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Multivariable functional relationships

Statistical modelling of complex multivariable functional relationships

Funding: DFG

Principal investigator: Prof. Dr. Willi Sauerbrei (IMBI)

Project members Prof. Dr. Willi Sauerbrei (IMBI), Dr. Harald Binder (IMBI)


There are various approaches in clinical research for the separation between variables with and without an influence on the outcome. All are criticised on bias of parameter estimates and insufficient replication stability. Continuous covariates add the difficulty of requiring a sensible assumptions about the functional relationship to the outcome. The traditional approaches, categorisation or assuming linear effects, have major disadvantages. Modelling non-linear effects in a multivariable framework splines and fractional polynomials (FPs) are promising approaches. Splines are the most flexible, and aim to model functional relationships locally. FPs are less flexible, but global, easier to interpret and more stable. Model building uses MFP, a multivariable version of FPs, while several variants exist in the class of spline approaches. For these general guidelines on the selection of functional relationship in a multivariable context are not available.
The properties of these approaches are unsufficiently known, and further simulation studies need to assess issues as type I and II error probabilities, stability of selected models or the possibility of shrinkage to correct for the bias from data driven model building. We will investigate the properties of both approaches with focus on MFP. Furthermore we try to improve modelling approaches in other applications by using the FP framework.