Advanced Analysis of Variance: An interview with author Chihiro Hirotsu

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  • Author: Statistics Views
  • Date: 13 Feb 2018

Towards the end of last year, Wiley was proud to publish Advanced Analysis of Variance, which introduces a revolutionary new model for the statistical analysis of experimental data.

In this important book, internationally acclaimed statistician, Chihiro Hirotsu, goes beyond classical analysis of variance (ANOVA) model to offer a unified theory and advanced techniques for the statistical analysis of experimental data. Dr. Hirotsu introduces the groundbreaking concept of advanced analysis of variance (AANOVA) and explains how the AANOVA approach exceeds the limitations of ANOVA methods to allow for global reasoning utilizing special methods of simultaneous inference leading to individual conclusions.

Focusing on normal, binomial, and categorical data, Dr. Hirotsu explores ANOVA theory and practice and reviews current developments in the field. He then introduces three new advanced approaches, namely: testing for equivalence and non-inferiority; simultaneous testing for directional (monotonic or restricted) alternatives and change-point hypotheses; and analyses emerging from categorical data. Using real-world examples, he shows how these three recognizable families of problems have important applications in most practical activities involving experimental data in an array of research areas, including bioequivalence, clinical trials, industrial experiments, pharmaco-statistics, and quality control, to name just a few.

thumbnail image: Advanced Analysis of Variance: An interview with author Chihiro Hirotsu

1. Congratulations on the recent publication of your book Advanced Analysis of Variance which introduces ‘a revolutionary new model for the statistical analysis of experimental data’. How did the writing process begin?

It’s been a very nice experience. I have written six single authored books on the analysis of variance, the analysis of medical data and the analysis of discrete data in Japanese, and wished to write finally an English book. There have been several invitations to write an English book from the foreign publishers but I thought it was too early since my research for developing new statistical methods was progressing. Then it was a good timing to publish an English book when I published a paper on the unifying approach to the shape and change-point hypotheses in CSDA in 2016.

2. In this book, you go beyond classical analysis of variance (ANOVA) model to offer a unified theory and advanced techniques for the statistical analysis of experimental data and introduce the ground-breaking concept of advanced analysis of variance (AANOVA) and explain how the AANOVA approach exceeds the limitations of ANOVA methods to allow for global reasoning utilizing special methods of simultaneous inference leading to individual conclusions. What led to you coming arriving at this theory?

I read a very useful book of ANOVA by Scheffe ́ repeatedly when I was a graduate student at University of Tokyo. At the same time I was very interested in applying the ANOVA techniques to the quality control in Japanese factories and then gradually inclined to the clinical trials both as a researcher and from the regulatory side. In the mean time I encountered many practical problems which cannot be solved by the methods explained in Scheffe ́’s or any other book in this field. Therefore it was a motivation of my research work to develop new statistical methods for the problems to which no appropriate method was available. They include a unifying approach to the shape and change-point hypotheses, row-wise multiple comparisons for the two-way data and the ANOVA techniques for the contingency tables. In particular the overall analysis by the F or the goodness of fit χ^2 is not always useful and identifying the best one among the candidates or classifying individuals of similar response profiles should often lead to a more reasonable conclusion.

3. Throughout the book, you offer three new advanced approaches, namely: testing for equivalence and non-inferiority; simultaneous testing for directional (monotonic or restricted) alternatives and change-point hypotheses; and analyses emerging from categorical data, all with real world samples. Please could you give us a taster of one of these approaches?

Use of accumulated statistics for the directional alternatives is theoretically and practically more useful as compared with the restricted likelihood ratio approach who’s distribution theory is a little complicated. It really widens the application of monotone, convex and sigmoid models. Also it is strange that its relationship with the change-point models has not been pointed out anywhere. Those statistics are so simple that they can be easily extended also to the two-way data including contingency tables.

4. What were your main objectives during the writing process?

My methods are originated from the real problems in the field of quality control and the clinical trials so that it is my pleasure to provide useful methods to those who have data to be analyzed in those fields. Also I tried to provide useful software.

5. If there is one piece of information or advice that you would want your reader to take away and remember after reading your book, what would that be?

Please remember that the two-way data including the contingency table can be approached almost similarly as the one-way data by a variety of ANOVA techniques. Further the restricted alternatives can be handled more easily sometimes because of the restrictions.

6. Who should read the book and why?

Graduate students, scientists and practitioners in the fields of the quality control and the clinical trials. I tried to cover from the basic theory to extended applications but I hope they could extend my approach further to tackle new problems.

7. Why is this book of particular interest now?

The practitioners in the field of the clinical trial are required to be more scientific than past. The social data from the other field, for example, are also requiring some statistical inference. Then the ANOVA techniques for the categorical data should be most useful.

8. Were there areas of the book that you found more challenging to write, and if so, why?

Maybe Chapters 6, 10 and 11. Chapter 6 develops an original and very useful approach to the shape and change-point hypotheses. It has a very nice theoretical basis and is yet of a very simple structure as compared with the restricted maximum likelihood approach so that it is extended to the two-way data both of normal and categorical. Further the row-wise multiple comparisons procedure is developed based on the accumulated statistics in Chapters 10 and 11 replacing the overall analysis by F and χ^2 test.

9. What is it about this area that fascinates you in particular?

It often concerns the important decision making. The statistical inference employed in Phase Ⅱ and Ⅲ of a clinical trial, for example, concerns the decision making which is definitely influential on the life science.

10. What was it that introduced you each to statistics as a discipline and what was it that led you to pursue the area as a career?

Actually my interest is the applied statistics with a rigid theoretical basis which can contribute to the real world such as quality control and clinical trial. The scientific decision making in those fields is so important and requires the knowledge about the fields in addition to a deep knowledge in statistics. There are infinite opportunities for developing new statistical methods in the real world and it is very exciting.


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