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vi

2.2.2  Likelihood function........................ 14

2.2.3  Bootstrapping method...................... 14

2.2.4  Sensitivity analysis........................ 15

2.2.5  Newton’s method......................... 16

2.3 Introduction to survival analysis..................... 18

2.3.1  Censoring............................. 18

2.3.2  Basic functions and curves.................... 19

2.3.3  Kaplan-Meier estimator ..................... 21

2.3.4  Cox regression model....................... 22

2.3.5  Breslow’s method......................... 23

2.4 Introduction to copulas......................... 23

2.4.1  Different copula functions.................... 24

2.4.2  Kendall’s τ ............................ 25

2.4.3  Transformation between т and a ................ 26

2.5 Literature review of the dependent censoring and sensitivity analysis 27

3 Regression Survival Analysis with Dependent Censoring          32

3.1 Dependent censoring and sensitivity analysis.............. 33

3.1.1  Dependent censoring....................... 33

3.1.2  Sensitivity analysis........................ 34

3.2 Why copulas and which copulas? .................... 36

3.2.1  Advantages of the copula approach............... 36

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