应用统计学丛书·生存分析 模型与应用 英文版PDF|Epub|txt|kindle电子书版本网盘下载

应用统计学丛书·生存分析 模型与应用 英文版PDF格式电子书版下载

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1 Introduction1

1.1 What is survival analysis and how is it applied?1

1.2 The history of survival analysis and its progress2

1.3 General features of survival data structure3

1.4 Censoring4

1.4.1 Mechanisms of right censoring5

1.4.2 Left censoring,interval censoring,and left truncation6

1.5 Time scale and the origin of time7

1.5.1 Observational studies8

1.5.2 Biomedical studies9

1.5.3 Health care utilization9

1.6 Basic lifetime functions10

1.6.1 Continuous lifetime functions10

1.6.2 Discrete lifetime functions12

1.6.3 Basic likelihood functions for right,left,and interval censoring14

1.7 Organization of the book and data used for illustrations16

1.8 Criteria for performing survival analysis17

2 Descriptive approaches of survival analysis20

2.1 The Kaplan-Meier(product-limit)and Nelson-Aalen estimators21

2.1.1 Kaplan-Meier estimating procedures with or without censoring21

2.1.2 Formulation of the Kaplan-Meier and Nelson-Aalen estimators24

2.1.3 Variance and standard error of the survival function27

2.1.4 Confidence intervals and confidence bands of the survival function29

2.2 Life table methods36

2.2.1 Life table indicators37

2.2.2 Multistate life tables40

2.2.3 Illustration:Life table estimates for older Americans44

2.3 Group comparison of survival functions46

2.3.1 Logrank test for survival curves of two groups48

2.3.2 The Wilcoxon rank sum test on survival curves of two groups51

2.3.3 Comparison of survival functions for more than two groups55

2.3.4 Illustration:Comparison of survival curves between married and unmarried persons58

2.4 Summary61

3 Some popular survival distribution functions63

3.1 Exponential survival distribution63

3.2 The Weibull distribution and extreme value theory68

3.2.1 Basic specifications of the Weibull distribution68

3.2.2 The extreme value distribution72

3.3 Gamma distribution73

3.4 Lognormal distribution77

3.5 Log-logistic distribution80

3.6 Gompertz distribution and Gompertz-type hazard models83

3.7 Hypergeometric distribution89

3.8 Other distributions91

3.9 Summary92

4 Parametric regression models of survival analysis93

4.1 General specifications and inferences of parametric regression models94

4.1.1 Specifications of parametric regression models on the hazard function94

4.1.2 Specifications of accelerated failure time regression models96

4.1.3 Inferences of parametric regression models and likelihood functions99

4.1.4 Procedures of maximization and hypothesis testing on ML estimates101

4.2 Exponential regression models103

4.2.1 Exponential regression model on the hazard function103

4.2.2 Exponential accelerated failure time regression model106

4.2.3 Illustration:Exponential regression model on marital status and survival among older Americans108

4.3 Weibull regression models113

4.3.1 Weibull hazard regression model114

4.3.2 Weibull accelerated failure time regression model115

4.3.3 Conversion of Weibull proportional hazard and AFT parameters117

4.3.4 Illustration:A Weibull regression model on marital status and survival among older Americans121

4.4 Log-logistic regression models127

4.4.1 Specifications of the log-logistic AFT regression model127

4.4.2 Retransformation of AFT parameters to untransformed log-logistic parameters129

4.4.3 Illustration:The log-logistic regression model on marital status and survival among the oldest old Americans131

4.5 Other parametric regression models135

4.5.1 The lognormal regression model136

4.5.2 Gamma distributed regression models137

4.6 Parametric regression models with interval censoring138

4.6.1 Inference of parametric regression models with interval censoring138

4.6.2 Illustration:A parametric survival model with independent interval censoring139

4.7 Summary142

5 The Cox proportional hazard regression model and advances144

5.1 The Cox semi-parametric hazard model145

5.1.1 Basic specifications of the Cox proportional hazard model145

5.1.2 Partial likelihood147

5.1.3 Procedures of maximization and hypothesis testing on partial likelihood150

5.2 Estimation of the Cox hazard model with tied survival times154

5.2.1 The discrete-time logistic regression model154

5.2.2 Approximate methods handling ties in the proportional hazard model155

5.2.3 Illustration on tied survival data:Smoking cigarettes and the mortality of older Americans157

5.3 Estimation of survival functions from the Cox proportional hazard model161

5.3.1 The Kalbfleisch-Prentice method162

5.3.2 The Breslow method164

5.3.3 Illustration:Comparing survival curves for smokers and nonsmokers among older Americans165

5.4 The hazard rate model with time-dependent covariates169

5.4.1 Categorization of time-dependent covariates169

5.4.2 The hazard rate model with time-dependent covariates171

5.4.3 Illustration:A hazard model on time-dependent marital status and the mortality of older Americans173

5.5 Stratified proportional hazard rate model176

5.5.1 Specifications of the stratified hazard rate model177

5.5.2 Illustration:Smoking cigarettes and the mortality of older Americans with stratification on three age groups178

5.6 Left truncation,left censoring,and interval censoring183

5.6.1 The Cox model with left truncation,left censoring,and interval censoring184

5.6.2 Illustration:Analyzing left truncated survival data on smoking cigarettes and the mortality of unmarried older Americans185

5.7 Qualitative factors and local tests191

5.7.1 Qualitative factors and scaling approaches191

5.7.2 Local tests193

5.7.3 Illustration of local tests:Educational attainment and the mortality of older Americans195

5.8 Summary199

6 Counting processes and diagnostics of the Cox model201

6.1 Counting processes and the martingale theory202

6.1.1 Counting processes202

6.1.2 The martingale theory204

6.1.3 Stochastic integrated processes as martingale transforms207

6.1.4 Martingale central limit theorems208

6.1.5 Counting process formulation for the Cox model211

6.2 Residuals of the Cox proportional hazard model213

6.2.1 Cox-Snell residuals213

6.2.2 Schoenfeld residuals214

6.2.3 Martingale residuals216

6.2.4 Score residuals218

6.2.5 Deviance residuals219

6.2.6 Illustration:Residual analysis on the Cox model of smoking cigarettes and the mortality of older Americans220

6.3 Assessment of proportional hazards assumption222

6.3.1 Checking proportionality by adding a time-dependent variable225

6.3.2 The Andersen plots for checking proportionality227

6.3.3 Checking proportionality with scaled Schoenfeld residuals228

6.3.4 The Arjas plots229

6.3.5 Checking proportionality with cumulative sums of martingale-based residuals230

6.3.6 Illustration:Checking the proportionality assumption in the Cox model for the effect of age on the mortality of older Americans232

6.4 Checking the functional form of a covariate236

6.4.1 Checking model fit statistics for different link functions236

6.4.2 Checking the functional form with cumulative sums of martingale-based residuals237

6.4.3 Illustration:Checking the functional form of age in the Cox model on the mortality of older Americans239

6.5 Identification of influential observations in the Cox model243

6.5.1 The likelihood displacement statistic approximation244

6.5.2 LMAX statistic for identification of influential observations247

6.5.3 Illustration:Checking influential observations in the Cox model on the mortality of older Americans248

6.6 Summary253

7 Competing risks models and repeated events255

7.1 Competing risks hazard rate models256

7.1.1 Latent failure times of competing risks and model specifications256

7.1.2 Competing risks models and the likelihood function without covariates259

7.1.3 Inference for competing risks models with covariates261

7.1.4 Competing risks model using the multinomial logit regression263

7.1.5 Competing risks model with dependent failure types266

7.1.6 Illustration of competing risks models:Smoking cigarettes and the mortality of older Americans from three causes of death268

7.2 Repeated events282

7.2.1 Andersen and Gill model(AG)283

7.2.2 PWP total time and gap time models(PWP-CP and PWP-GT)286

7.2.3 The WLW model and extensions288

7.2.4 Proportional rate and mean functions of repeated events291

7.2.5 Illustration:The effects of a medical treatment on repeated patient visits294

7.3 Summary308

8 Structural hazard rate regression models310

8.1 Some thoughts about the structural hazard regression models310

8.2 Structural hazard rate model with retransformation of random errors313

8.2.1 Model specification314

8.2.2 The estimation of the full model317

8.2.3 The estimation of reduced-form equations318

8.2.4 Decomposition of causal effects on hazard rates and survival functions323

8.2.5 Illustration:The effects of veteran status on the mortality of older Americans and its pathways327

8.3 Summary344

9 Special topics347

9.1 Informative censoring347

9.1.1 Selection model348

9.1.2 Sensitivity analysis models351

9.1.3 Comments on current models handling informative censoring352

9.2 Bivariate and multivariate survival functions352

9.2.1 Inference of the bivariate survival model353

9.2.2 Estimation of bivariate and multivariate survival models355

9.2.3 Illustration of marginal models handling multivariate survival data359

9.3 Frailty models359

9.3.1 Hazard models with individual frailty360

9.3.2 The correlated frailty model364

9.3.3 Illustration of frailty models:The effect of veteran status on the mortality of older Americans revisited366

9.4 Mortality crossovers and the maximum life span376

9.4.1 Basic specifications378

9.4.2 Relative acceleration of the hazard rate and timing of mortality crossing381

9.4.3 Mathematical conditions for maximum life span and mortality crossover383

9.5 Survival convergence and the preceding mortality crossover384

9.5.1 Mathematical proofs for survival convergence and mortality crossovers385

9.5.2 Simulations387

9.5.3 Explanations for survival convergence and the preceding mortality crossover393

9.6 Sample size required and power analysis398

9.6.1 Calculation of sample size required399

9.6.2 Illustration:Calculating sample size required401

9.7 Summary403

Appendix A The delta method405

Appendix B Approximation of the variance-covariance matrix for the predicted probabilities from results of the multinomial iogit model407

Appendix C Simulated patient data on treatment of PTSD(n=255)410

Appendix D SAS code for derivation of ？ estimates in reduced-form equations417

Appendix E The analytic result of к*(x)422

References424

Index438