Statistical Methods for Survival Data Analysis.
- 1st ed.
- 1 online resource (508 pages)
- New York Academy of Sciences Series .
- New York Academy of Sciences Series .
Intro -- Statistical Methods for Survival Data Analysis -- Copyright -- Contents -- Preface -- 1 Introduction -- 1.1 Preliminaries -- 1.2 Censored Data -- 1.2.1 Type I Censoring -- 1.2.2 Type II Censoring -- 1.2.3 Type III Censoring -- 1.3 Scope of the Book -- 2 Functions of Survival Time -- 2.1 Definitions -- 2.1.1 Survivorship Function (or Survival Function) -- 2.1.2 Probability Density Function (or Density Function) -- 2.1.3 Hazard Function -- 2.2 Relationships of the Survival Functions -- Exercises -- 3 Examples of Survival Data Analysis -- 3.1 Example 3.1: Comparison of Two Treatments and Three Diets -- 3.1.1 Comparison of Two Treatments -- 3.1.2 Comparison of Three Diets -- 3.2 Example 3.2: Comparison of Two Survival Patterns Using Life Tables -- 3.3 Example 3.3: Fitting Survival Distributions to Tumor-Free Times -- 3.4 Example 3.4: Comparing Survival of a Cohort with that of a General Population - Relative Survival -- 3.5 Example 3.5: Identification of Risk Factors for Incident Events -- 3.6 Example 3.6: Identification of Risk Factors for the Prevalence of Age-Related Macular Degeneration -- 3.7 Example 3.7: Identification of Significant Risk Factors for Incident Hypertension Using Related Data (Repeated Measurements) in a Longitudinal Study -- Exercises -- 4 Nonparametric Methods of Estimating Survival Functions -- 4.1 Product-Limit Estimates of Survivorship Function -- 4.2 N elson-Aalen Estimates of Survivorship Function -- 4.3 Life-Table Analysis -- 4.3.1 Population Life Tables -- 4.3.2 Clinical Life Tables -- 4.4 Relative Survival Rates -- 4.5 Standardized Rates and Ratios -- Exercises -- 5 Nonparametric Methods for Comparing Survival Distributions -- 5.1 Comparison of Two Survival Distributions -- 5.1.1 Gehan's Generalized Wilcoxon Test -- 5.1.2 The Cox-Mantel Test -- 5.1.3 The Logrank Test. 5.1.4 Peto and Peto's Generalized Wilcoxon Test -- 5.1.5 Cox's F-Test -- 5.1.6 Comments on the Tests -- 5.2 The Mantel and Haenszel Test -- 5.3 Comparison of K (K > -- 2) Samples -- 5.3.1 An Extended Test Using Scores -- 5.3.2 Extended Logrank (Chi-Square) Test -- Exercises -- 6 Some Well-Known Parametric Survival Distributions And Their Applications -- 6.1 Exponential Distribution -- 6.2 Weibull Distribution -- 6.3 Lognormal Distribution -- 6.4 Gamma, Generalized Gamma, and Extended Generalized Gamma Distributions -- 6.5 Log-Logistic Distribution -- 6.6 Other Survival Distributions -- Exercises -- 7 Estimation Procedures for Parametric Survival Distributions Without Covariates -- 7.1 General Maximum Likelihood Estimation Procedure -- 7.1.1 Estimation Procedures for Data with Right-Censored Observations -- 7.1.2 Estimation Procedures for Data with Right-, Left-, and Interval-Censored Observations -- 7.2 Exponential Distribution -- 7.2.1 One-Parameter Exponential Distribution -- 7.2.2 Estimation of l for Data without Censored Observations -- 7.2.3 Estimation of l for Data with Censored Observations -- 7.2.4 The Two-Parameter Exponential Distribution -- 7.2.5 Estimation of l and G for Data without Censored Observations -- 7.2.6 Estimation of l and G for Data with Censored Observations -- 7.3 Weibull Distribution -- 7.4 Lognormal Distribution -- 7.4.1 Estimation of m and s 2 for Data without Censored Observations -- 7.4.2 Estimation of m and s2 for Data with Censored Observations -- 7.5 The Extended Generalized Gamma Distribution -- 7.6 The Log-Logistic Distribution -- 7.7 Gompertz Distribution -- 7.7.1 Estimation of l and g for Data with or without Censored Observations -- 7.8 Graphical Methods -- 7.8.1 Probability Plotting -- 7.8.1.1 Exponential Distribution -- 7.8.1.2 Weibull Distribution -- 7.8.1.3 Lognormal Distribution. 7.8.1.4 Log-Logistic Distribution -- 7.8.2 Hazard Plotting -- 7.8.2.1 Exponential Distribution -- 7.8.2.2 Weibull Distribution -- 7.8.2.3 Lognormal Distribution -- 7.8.2.4 Log-Logistic Distribution -- 7.8.3 The Cox-Snell Residual Method -- Exercises -- 8 Tests of Goodness-of-Fit and Distribution Selection -- 8.1 Goodness-of-Fit Test Statistics Based on Asymptotic Likelihood Inferences -- 8.1.1 Testing a Subset of Parameters in a Distribution -- 8.1.2 Testing All Parameters in a Distribution -- 8.2 Tests for Appropriateness of a Family of Distributions -- 8.3 Selection of a Distribution by Using BIC or AIC Procedure -- 8.4 Tests for a Specific Distribution with Known Parameters -- 8.5 Hollander and Proschan's Test for Appropriateness of a Given Distribution with Known Parameters -- Exercises -- 9 Parametric Methods for Comparing Two Survival Distributions -- 9.1 Log-Likelihood Ratio Test for Comparing Two Survival Distributions -- 9.2 Comparison of Two Exponential Distributions -- 9.2.1 The Log-Likelihood Ratio Test -- 9.2.2 Cox's F-Test for Exponential Distributions -- 9.3 Comparison of Two Weibull Distributions -- 9.4 Comparison of Two Gamma Distributions -- Exercises -- 10 Parametric Methods for Regression Model Fitting and Identification of Prognostic Factors -- 10.1 Preliminary Examination of Data -- 10.2 General Structure of Parametric Regression Models and Their Asymptotic Likelihood Inference -- 10.3 Exponential AFT Model -- 10.4 Weibull AFT Model -- 10.5 Lognormal AFT Model -- 10.6 The Extended Generalized Gamma AFT Model -- 10.7 Log-Logistic AFT Model -- 10.8 Other Parametric Regression Models -- 10.8.1 Model 1 -- 10.8.2 Model 2 -- 10.9 Model Selection Methods -- 10.9.1 Selection of Most Significant Covariates for a Known Parametric Model -- 10.9.1.1 Forward Selection Procedure -- 10.9.1.2 Backward Selection Procedure. 10.9.1.3 Stepwise Selection Procedure -- 10.9.1.4 Information Criterion (AIC and BIC) Procedures -- 10.9.2 Selection of a Parametric Model with a Fixed Subset of Covariates -- 10.9.3 Selection of a Parametric Model and an Optimal Subset of Covariates Simultaneously: The AIC and BIC Procedures -- 10.9.4 Cox-Snell Residual Procedure with Covariates -- Exercises -- 11 Identification of Risk Factors Related to Survival Time: Cox Proportional Hazards Model -- 11.1 The Proportional Hazards Model -- 11.2 The Partial Likelihood Function -- 11.2.1 Estimation Procedures without Tied Survival Times -- 11.2.2 Estimation Procedure with Tied Survival Times -- 11.2.2.1 Continuous Time Scale -- 11.3 Identification of Significant Covariates -- 11.4 Estimation of the Survivorship Function with Covariates -- 11.5 Adequacy Assessment of the Proportional Hazards Model -- 11.5.1 Checking the Proportional Hazards Assumption -- 11.5.2 Assessing the Proportional Hazards Model by Residuals -- 11.5.2.1 Cox-Snell Residuals -- 11.5.2.2 Deviance and Martingale Residuals -- 11.5.2.3 Schoenfeld Residuals -- 11.5.2.4 Martingale-Based Residuals of Lin, Wei, and Ying -- Exercises -- 12 Identification of Prognostic Factors Related to Survival Time: Non-Proportional Hazards Models -- 12.1 Models with Time-Dependent Covariates -- 12.2 Stratified Proportional Hazards Model -- 12.3 Competing Risks Model -- 12.4 Recurrent Event Models -- 12.4.1 Prentice, Williams, and Peterson (PWP) Model -- 12.4.2 Andersen-Gill (AG) Model -- 12.4.3 Wei, Lin, and Weissfeld (WLW) Model -- 12.5 Models for Related Observations -- Exercises -- 13 Identification of Risk Factors Related to Dichotomous and Polychotomous Outcomes -- 13.1 Univariate Analysis -- 13.1.1 Comparing the Distributions of Risk Variables Among Groups -- 13.1.2 Chi-Square Test and Odds Ratio. 13.2 Logistic and Conditional Logistic Regression Models for Dichotomous Outcomes -- 13.2.1 Logistic Regression Model for Prospective Studies -- 13.2.2 Logistic and Conditional Logistic Regression Model for Retrospective Studies -- 13.2.2.1 1:R Matched Design -- 13.2.2.2 n1:n0 Matched Design or Stratified Design -- 13.2.3 Other Models for Dichotomous Outcomes -- 13.3 Models for Polychotomous Outcomes -- 13.3.1 Models for Nominal Polychotomous Outcomes: Generalized Logistic Regression Models -- 13.3.2 Model for Ordinal Polychotomous Outcomes: Ordinal Regression Models -- 13.4 Models for Related Observations -- Exercises -- Appendix -- References -- Index.
9781118593110
Failure time data analysis. Medicine-Research-Statistical methods. Prognosis-Statistical methods.