Fractional Polynomial Models as Special Cases of Bayesian Generalized Nonlinear Models

We propose a framework for fitting multivariable fractional polynomial models as specialcases of Bayesian generalized nonlinear models, applying an adapted version of the geneticallymodified mode jumping Markov chain Monte Carlo algorithm. The universality of the Bayesiangeneralized nonlinear models allows us to employ a Bayesian version of fractional polynomials inany supervised learning task, including regression, classification, and time-to-event data analysis.We show through a simulation study that our novel approach performs similarly to the classicalfrequentist multivariable fractional polynomials approach in terms of variable selection, identificationof the true functional forms, and prediction ability, while naturally providing, in contrast to itsfrequentist version, a coherent inference framework. Real-data examples provide further evidence infavor of our approach and show its flexibility.

Automated summary

This paper proposes a framework for fitting multivariable fractional polynomial models as special cases of Bayesian generalized nonlinear models. By applying an adapted version of the genetically modified mode jumping Markov chain Monte Carlo algorithm, the Bayesian version of fractional polynomials can be used in any supervised learning task.