Seminar: Friday March 7, 2pm
The University of Reading
School of Applied Statistics, room AS-G01
Willi Sauerbrei (Institute of Medical Biometry and Medical Informatics,
University Hospital of Freiburg, Germany)
ISSUES IN MULTIVARIABLE REGRESSION MODEL BUILDING WITH CONTINUOUS COVARIATES
The number of variables in a regression model is often too large and a more
parsimonious model may have advantages. Several variable selection
strategies (eg all-subset selection with various penalties for model
complexity, or stepwise procedures) have been proposed for a long time. As
there are few analytical studies about their properties, their usefulness is
discussed controversially. Replication stability, model complexity,
selection bias and overfitting are considered as critical issues
(Sauerbrei, 1999). With continuous predictors the usual assumption of
linearity may be violated and estimation of the functional form may improve
the fit of a model. A procedure, based on fractional polynomials (M-FP), for
simultaneously estimating the functional form and deleting uninfluential
variables has been proposed (Royston & Altman, 1994; Sauerbrei & Royston,
1999). The flexibility of the procedure for characterising the functional
forms must be considered an advantage. However, it may introduce further
instability in selected factors and result in overfitting of the data. By
analysing medical data in the framework of a Cox-model respectively a
logistic regression model, we will discuss issues of the M-FP procedure. In
our studies effects of individual factors are also of interest, developing a
good predictor is not sufficient. Model stability of M-FP will be
investigated by extending a bootstrap resampling approach addressing issues
of model stability in terms of the inclusion or exclusion of a factor
(Sauerbrei & Schumacher, 1992; Royston & Sauerbrei, 2003)
References:
Royston P and Altman DG: Regression using fractional polynomials of
continuous covariates: parsimonious parametric modelling (with disc.)
Applied Statistics, 43: 429-467, 1994
Royston P and Sauerbrei W: Stability of multivariable fractional polynomial
models with selection of variables and transformations: a bootstrap
investigation. Statistics in Medicine, 2003, to appear
Sauerbrei W: The use of resampling methods to simplify regression models in
medical statistics. Applied Statistics, 48:313-329, 1999
Sauerbrei W and Royston P: Building multivariable prognostic and diagnostic
models: transformation of the predictors using fractional polynomials.
Journal of the Royal Statistical Society, Series A, 162: 71-94, 1999
Sauerbrei W and Schumacher M: A bootstrap resampling procedure for model
building: Application to the Cox regression model. Statistics in Medicine,
11: 2093-2109, 1992
Travel information: http://www.rdg.ac.uk/Statistics/info/direc.html
Other seminars: http://www.rdg.ac.uk/Statistics/diary/seminars.html
Posted by: Howard Grubb ([log in to unmask])
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