Modelling interactions with continuous variables

Background: In regression models continuous variables are often either categorized or linearity is assumed. However, both approaches can have major disadvantages and modelling non-linear functions may improve the fit. Methods: The multivariable fractional polynomial (MFP) approach determines simultaneously a suitable functional form and deletes uninfluential variables (Royston & Sauerbrei, 2008, Sauerbrei et al, 2007a). Extensions of MFP have been developed to investigate for interactions of continuous covariates with treatment (or more generally with a categorical variable, MFPI) and for two continuous covariates (MFPIgen). Both strategies allow to adjust for other covariates when investigating for interactions. Results: Analyzing two large studies with the Cox-model and respectively the logistic model it will be shown that interactions can be easily overlooked and that mismodelling of non-linear main effects may introduce spurious interactions. Conclusions: In a multivariable context it is import to model continuous variables sensibly. MFP and its extensions for interactions are useful approaches for this important task. References: Royston P, Sauerbrei, W (2004): A new approach to modelling interactions between treatment and continuous covariates in clinical trials by using fractional polynomials. Statistics in Medicine, 23:2509–2525. Royston P, Sauerbrei, W (2008): 'Multivariable Model-Building – A pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables'. Wiley. Sauerbrei W, Royston, P, Binder H (2007a): Selection of important variables and determination of functional form for continuous predictors in multivariable model building. Statistics in Medicine, 26: 5512–5528. Sauerbrei W, Royston, P, Zapien, K (2007): Detecting an interaction between treatment and a continuous covariate: a comparison of two approaches. Computational Statistics and Data Analysis, 51: 4054–4063