Quantile regression is an approach to data at a loss of homogeneity, for example (1) data with outliers, (2) skewed data like corona - deaths data, (3) data with inconstant variability, (4) big data. In clinical research many examples can be given like circadian phenomena, and diseases where spreading may be dependent on subsets with frailty, low weight, low hygiene, and many forms of lack of healthiness. Stratified analyses is the laborious and rather explorative way of analysis, but quantile analysis is a more fruitful, faster and completer alternative for the purpose. Considering all of this, we are on the verge of a revolution in data analysis. The current edition is the first textbook and tutorial of quantile regressions for medical and healthcare students as well as recollection/update bench, and help desk for professionals. Each chapter can be studied as a standalone and covers one of the many fields in the fast growing world of quantile regressions. Step by step analyses of over 20 data files stored at extras.springer.com 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 quantile regression methods for the benefit of physicians, students, and investigators.
Author(s): Ton J. Cleophas, Aeilko H. Zwinderman
Publisher: Springer
Year: 2022
Language: English
Pages: 282
City: Cham
Preface
Contents
Chapter 1: General Introduction
1.1 Summary
1.2 Introduction
1.3 Principle of Regression Analysis
1.4 Principle of Quantile Regression
1.5 History and Background of Quantile Regression
1.6 Data Example
1.7 Separating Quantiles, Traditional and Quantile-wise
1.8 Special Case
1.9 Quantile Regression Both for Continuous and Discrete Outcome Variables
1.10 References
Chapter 2: Mathematical Models for Separating Quantiles from One Another
2.1 Summary
2.2 Introduction
2.3 Maximizing Linear Functions with the Help of Support Vectors
2.4 Lagrangian Multiplier Method
2.5 Maximizing Linear Functions with the Help of Rectangles
2.6 Maximizing Linear Functions with the Help of Simplex Algorithms
2.7 The Intuition of Quantile Regression
2.8 Special Case
2.9 Traditional Statistical Methods Applied in This Edition
2.10 Conclusions
2.11 References
Part I: Simple Univariate Regressions Versus Quantile
Chapter 3: Traditional and Robust Regressions Versus Quantile
3.1 Summary
3.2 Introduction
3.3 Traditional and Robust Regression
3.4 Quantile Regressions
3.5 Conclusion
3.6 References
Chapter 4: Autocorrelations Versus Quantile Regressions
4.1 Summary
4.2 Introduction
4.3 Autoregression Analysis
4.4 Quantile Regressions
4.5 Conclusions
4.6 References
Chapter 5: Discrete Trend Testing Versus Quantile Regression
5.1 Summary
5.2 Introduction
5.3 Discrete Trend Analysis
5.4 Quantile Regressions
5.5 Conclusion
5.6 References
Chapter 6: Continuous Trend Testing Versus Quantile Regression
6.1 Summary
6.2 Introduction
6.3 Linear Trend Testing of Continuous Data
6.4 Quantile Regressions
6.5 Conclusion
6.6 References
Chapter 7: Binary Poisson/Negative Binomial Regressions Versus Quantile
7.1 Summary
7.2 Introduction
7.3 Binary Poisson and Negative Binomial Regressions
7.4 Quantile Regressions
7.5 Conclusion
7.6 References
Chapter 8: Robust Standard Errors Regressions Versus Quantile
8.1 Summary
8.2 Introduction
8.3 Robust Standard Errors
8.4 Quantile Regressions
8.5 Conclusion
8.6 References
Chapter 9: Optimal Scaling Versus Quantile Regression
9.1 Summary
9.2 Introduction
9.3 Optimal Scaling
9.4 Quantile Regression
9.5 Conclusions
9.6 References
Chapter 10: Intercept only Poisson Regression Versus Quantile
10.1 Summary
10.2 Introduction
10.3 Poisson Intercept Only
10.4 Quantile Regressions
10.5 Conclusion
10.6 References
Part II: Multiple Variables Regressions Versus Quantile
Chapter 11: Four Predictors Regressions Versus Quantile
11.1 Summary
11.2 Introduction
11.3 Four Predictors Regressions
11.4 Quantile Regressions
11.5 Conclusion
11.6 References
Chapter 12: Gene Expressions Regressions, Traditional Versus Quantile
12.1 Summary
12.2 Introduction
12.3 Gene Expressions Regression
12.4 Quantile Regressions
12.5 Conclusion
12.6 References
Chapter 13: Koenker´s Multiple Variables Analysis with Quantile Modeling
13.1 Summary
13.2 Introduction
13.3 SAS Statistical Software Graphs Interpreted
13.4 First Four Graphs
13.5 The Second Set of Four Graphs
13.6 The Third Set of Four Graphs
13.7 The Fourth Set of Four Graphs
13.8 Conclusion
13.9 References
Chapter 14: Interaction Adjusted Regression Versus Quantile
14.1 Summary
14.2 Introduction
14.3 Interaction Adjusted Regression
14.4 Quantile Regressions
14.5 Conclusion
14.6 References
Chapter 15: Quantile Regression to Study Corona Deaths
15.1 Summary
15.2 Introduction
15.3 Methods and Main Results
15.4 Conclusion
15.5 References
Chapter 16: Laboratory Values Predict Survival Sepsis, Traditional Regression Versus Quantile
16.1 Summary
16.2 Introduction
16.3 Traditional Regression
16.4 Quantile Regressions
16.5 Conclusion
16.6 References
Chapter 17: Multinomial Regression Versus Quantile
17.1 Summary
17.2 Introduction
17.3 Multinomial Regressions and More
17.4 Quantile Regressions
17.5 Conclusions
17.6 References
Chapter 18: Regressions with Inconstant Variability, Traditional and Weighted Least Squares Analysis Versus Quantile
18.1 Summary
18.2 Introduction
18.3 Regressions with Inconstant Variability
18.4 Quantile Regressions
18.5 Conclusion
18.6 References
Chapter 19: Restructuring Categories into Multiple Binary Variables Versus Quantile Regressions
19.1 Summary
19.2 Introduction
19.3 Traditional Multiple Regression After Restructuring Predictive Categories into Multiple Binary Variables
19.4 Quantile Regressions
19.5 Conclusion
19.6 References
Chapter 20: Poisson Events per Person per Period of Time Versus Quantile Regression
20.1 Summary
20.2 Introduction
20.3 3. Poisson Events per Person per Period of Time
20.4 Quantile Regression
20.5 Conclusion
20.6 References
Part III: Special Regressions Versus Quantile
Chapter 21: Two Stage Least Squares Analysis Versus Quantile
21.1 Summary
21.2 Introduction
21.3 Two Stage Least Squares (SLS)
21.4 Quantile Regressions
21.5 Conclusion
21.6 References
Chapter 22: Partial Correlations Versus Quantile Regressions
22.1 Summary
22.2 Introduction
22.3 Partial Correlations
22.4 Quantile Regressions
22.5 Conclusions
22.6 References
Chapter 23: Random Intercepts Regression Versus Quantile
23.1 Summary
23.2 Introduction
23.3 Random Intercept Regression
23.4 Quantile Regressions
23.5 Quantile Regression with Intercept Included
23.6 Conclusion
23.7 References
Chapter 24: Regression Trees Versus Quantile Regression
24.1 Summary
24.2 Introduction
24.3 Regression Trees
24.4 Quantile Regressions
24.5 Conclusions
24.6 References
Chapter 25: Kernel Regression Versus Quantile Regression
25.1 Summary
25.2 Introduction
25.3 Kernel Regression
25.4 Quantile Regressions
25.5 Conclusions
25.6 References
Chapter 26: Quasi-likelihood Regressions vs Quantile
26.1 Summary
26.2 Introduction
26.3 Quasi-likelihood Regressions
26.4 Quantile Regressions
26.5 Conclusion
26.6 References
Chapter 27: Summaries
Index
