, Germany. wfs@imbi.uni-freiburg.de <wfs@imbi.uni-freiburg.de>
Willi
W
Sauerbrei
Patrick
P
Royston
Harald
H
Binder
D000428:Alcohol Drinking / Q000009:adverse effects; D000970:Antineoplastic Agents / Q000627:therapeutic use; D001932:Brain Neoplasms / Q000188:drug therapy / Q000401:mortality; D016000:Cluster Analysis; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D015340:Epidemiologic Research Design; D005910:Glioma / Q000188:drug therapy / Q000401:mortality; D015233:Models, Statistical; D009062:Mouth Neoplasms / Q000209:etiology; D015999:Multivariate Analysis; D011237:Predictive Value of Tests; D011379:Prognosis; D012044:Regression Analysis; D015203:Reproducibility of Results; D012107:Research Design; D016019:Survival Analysis; D014481:United States
D000970:Antineoplastic Agents