[Turing-Southampton] S3RI seminar: Willi Sauerbrei (University of Freiburg)

[Chieh-Hsi Wu]

Dear all,

Hope you've been having a good week.

At the S3RI seminar today at 2 PM, we have Professor Willi Sauerbrei (University of Freiburg) giving a talk on

"Multivariable regression modelling - Issues in selection of variables and functional forms of continuous variables."

Please see below for the details of the talk and how to join the seminar online.



Hope to see you at the seminar later today!



Kind regards,

Jessie




Multivariable regression modelling - Issues in selection of variables and functional forms of continuous variables

Willi Sauerbrei1, Edwin Kipruto1

1Institute of Medical Biometry and Statistics, University of Freiburg, Germany



In deriving a multivariable regression model for description, selection of variables and determination of functional forms for continuous variables are central issues. In a recent review of methods, TG2 of the STRATOS initiative identified seven methodological issues which require better understanding, further research and more comparisons of methods proposed [1]. In this talk we briefly discuss issues related to selection bias and the role of shrinkage to correct for it, and modelling of continuous variables.

The nonnegative garrote (NNG) [2] combines variable selection and shrinkage, however, it is often ignored in practice because of its dependence on ordinary least squares estimates from the full model which performs poorly in high degree of multicollinearity and cannot be used for the analysis of high-dimensional data. To extend the approach, other initial estimators have been proposed such as ridge or lasso estimators. In an example the performance of NNG will be compared with the lasso, adaptive lasso and relaxed lasso.

Although severe weaknesses are known, categorisation or the assumption of a linear effect are still the most popular approaches to determine the functional form for continuous variables. The multivariable fractional polynomial (MFP) approach combines variable selection using backward elimination and function selection for continuous variables using fractional polynomial functions [3]. Regression diagnostics, such as detection of influential points and plots of residuals may reveal lack of fit or other peculiarities of a selected model. Single observations may be responsible for the selection of a linear, a monotonic non-linear or even a non-monotonic function. Using synthetic data we will discuss approaches to identify influential points, consider model reproducibility and investigate the effect of sample size on MFP models. We will show that with a sufficiently large sample size and a carefully check on regression diagnostics, MFP is a suitable approach to identify variables with a stronger effect and suitable functional forms for continuous variables.



[1] Sauerbrei W, Perperoglou A, Schmid M, Abrahamowicz M, Becher H, Binder H, Dunkler D, Harrell Jr. FE, Royston P, Heinze G for TG2 of the STRATOS initiative (2020). State of the art in selection of variables and functional forms in multivariable analysis - outstanding issues. Diagnostic and Prognostic Research, 4:3, 1-18. DOI: 10.1186/s41512-020-00074-3

[2] Breiman, L. (1995). Better subset regression using the nonnegative garrote. Technometrics, 37(4), 373-384.



[3] Royston, P., Sauerbrei, W. (2008): ‘Multivariable Model-Building – A pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables’. Wiley



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