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E-raamat: Model-Based Recursive Partitioning with Adjustment for Measurement Error: Applied to the Cox's Proportional Hazards and Weibull Model

  • Formaat: PDF+DRM
  • Sari: BestMasters
  • Ilmumisaeg: 27-Jan-2015
  • Kirjastus: Springer Spektrum
  • Keel: eng
  • ISBN-13: 9783658085056
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Model-Based Recursive Partitioning with Adjustment for Measurement Error: Applied to the Cox's Proportional Hazards and Weibull ModelSuurem pilt
  • Formaat: PDF+DRM
  • Sari: BestMasters
  • Ilmumisaeg: 27-Jan-2015
  • Kirjastus: Springer Spektrum
  • Keel: eng
  • ISBN-13: 9783658085056
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?Model-based recursive partitioning (MOB) provides a powerful synthesis between machine-learning inspired recursive partitioning methods and regression models. Hanna Birke extends this approach by allowing in addition for measurement error in covariates, as frequently occurring in biometric (or econometric) studies, for instance, when measuring blood pressure or caloric intake per day. After an introduction into the background, the extended methodology is developed in detail for the Cox model and the Weibull model, carefully implemented in R, and investigated in a comprehensive simulation study.
1 Introduction
1(2)
2 Theoretical Background
3(32)
2.1 Cox Model and Measurement Error
3(18)
2.1.1 Measurement Error Model
5(1)
2.1.2 Adjustment for Measurement Error in Cox Model
6(3)
2.1.3 Corrected Log-Likelihood and Score Function in Cox and Weibull Model
9(12)
2.2 Model-Based Recursive Partitioning
21(14)
2.2.1 Introduction to Classification and Regression Trees
22(2)
2.2.2 Model-Based Recursive Partitioning
24(11)
3 Implementation
35(20)
3.1 Model-Based Recursive Partitioning in R
35(4)
3.2 Fitting a MOB Weibull Model with Adjustment for Measurement Error
39(16)
4 Simulation Study
55(40)
4.1 Check the fit Function
56(15)
4.1.1 Check the fit Function - only W
57(9)
4.1.2 Check the fit Function - W and F
66(5)
4.2 Structural Changes
71(14)
4.2.1 Structural Changes - single
72(8)
4.2.2 Structural Changes - multi
80(5)
4.3 One Global Model Fit vs. MOB
85(7)
4.4 Conclusion of the Simulation Study
92(3)
5 Conclusion
95(6)
Appendix
101(134)
A R-Code
101(6)
A.1 SurvRegcorr.r
101(6)
B Proofs and Derivations
107(14)
B.1 Cox Model - Corrected Log-Likelihood
107(1)
B.2 Cox Model - Corrected Score Functions
108(2)
B.3 Weibull Model - Log-Likelihood
110(1)
B.3.1 Version 2
110(1)
B.3.2 Version 2 --- Version 1
110(1)
B.4 Weibull Model - Corrected Log-Likelihood
111(2)
B.5 Weibull Model - Corrected Score Functions
113(1)
B.6 Weibull Model - Corrected Log-Likelihood with Interaction Term
114(4)
B.7 Generating Failure Times
118(1)
B.8 Mean Expected Failure Time
119(2)
C Results of the Simulation Study
121(114)
C.1 Check the fit function - only W
121(1)
C.1.1 beta.true --- -0.2, tau.true --- -0.3, prob.cens --- 35% and V ~ N(0, 1)
121(10)
C.1.2 beta.true --- -0.2, tau.true --- -0.3, prob.cens --- 35% and V ~ Unit f(0, √12)
131(9)
C.1.3 beta.true --- 0.4, tau.true --- 0.5, prob.cens --- 0% and V ~ N(0, 1)
140(9)
C.1.4 beta.true --- 0.4, tau.true --- 0.5, prob.cens --- 0% and V ~ Unit f(0, √12)
149(9)
C.2 Check the fit function - W and F
158(1)
C.2.1 beta.V.true --- 0.6, beta.F.true --- -0.1, tau.true --- -0.5, prob.cens --- 0% and V ~ N(0, 1)
158(15)
C.2.2 beta.V.true --- 0.6, beta.F.true --- -0.1, tau.true --- -0.5, prob.cens --- 0% and V ~ Unit f(0, √12)
173(15)
C.3 Structural Changes - single
188(1)
C.3.1 beta.1.true --- 0.6, beta.2.true --- -0.2, tau.1.true --- 0.5, tau.2.true --- -0.4, prob.cens --- 35% and V ~ N(0, 1)
188(21)
C.4 Structural Changes - multi
209(9)
C.4.1 Summary of Parameter Estimation
218(6)
C.5 One Global Model Fit vs. MOB
224(1)
C.5.1 beta.1.true --- 0.6, beta.2.true --- -0.2, tau.1.true --- 0.5, tau.2.true --- -0.4, prob.cens --- 0% and V ~ N(0, 1)
224(11)
Bibliography 235
Hanna Birke wrote her master thesis under the supervision of Prof. Dr. Thomas Augustin at the department of statistics of the LMU Munich and is currently working on her doctoral thesis.
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