International Biometric Society Investigating interactions in multivariable model-building with continuous covariates

In multivariable model-building interactions between two continuous predictors are often ignored. If considered, the most popular approach is to assume linearity for both variables and test the multiplicative interaction term for significance. However, the model may fit poorly if one or both of the main effects is non-linear. Fractional polynomials (Royston & Altman 1994, Sauerbrei & Royston 1999) have been proposed for investigating main effects of predictors for possible non-linearity. With the multivariable fractional polynomial procedure (MFP), selection of variables and simultaneous determination of functional relationships are possible. If the main effects of two continuous variables derived by MFP include non-linear functions, Royston & Sauerbrei (2008) proposed considering products of these FP functions, which may also be linear, as a candidate for the interaction between the two continuous covariates. This procedure called MFPIgen is a generalization of the MFPI procedure which investigates interactions between a continuous and a binary variable (Royston & Sauerbrei 2004). Key issues of the method will be illustrated by assessing predictors for 10-year all