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

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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.


Author(s): Ton J. Cleophas, Aeilko H. Zwinderman
Publisher: Springer
Year: 2023

Language: English
Pages: 229
City: Cham

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