gms | German Medical Science

Kongress Medizin und Gesellschaft 2007

17. bis 21.09.2007, Augsburg

Modeling continuous by continuous interactions in observational studies

Meeting Abstract

Search Medline for

  • Willi Sauerbrei - Institut für Medizinische Biometrie und Informatik, Universitätsklinikum Freiburg, Freiburg
  • Patrick Royston - MRC Clinical Trials Unit, London

Kongress Medizin und Gesellschaft 2007. Augsburg, 17.-21.09.2007. Düsseldorf: German Medical Science GMS Publishing House; 2007. Doc07gmds342

The electronic version of this article is the complete one and can be found online at:

Published: September 6, 2007

© 2007 Sauerbrei et al.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( You are free: to Share – to copy, distribute and transmit the work, provided the original author and source are credited.



Background: Interactions between two continuous predictors are of interest in many observational studies. A popular approach is to assume linearity for both variables and test the multiplicative term for significance. The model may fit poorly if one or both of the main effects is non-linear.

Material and methods: Fractional polynomials [1], [2] 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 derived with MFP include non-linear functions, products of these functions may be included as candidates for interactions. To investigate an interaction between a categorical and a continuous covariate the MFPI procedure was proposed [3]. To handle continuous by continuous interactions we will propose a natural extension of it, called MFPIgen. Key issues of the method will be illustrated by assessing predictors for 10-year all-cause mortality in the Whitehall I data set, a large cohort study (N=17260, 1670 events) in British men. Six continuous and one categorical predictor will be considered in a logistic regression model.

Results: All predictors have a significant effect on the outcome. Some of the continuous predictors have a non-linear effect. We will illustrate that spurious interactions can be introduced in the model by erroneously assuming linear interaction terms.

Conclusion: Our new procedure allows the analyst to consider continuous by continuous interactions in a systematic way. It can also handle non-linear effects, an important issue too often ignored in practical data analysis. To reduce the chance of spurious interactions being detected, a stringent significance level such as 1% should be used.


Royston P, Altman DG. Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling (with discussion). Applied Statistics. 1994;43:429-67.
Sauerbrei W, Royston P. Building multivariable prognostic and diagnostic models: transformation of the predictors by using fractional polynomials. JRSS-A. 1999;165:71-94.
Royston P, Sauerbrei W. A new approach to modelling interactions between treatment and continuous covariates in clinical trials by using fractional polynomials. Stat Med. 2004;23:2509-25.