Variable Selection and Model Choice in Survival Models with Time-Varying Effects

Flexible hazard regression models based on penalised splines allow to extend the classical Cox-model via the inclusion of time-varying and nonparametric eects (Kneib & Fahrmeir 2007). Despite their immediate appeal in terms of exi-

[1]  Peter Buhlmann,et al.  BOOSTING ALGORITHMS: REGULARIZATION, PREDICTION AND MODEL FITTING , 2007, 0804.2752.

[2]  Daniel Zelterman,et al.  Modeling Survival Data: Extending the Cox Model , 2002, Technometrics.

[3]  Benjamin Hofner,et al.  ACTIVITY-GUIDED ANTITHROMBIN III THERAPY IN SEVERE SURGICAL SEPSIS: EFFICACY AND SAFETY ACCORDING TO A RETROSPECTIVE DATA ANALYSIS , 2008, Shock.

[4]  G. Tutz,et al.  Generalized Additive Modeling with Implicit Variable Selection by Likelihood‐Based Boosting , 2006, Biometrics.

[5]  G. Brier.  VERIFICATION OF FORECASTS EXPRESSED IN TERMS OF PROBABILITY , 1950 .

[6]  Yoav Freund,et al.  Experiments with a New Boosting Algorithm , 1996, ICML.

[7]  Paul H. C. Eilers,et al.  Flexible smoothing with B-splines and penalties , 1996 .

[8]  Ralf Bender,et al.  Generating survival times to simulate Cox proportional hazards models , 2005, Statistics in medicine.

[9]  P. Royston,et al.  Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling. , 1994 .

[10]  L. Fahrmeir,et al.  A Mixed Model Approach for Geoadditive Hazard Regression , 2007 .

[11]  M. Schumacher,et al.  Consistent Estimation of the Expected Brier Score in General Survival Models with Right‐Censored Event Times , 2006, Biometrical journal. Biometrische Zeitschrift.

[12]  P. Bühlmann,et al.  Boosting with the L2-loss: regression and classification , 2001 .

[13]  P. Royston,et al.  A New Proposal for Multivariable Modelling of Time‐Varying Effects in Survival Data Based on Fractional Polynomial Time‐Transformation , 2007, Biometrical journal. Biometrische Zeitschrift.

[14]  C. J. Stone,et al.  Logspline Density Estimation for Censored Data , 1992 .

[15]  Torsten Hothorn,et al.  Flexible boosting of accelerated failure time models , 2008, BMC Bioinformatics.

[16]  Torsten Hothorn,et al.  Boosting additive models using component-wise P-Splines , 2008, Comput. Stat. Data Anal..

[17]  Jun Yan.  Survival Analysis: Techniques for Censored and Truncated Data , 2004 .

[18]  Yoav Freund,et al.  A decision-theoretic generalization of on-line learning and an application to boosting , 1995, EuroCOLT.

[19]  C. R. Deboor,et al.  A practical guide to splines , 1978 .

[20]  J. Friedman.  Greedy function approximation: A gradient boosting machine. , 2001 .

[21]  Paul Dierckx,et al.  Curve and surface fitting with splines , 1994, Monographs on numerical analysis.

[22]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[23]  H. J. Larson,et al.  Introduction to the Theory of Statistics , 1973 .

[24]  R. Schapire.  The Strength of Weak Learnability , 1990, Machine Learning.

[25]  Eric R. Ziegel,et al.  Multivariate Statistical Modelling Based on Generalized Linear Models , 2002, Technometrics.

[26]  David A. Schoenfeld,et al.  Partial residuals for the proportional hazards regression model , 1982 .

[27]  Robert Gray,et al.  Flexible Methods for Analyzing Survival Data Using Splines, with Applications to Breast Cancer Prognosis , 1992 .

[28]  B. Silverman,et al.  Some Aspects of the Spline Smoothing Approach to Non‐Parametric Regression Curve Fitting , 1985 .

[29]  Peter Buhlmann.  Boosting for high-dimensional linear models , 2006, math/0606789.

[30]  R. Tibshirani,et al.  Exploring the nature of covariate effects in the proportional hazards model. , 1990, Biometrics.

[31]  Harald Binder,et al.  Allowing for mandatory covariates in boosting estimation of sparse high-dimensional survival models , 2008, BMC Bioinformatics.

[32]  Trevor Hastie,et al.  [Flexible Parsimonious Smoothing and Additive Modeling]: Discussion , 1989 .

[33]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[34]  Clifford M. Hurvich,et al.  Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion , 1998 .