Modern Survival Analysis in Clinical Research: Cox Regressions Versus Accelerated Failure Time Models

Description

An important novel menu for Survival Analysis entitled Accelerated Failure Time (AFT) models has been published by IBM (international Businesss Machines) in its SPSS statistical software update of 2023. Unlike the traditional Cox regressions that work with hazards, which are the ratio of deaths and non-deaths in a sample, it works with risk of death, which is the proportion of deaths in the same sample. The latter approach may provide better sensitivity of testing, but has been seldom applied, because with computers risks are tricky and hazards because they are odds are fine. This was underscored in 1997 by Keiding and colleague statisticians from Copenhagen University who showed better-sensitive goodness of fit and null-hypothesis tests with AFT than with Cox survival tests. So far, a controlled study of a representative sample of clinical Kaplan Meier assessments, where the sensitivity of Cox regression is systematically tested against that of AFT modeling, has not been accomplished. This edition is the first textbook and tutorial of AFT modeling both for medical and healthcare students and for professionals. Each chapter can be studied as a standalone, and, using, real as well as hypothesized data, it tests the performance of the novel methodology against traditional Cox regressions. Step by step analyses of over 20 data files stored at Supplementary Files at Springer Interlink are included for self-assessment. We should add that the authors are well qualified in their field. Professor Zwinderman is past-president of the International Society of Biostatistics (2012-2015) and Professor Cleophas is past-president of the American College of Angiology (2000-2002). From their expertise they should be able to make adequate selections of modern data analysis methods for the benefit of physicians, students, and investigators. The authors have been working and publishing together for 25 years and their research can be characterized as a continued effort to demonstrate that clinical data analysis is not mathematics but rather a discipline at the interface of biology and mathematics. Preface Contents Chapter 1: Regression Analysis 1.1 Introduction 1.2 History 1.3 Methodologies of Regression Analysis 1.3.1 Linear Regression 1.3.2 Logistic Regression 1.3.3 Cox Regression 1.4 Conclusion References Chapter 2: Cox Regressions 2.1 Introduction 2.2 History of Cox Regressions 2.3 Principles of Cox Regressions 2.4 Conclusion References Chapter 3: Accelerated Failure Time Models 3.1 Introduction 3.2 History of Failure Time Models 3.3 Methodology of Failure Time Models 3.4 Graphs of Successful Functions to Analyze Accelerated Failure Time Models 3.5 Conclusion References Chapter 4: Simple Dataset with Event as Outcome and Treatment as Predictor 4.1 Introduction 4.2 Data Example 4.3 Data Analysis in SPSS Statistical Software Version 29 4.4 Cox Regression 4.5 Accelerated Failure Time with Weibull Distribution 4.6 Accelerated Failure Time Model with Exponential Distribution 4.7 Accelerated Failure Time Model with Log Normal Distribution 4.8 Accelerated Failure Time Model with Log Logistic Distribution 4.9 Conclusion References Chapter 5: Simple Dataset with Death as Outcome and Treatment Modality, Cholesterol, and Age as Predictors 5.1 Introduction 5.2 Data Example 5.3 Data Analysis in SPSS Statistical Software Version 29 5.4 Three Predictors Cox Regression 5.5 Three Predictors Accelerated Failure Time (AFT) with Weibull Distribution 5.6 Three Predictors Accelerated Failure Time Model with Exponential Distribution 5.7 Three Predictors Accelerated Failure Time with Log Normal Distribution 5.8 Three Predictors Accelerated Failure Time with Log Logistic Distribution 5.9 Conclusion References Chapter 6: Glioma Brain Cancer 6.1 Introduction 6.2 Data Example 6.3 Data Analysis in SPSS Statistical Software Version 29 6.4 Cox Regression 6.5 Accelerated Failure Time (AFT) Model with Weibull Distribution 6.6 The Accelerated Failure Time (AFT) with Exponential Distribution 6.7 Accelerated Failure Time (AFT) with Log Normal Distribution 6.8 Accelerated Failure Time with Log-logistic Distribution 6.9 Conclusion References Chapter 7: Linoleic Acid for Colonic Carcinoma 7.1 Introduction 7.2 Data Example 7.3 Data Analysis in SPSS Statistical Software Version 29 7.4 Cox Regression 7.5 Accelerated Failure Time (AFT) with Weibull Distribution 7.6 Accelerated Failure Time (AFT) with Exponential Distribution 7.7 Accelerated Failure Time (AFT) with Log Normal Distribution 7.8 Accelerated Failure Time (AFT) with Log Logistic Distribution 7.9 Conclusion References Chapter 8: The Effect on Survival of Maintained Chemotherapy with Acute Myelogenous Leucemia 8.1 Introduction 8.2 Data Example 8.3 Data Analysis in SPSS Statistical Software Version 29 8.4 Cox Regression 8.5 Accelerated Failure Time (AFT) with Weibull Distribution 8.6 Accelerated Failure Time (AFT) with Exponential Distribution 8.7 Accelerated Failure Time (AFT) with Log Normal Distribution 8.8 Accelerated Failure Time (AFT) with Log Logistic Distribution 8.9 Conclusion References Chapter 9: Eighty Four Month Parallel Group Mortality Study 9.1 Introduction 9.2 Data Example 9.3 Data Analysis in SPSS Statistical Software Version 29 9.4 Cox Regression 9.5 Accelerated Failure Time (AFT) Model with the Weibull Distribution 9.6 Accelerated Failure Time (AFT) Model with the Exponential Distribution 9.7 Accelerated Failure Time (AFT) Model with the Log Normal Distribution 9.8 Accelerated Failure Time (AFT) Model with Log Logistic Distribution 9.9 Conclusion References Chapter 10: The Effect on Survival from Stages 1 and 2 Histiocytic Lymphoma 10.1 Introduction 10.2 Data Example 10.3 Data Analysis Using SPSS Statistical Software Version 29 10.4 Cox Regression 10.5 Accelerated Failure Time (AFT) with Weibull Distribution 10.6 Accelerated Failure Time (AFT) with Exponential Distribution 10.7 Accelerated Failure Time (AFT) with Log Normal Distribution 10.8 Accelerated Failure Time (AFT) with Log Logistic Distribution 10.9 Conclusion References Chapter 11: Survival of 64 Lymphoma Patients with or Without B Symptoms 11.1 Introduction 11.2 Data Example 11.3 Data Analysis in SPSS Statistical Software Version 29 11.4 Cox Regression 11.5 Accelerated Failure Time (AFT) Model with Weibull Distribution 11.6 Accelerated Failure Time (AFT) Model with Exponential Distribution 11.7 Accelerated Failure Time (AFT) Model with Log Normal Distribution 11.8 Accelerated Failure Time (AFT) Model with Log Logistic Distribution 11.9 Conclusion References Chapter 12: Effect on Time-to-Event of Group Membership 12.1 Introduction 12.2 Data Example 12.3 Data Analysis Using SPSS Statistical Software Version 29 12.4 Cox Regression 12.5 Accelerated Failure Time (AFT) Model with Weibull Distribution 12.6 Accelerated Failure Time (AFT) with Exponential Distribution 12.7 Accelerated Failure Time (AFT) with Log Normal Distribution 12.8 Accelerated Failure Time (AFT) with Log Logistic Distribution 12.9 Conclusion References Chapter 13: The Effect on Survival of Group Membership 13.1 Introduction 13.2 Data Example 13.3 Data Analysis Using SPSS Statistical Software Version 29 13.4 Cox Regression 13.5 Accelerated Failure Time (AFT) Models with Weibull Distribution 13.6 Accelerated Failure Time (AFT) Models with Exponential Distribution 13.7 Accelerated Failure Time (AFT) Model with Log Normal Distribution 13.8 Accelerated Failure Time (AFT) Model with Log Logistics Distribution 13.9 Conclusion References Chapter 14: Deaths from Carcinoma After Exposure to Carcinogens in Rats 14.1 Introduction 14.2 Data Example 14.3 Data Analysis Using SPSS Statistical Software Version 29 14.4 Cox Regression 14.5 Accelerated Failure Time (AFT) Model with Weibull Distribution 14.6 Accelerated Failure Time (AFT) Model with Exponential Distribution 14.7 Accelerated Failure Time (AFT) Model with Log Normal Distribution 14.8 Accelerated Failure Time (AFT) Model with Log Logistics Distribution 14.9 Conclusion References Chapter 15: Effect of Group Membership on Survival 15.1 Introduction 15.2 Data Example 15.3 Data Analysis Using SPSS Statistical Software Version 29 15.4 Cox Regression 15.5 Accelerated Failure Time (AFT) Models with Weibull Distribution 15.6 Accelerated Failure Time (AFT) Model with Exponential Distribution 15.7 Accelerated Failure Time (AFT) Model with Log Normal Distribution 15.8 Accelerated Failure Time (AFT) Model with Log Logistics Distribution 15.9 Conclusion References Chapter 16: Multiple Variables Regression Study of 2421 Stroke Patients Assessed for Time to Second Stroke 16.1 Introduction and Data Example 16.2 Data Analysis in SPSS Statistical Software Version 29 16.3 Cox Regression 16.4 Accelerated Failure Time (AFT) with Weibull Distribution 16.5 Accelerated Failure Time (AFT) with Exponential Distribution 16.6 Accelerated Failure Time (AFT) with Log Normal Distribution 16.7 Accelerated Failure Time (AFT) with Log Logistic Distribution 16.8 Conclusion References Chapter 17: Hypothesized 55 Patient Study of Effect of Treatment Modality on Survival 17.1 Introduction 17.2 Data Example 17.3 Data Analysis Using SPSS Statistical Software Version 29 17.4 Cox Regression 17.5 Accelerated Failure Time (AFT) with Weibull’s Distribution 17.6 Accelerated Failure Time (AFT) with Exponential Distribution 17.7 Acccelerated Failure Time (AFT) with Log Normal Distribution 17.8 Accelerated Failure Time (AFT) with Log Logistic Distribution 17.9 Conclusion References Chapter 18: One Year Follow-Up Study with Many Censored Patients 18.1 Introduction 18.2 Data Example 18.3 Data Analysis Using SPSS Statistical Software Version 29 18.4 Cox Regression 18.5 Accelerated Failure Time (AFT) with Weibull Distribution 18.6 Accelerated Failure Time (AFT) Model with Exponential Distribution 18.7 Accelerated Failure Time (AFT) Model with Log Normal Distribution 18.8 Accelerated Failure Time (AFT) Model with Log Logistics Distribution 18.9 Conclusion References Chapter 19: Alcohol Relapse After Detox Program Treated with or Without a Personal Coach 19.1 Introduction 19.2 Data Example 19.3 Data Analysis Using SPSS Statistical Software Version 29 19.4 Cox Regression 19.5 Accelerated Failure Time (AFT) Models with Weibull Distribution 19.6 Accelerated Failure Times (AFT) Model with Exponential Distribution 19.7 Accelerated Failure Time (AFT) Model with Log Normal Distribution 19.8 Accelerated Failure Times (AFT) Model with Log Logistics Distribution 19.9 Conclusion References Chapter 20: Alcohol Relapse After Detox Program with 3 Predictors 20.1 Introduction 20.2 Data Example 20.3 Data Analysis Using SPSS Statistical Software Version 29 20.4 Cox Regression 20.5 Accelerated Failure Time (AFT) Model with Weibull Distribution 20.6 Accelerated Failure Time Model with Exponential Distribution 20.7 Accelerated Failure Time (AFT) with Log Normal Distribution 20.8 Accelerated Failure Time (AFT) Model with Log Logistics Distribution 20.9 Conclusion References Chapter 21: Ayurvedic Therapy for Human Immunodeficiency Virus 21.1 Introduction 21.2 Data Example 21.3 Data Analysis Using SPSS Statistical Software Version 29 21.4 Cox Regression 21.5 Accelerated Failure Time (AFT) Model with Weibull Distribution 21.6 Accelerated Failure Time (AFT) Model with Exponential Distribution 21.7 Accelerated Failure Time (AFT) Model with Log Normal Distribution 21.8 Accelerated Failure Time (AFT) Model with Log Logistics Distribution 21.9 Conclusion References Chapter 22: Time to Event Regressions Other Than Cox Regressions 22.1 Introduction 22.2 Cox with Time Dependent Predictors 22.3 Segmented Cox 22.4 Interval Censored Regressions 22.5 Autocorrelations 22.6 Polynomial Regressions 22.7 Conclusion References Chapter 23: Abstracts of the Chapters 1 to 22 References