Book Reviews

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Jing Ning

The University of Texas MD Anderson Cancer Center

Elements of Nonlinear Time Series Analysis and Forecasting. Jan G. De Gooijer. Switzerland: Springer International Publishing, 2017, xxi + 618 pp., $159.99(H), ISBN: 978–3–31–943251–9.

This is an excellent addition to the library of books on time series analysis. The most attractive feature of this book is that it places importance on developing intuition about nonlinear time series rather than the more formal theorem-proof approach. It is abundant with data examples and simulations that enhance understanding of the stochastic properties of the models. In my opinion, the approach taken is the best pedagogical technique to learn about time series models. This book gives realizations from many models: bilinear (BL), nonlinear moving average (NLMA), self-exciting threshold autoregressive moving average (SETARMA), and so on. Visualizing these realizations is helpful to differentiate features and thus build intuition for choosing an appropriate class of models for particular s. The book is self-contained with pseudo-codes and theory and thus gives a multilayer approach to presenting the material, as technical details are placed at the end of each section to serve those readers with the need for formalities.

This book is an ideal resource for a serious student of nonlinear time series and even for a researcher with a good background on linear time series but with very little or no exposure to nonlinear time series. Its level and treatment of the subject is suitable for graduate students in statistics, econometrics, electrical engineering, and applied mathematics who have had proper coursework on mathematical statistics, linear time series, and regression analysis. The coverage of the book is comprehensive: classical nonlinear models; tests of linearity (in both spectral and time domain); model estimation and diagnostics; forecasting (semiparametric, nonparametric, and approximate methods); vector-valued nonlinear time series. The organization of each chapter gives the reader the freedom to explore the topics at various depths. The main body for each chapter gives a big picture exposition of the main ideas (e.g., models, tests, assumptions, methods) and thus attempts to build intuition, with in-depth formalities and theory provided at the end of each section. Any reader who is not familiar with the lay of the land of nonlinear time series will appreciate the summary of terminology and acronyms for the very large number of models. Each section also provides additional references with brief descriptions that will be helpful for digging deeper into the technical details.

I can see how this book can serve the needs of a semester-long course on nonlinear time series that follows after a classic course on linear time series covering general linear processes, ARIMA models, GARCH models, spectral analysis, and nonstationary time series. For this course on nonlinear time series (14 weeks × 3 hr per week), I would cover Chapter 1 (Introduction with many data examples), Chapter 2 (Classical Nonlinear Models), Chapter 3 (Probabilistic Properties), Chapter 4 (Spectral Tests of Linearity), Chapter 5 (Time Domain Tests of Linearity), Chapter 6 (Model Estimation, Selection and Diagnostics), Chapters 9 and 10 (Forecasting), and Chapter 11 (Multivariate Time Series). I would assign three or four problem sets based on the theory and data analytic problems provided at the end of each section. I would also require an individual article that covers in-depth data analysis using the various models presented or in-depth simulation studies on the various tests and methods.

The book comes with a solutions manual for the instructor, which helps in organizing and preparing for a course. One weak point about this book is that the delivery of the codes could be made to be more friendly for the instructor. A good template would be the one provided in the book Time Series Analysis and Its Applications: With R Examples (4th ed.) by Shumway and Stoffer (http://www.stat.pitt.edu/stoffer/tsa4/). Moreover, this book could be improved in the future by adding a special section that compares and contrasts the different classical models in Chapter 2.

I would recommend this book to any scholar who is about to embark on serious research in nonlinear time series, along with (1) Nonlinear and Nonstationary Time Series Analysis by Priestley; (2) Nonlinear Time Series: Theory, Methods and Applications with R Examples by Douc, Moulines, and Stoffer; (3) Nonlinear Time Series: Nonparametric and Parametric Methods by Fan and Yao; and (4) Threshold Models in Nonlinear Time Series Analysis by Tong.

Hernando Ombao

King Abdullah University of Science and Technology

Handbook of Methods for Designing,Monitoring, and Analyzing Dose-Finding Trials. John O'Quigley, Alexia Iasonos, and Björn Bornkamp, eds. Boca Raton, FL: Chapman & Hall/CRC Press, 2017, xiv + 306 pp., $129.95(H), ISBN: 978–1–49–874610–6.

In recent years, model-based methods for dose-finding have become more commonly used and there is growing interest in methods that can be applied to more complex dose-finding trials. A book offering a comprehensive overview that clearly specifies the questions novel techniques can answer would be of great utility. The aim of the Handbook of Methods for Designing, Monitoring, and Analyzing Dose-Finding Trials, edited by John O’Quigley, Alexia Iasonos, and Björn Bornkamp, is to provide such an overview.

The editors have assembled a stellar group of authors, most of whom are leading experts in the field, to provide an overall picture of various methods that are useful when embarking on a trial to identify the correct dose for use in a further study. Given the enormous number of papers in this field, a book summarizing the most recent developments that can be used as the starting point for young researchers or as a reference for established researchers would be tremendously useful. Furthermore, a hands-on guide illustrating how to apply novel dose-finding methods would be invaluable. Unfortunately, we found the Handbook of Methods for Designing, Monitoring, and Analyzing Dose-Finding Trials to be uneven, achieving these needs in some chapters of the book but not in others.

The first part of the book, “Phase I designs,” provides an overview of methods for single agent trials covering binary, ordinal, and time-to-event endpoints. The overview includes methods that become the basis for further developments described later and upon which more complex approaches are constructed. The first chapter also provides an extensive list of useful statistical software that is available to the reader and also provides references for studies comparing different dose-finding methods. A similar provision of relevant software and comparison studies would have been a useful addition to the remaining chapters in the first two parts of the book.

The second part of the book introduces more advanced dose-finding designs for clinical trials of increased complexity. Chapter 5 provides methods for evaluating both toxicity and efficacy of cytotoxic drugs simultaneously. The authors provide step-by-step guidelines for dealing with particular challenges in Phase I/II trials such as delayed responses or missing data. While the overview of the methods is extensive, it is not clear to what extent they are suitable for cytostatic drugs: Wages and Tait (2015) and Riviere, Dubois, and Zohar (2016) have argued that specialized methods for dose-finding are necessary for these studies. Chapter 6 describes dose-finding designs for dual combination trials. The authors indicate that there is a large number of model-based designs for the considered setting, provide an extensive list, and focus on the nonparametric Bayesian optimal interval (BOIN) design. Model-based designs are not discussed here in detail, so we believe that a reader of Chapter 6 would benefit from supplementing their study with the more comprehensive comparison provided by Riviere, Dubois, and Zohar (2015).

The subsequent chapters discuss the very flexible partial ordering continual reassessment method (POCRM) and its application to dose-schedule finding studies. In addition, these chapters discuss the crucial problem of heterogeneity of patients and introduce the nonparametric optimal benchmark: a useful tool to evaluate the performance of novel designs. Since this book has been published, Wages and Varhegyi (2017) have released a user-friendly implementation of the benchmark that the reader might want to consider using. Chapter 10 provides the reader with experiences of practical implementations of the continual reassessment method (CRM, O’Quigley, Pepe, and Fisher 1990). The authors consider several aspects of the design and how they can be tailored to the needs of the trials. We believe that, given its title, the focus of this chapter should have been a bit broader than the specifics of the CRM and should have considered additional practical challenges in dose-finding studies (e.g., decision-making procedure, time required for analysis, etc.).

Given the title of the book, we were surprised to discover that no methods for phase I trials outside of oncology have been discussed in the first two parts of the book. We also found a notable absence of any methods based on a two-parameter logistic regression model (e.g., Whitehead and Williamson 1998). Although Chapter 10 claims that it “does not provide any benefits,” methods based on a two-parameter model are widely used in practice and the statement about the lack of potential benefits is controversial at best. In particular, the Bayesian logistic regression method (Neuenschwander, Branson, and Gsponer 2008) is one of the most commonly used designs in the pharmaceutical industry, and providing it would give the reader a taste of currently employed methods. While we appreciate that it is impossible to cover every available method in a single book, in our opinion this omission limits the utility of the book.

The final part of the book provides a detailed description of Phase II dose-finding methods and we found this part particularly well constructed and a pleasure to read. Most of the chapters in this part include a step-by-step guide to applying these methods using the R package DoseFinding (Bornkamp, Pinheiro, and Bretz 2018), including the code necessary to implement the described designs. Additionally, the same motivating examples are used from chapter to chapter, which helps tremendously to keep the reader focused. These two features allow an investigator to conduct the initial simulation analysis for the planned clinical trial by the means provided in the book only. If the book had followed the same structure throughout, it would have become indispensable for any group undertaking early phase dose-finding studies.

Overall, we think that this book fills an important niche: it provides a good overview of novel dose-finding techniques that are motivated by practical clinical needs and at the same time relates these designs to applications in various stages of dose-finding. We identified some shortcomings, and the chapters are somewhat uneven in many respects: inconsistent reference styles, different presentational approaches, even different intended audiences. Still, the book proves to be a well written, engaging, and useful reference with plenty of motivating clinical trials and illustrations.

Pavel Mozgunov and Thomas Jaki

Lancaster University

http://orcid.org/0000-0002-1096-188X

Statistical Analysis with Measurement Error or Misclassification: Strategy, Method, and Application. Grace Y. Yi. New York, NY: Springer, 2017, xxvii + 479 pp., $139.99(H), ISBN: 978–1–49–396638–7.

This book covers a wide range of topics in a unified framework where measurement error and misclassification problems receive careful treatments, from both practical and theoretical points of view. In particular, the author zooms in on five research fields that are popular playgrounds, especially among biostatisticians and epidemiologists: survival analysis, recurrent event data analysis, longitudinal data analysis, multi-state models, and case–control studies. These constitute Chapters 3 to 7 of the book, with more coverage on mismeasured covariates than on mismeasured responses.

Before starting this central part of the book, the author reviews widely applicable estimation methods in general contexts, without the complication of measurement error. Other concepts and issues to be revisited frequently in later chapters, such as identifiability, model misspecification, and asymptotics, are also briefly reviewed in Chapter 1. In Chapter 2, the author clarifies the types of measurement error to be considered, presents commonly entertained models for them, and outlines general strategies for taking measurement error into account when drawing inference. The first two chapters prepare one well for the methodology development in specific contexts in follow-up chapters. For more technically engaged readers, these reviews can quickly set them on the same page as the author in terms of notational conventions, and the backdrop of measurement error problems in general. Readers less familiar with parts of the background information can gain some intuition of key ideas conveyed in these reviews. For example, in Section 1.2.3, the convergence rate of an estimator is described as a “magnifier,” by which one multiplies the difference between the estimator and the truth so that the resultant scaled difference follows a nondegenerate asymptotic distribution. This analogy of convergence rates is intuitive enough to connect with readers at various levels of previous exposure to large sample theories.

After considering mostly mismeasured covariates in Chapters 3 to 7, the author devotes Chapter 8 to considerations of mismeasured responses, with error-free or error-prone covariates. Finally, a list of important topics in measurement error literature not systematically covered in this book is given in Chapter 9, along with a brief survey of existing works on each topic. Evidently, the author has a wide command of the literature on measurement error. Besides the survey of literature in Chapter 9, a good collection of existing works most relevant to materials discussed is available in each chapter in the section of Bibliographic Notes and Discussions. Readers who wish to try their wings in the field of measurement error may be able to find open research problems in these sections, besides Chapter 9.

In Chapters 3 to 7, five specific research fields are set as the stages for measurement error problems. In each chapter, the author follows a similar road map to present materials. Each of these five chapters begins with a succinct introduction of the research branch considered in that chapter, without measurement error in the picture just yet. These introductions are necessary for one to consider properties of naive inference based on error-prone data, that is, inference that ignores measurement error. Moreover, each introduction is an excellent read for someone unfamiliar with the corresponding research area. Following the introduction is investigation of the effects of measurement error. Then several inference methods adequately addressing measurement error and yielding consistent estimators are chosen to present in detail. In the opening remarks of a chapter, the author makes timely remarks on important distinctions in data structure, modeling, or sampling in the current context compared to the previous chapter(s). For example, it is made crystal clear at the beginning of Chapter 7 that, in case–control studies, both measurement error mechanisms and sample schemes differ from those seen in earlier chapters. Having a uniform coherent structure of presentation in this part of the book prevents readers from losing sight of the big picture even when one is in the midst of a long derivation, which is often inevitable when elaborating a complicated method. The author skillfully offers insights following technically involved derivations, which lead one to see through to the gist of potentially complex mathematical arguments.

Across this middle part of the book, one can see the reappearance of similar approaches for studying effects of measurement error and strategies for correcting naive inference in the presence of measurement error. For instance, the expectation correction method, the insertion correction method, and the conditional score method are frequently demonstrated in different contexts to account for measurement error in parameter estimation. Even though these methods are repeatedly used, the author captures novelties or tweaking that appear in each context to address complications caused by measurement error. An example of such clever adjustments of a routinely used method is the pseudo conditional score method unfolded in Section 6.5. Besides highlighting the novelties of a particular method, the author also gives insightful summaries of methods she chose to present in greater detail, such as the conditional score method for dealing with measurement error in matched case–control studies in Section 7.5. Readers who have gone through some earlier chapters before coming to Chapter 7 are most likely to have become familiar with the rationale behind the conditional score method. The author’s summary comments on this particular conditional score method on page 335 underscore the trick of using the difference-covariate vectors to construct the likelihood function, which allows one to bypass nuisance parameters. Delicate technicalities like this one can be more fully appreciated by readers with a solid background in mathematical statistics. Readers who skip parts of the technical discussions may find similar themes in methodology development repeated without recognizing certain subtle differences.

I appreciate the author’s unwavering effort in answering the question, “What if one ignores measurement error?” The effects of measurement error can get complicated and sometimes counterintuitive. The author strikes a nice balance between generality and interpretability when illustrating what naive inference produces. For instance, in Section 5.2.1, naively adopting the generalized estimating equations (GEE) method to carry out marginal analysis of longitudinal data with covariate measurement error amounts to using the GEE evaluated at error-prone data. Although writing down the naive estimation equations is trivial when one has the GEE in the error-free case, properties of estimators as solutions to the naive GEE are difficult to perceive by simply comparing the naive GEE and the error-free GEE. Following some generic discussions on the naive estimation function in Section 5.2.1, the author gives Example 5.2, where the model for the longitudinal response given covariates is more concrete and simplified. Assumptions are added to this longitudinal model until the naive GEE can be solved explicitly, making the connection between the naive estimators and the truth more transparent. This connection leads to interesting and insightful findings on which parameter may or may not be affected by measurement error, and the bias direction of an estimator compromised by measurement error.

This book can serve well as a textbook for a graduate-level course on measurement error in a (bio)statistics department, unless one is more interested in the Bayesian paradigm for solving measurement error problems. Besides ample real life applications presented in the book, from which students can appreciate practical relevance of measurement error problems, the Supplementary Problems at the end of each of Chapters 1 to 8 are carefully designed to help readers get acquainted with, and sometimes dig deeper on, concepts and methods introduced in that chapter. Most of the exercises directly relate to problems considered in published articles. A diligent student (with an adequate background in mathematical statistics) working on these exercises will comprehend related publications at an advanced level. By attempting these problems, graduate students can become careful, critical, and mindful readers.