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53. Jahrestagung der Deutschen Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie e. V. (GMDS)

Deutsche Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie

15. bis 18.09.2008, Stuttgart

Modelling continuous variables with a spike at zero – on issues of a fractional polynomial based procedure

Meeting Abstract

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  • Willi Sauerbrei - Institut für Medizinische Biometrie und Informatik, Universitätsklinikum Freiburg, Freiburg, Deutschland
  • Patrick Royston - MRC Clinical Trials Unit, London, UK
  • Heiko Becher - Hygiene Institut, Universität Heidelberg, Heidelberg, Deutschland

Deutsche Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie. 53. Jahrestagung der Deutschen Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie (gmds). Stuttgart, 15.-19.09.2008. Düsseldorf: German Medical Science GMS Publishing House; 2008. DocMI7-6

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

Published: September 10, 2008

© 2008 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.




In clinical epidemiology, a frequently occurring problem is to model a dose/response function for a variable X which has value 0 for a proportion of individuals (“spike at zero”), and a quantitative value for the others, e.g. cigarette consumption or an occupational exposure. When the individuals with X = 0 are seen as a distinct sub-population, it may be necessary to model the outcome in the subpopulation explicitly with a dummy variable, and the rest of the distribution as a positive continuous variable using a dose-response relationship [1].


The concept of fractional polynomials [2] has been shown to be useful for estimating dose-response relationships for continuous variables. A multivariable procedure (MFP) is available to select variables and to determine the functional relationship in many types of regression models. A modification of the function selection component for variables with a spike at zero was proposed in chap 4 of Royston & Sauerbrei [3]. A binary variable indicating zero values of X is added to the model. The procedure considers in two stages whether X has any effect, whether individuals with X = 0 should be considered as a separate subgroup and whether an FP functional relationship for the positive values improves the model fit.


In three examples with substantial differences in the distributions of X, strength of the effects and correlations with other variables, we will discuss in a multivariable context issues concerning the modelling of a continuous variable with a spike at zero. The examples will illustrate that sometimes a binary component will be sufficient for a good model fit, whereas in other cases an FP function, with or without the binary component, is a better model.


We propose a new procedure which will often improve modeling of continuous variables with a spike at zero. Adjustment for other important predictors can be done in the usual way.


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Royston P, Sauerbrei W. Multivariable regression modelling. A pragmatic approach based on fractional polynomials for modelling continuous variables. Wiley; 2008.