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The multivariable fractional polynomial (MFP) procedure combines variableselection with a function selection procedure (FSP). For continuous variables,a closed test procedure is used to decide between no effect, linear, FP1 or FP2functions. Influential observations (IPs) and small sample size can both havean impact on a selected fractional polynomial model. In this paper, we usedsimulated data with six continuous and four categorical predictors toillustrate approaches which can help to identify IPs with an influence onfunction selection and the MFP model. Approaches use leave-one or two-out andtwo related techniques for a multivariable assessment. In seven subsamples wealso investigated the effects of sample size and model replicability. Forbetter illustration, a structured profile was used to provide an overview ofall analyses conducted. The results showed that one or more IPs can drive thefunctions and models selected. In addition, with a small sample size, MFP mightnot be able to detect non-linear functions and the selected model might differsubstantially from the true underlying model. However, if the sample size issufficient and regression diagnostics are carefully conducted, MFP can be asuitable approach to select variables and functional forms for continuousvariables.

Effects of Influential Points and Sample Size on the Selection and Replicability of Multivariable Fractional Polynomial Models