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Generalisation of the Fractional Polynomial procedure for semi-continuous variables in epidemiology and clinical research

Duration: 24 months

Principal Investigator:
Prof. Dr. Wilhelm Sauerbrei (IMBI)
Prof. Dr. Heiko Becher

Project members:
Prof. Dr. Wilhelm Sauerbrei (IMBI)
Carolin Jenkner (IMBI)


In epidemiology and in clinical research, risk factors X often have a non-standard distribution. A common situation is that a proportion of individuals have exposure zero, and those exposed have some continuous distribution. Examples for this are smoking, duration of breastfeeding, or alcohol consumption. These variables are called “semi-continuous variables, or “variables with spike at zero”. The empirical distribution of laboratory values and other measurements may have a semi-continuous distribution as a result of the lower detection limit of the measurement. Modelling of the dose-response function is then possible with a method developed by the applicants which is an extension of the fractional polynomial approach. In this project we have the following aims: (i) to develop the theoretical justifications for the procedure by investigating relevant distribution classes, (ii) to check the performance of this procedure, and of a recently suggested modification of this procedure with simulation studies, (iii) to expand the procedure to the multivariable case, and to interactions, (iv) to use multivariable models to derive and investigate the effect of different metrics (e.g. cumulative, average dose) on the procedure performance and (v) to apply the methods to available data from several epidemiological and clinical studies. The project aims are: - to develop new improved methods for analysis of studies with semi-quantitative variables, - to apply these to recent studies and – to provide software tools to disseminate the methods.


  • Becher H, Lorenz E, Royston P, Sauerbrei W. (2012) Analysing covariates with spike at zero: a modified FP procedure and conceptual issues, Biom J 54:686-700.
  • Lorenz E, Jenkner C, Sauerbrei W, Becher H (2015) Dose-response modelling for bivariate covariates with and without a spike at zero: Theory and application to binary outcomes, Stat Neerl 69 374-398.
  • Jenkner C, Lorenz E, Becher H, Sauerbrei W. (2016) Modeling Continuous Predictors With a ’Spike’ at Zero: Bivariate Approaches. Biom J (in press)
  • Lorenz E, Jenkner C, Sauerbrei W, Becher H (2016) Modeling variables with a spike at zero. Examples and practical recommendations. Am J Epidemiol, to appear