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Flowgraph models for multistate time-to-event data (Wiley Series in Probability and Statistics)
Huzurbazar A., Wiley-Interscience, 2004. Type: Book (9780471265146)
Date Reviewed: Jun 2 2005

The Wiley Series in Probability and Statistics publishes substantive books, covering the theory and applications of the field. Time-to-event analysis is also known as survival analysis. Examples of an event could simply be a response, failure, or recurrence of some disease. For example “time passed until recurrence of cancer” in a particular study would be the type of data to be analyzed. Another example is the notion of reliability measured as time-to-failure. Survivor function and reliability function can be defined as S(t) = Pr {T > t} = 1 - F(t).

The need for special time-to-event analysis methods (and a book like this) partly derives from the presence of “censored observations,” in the sense that, for some units, the event of interest has not occurred at the time the data is analyzed. The focus of this book is on multistate stochastic models for “censored time-to-event data with competing risks and recurrent event[s].” Multistate survival analysis usually involves a series of detailed regression analyses that describe transitions between various states. Flowgraph models can also be used in multistate analysis. In other words, the scope of this book is, as expressed in the title, to expose flowgraph models for time-to-event data analysis, with an emphasis on survival and reliability problems. The book is not an easy read. The information is condensed. However, this feature (with the examples given) also makes the book very useful for a serious reader who is interested in flowgraph-model bas!ed analysis of time-to-event data. In the preface, the author explains the practicality of using flowgraphs as a methodology for the data analysis of semi-Markov processes. I agree with the author’s assessment that flowgraphs bring together “applied probability techniques such as transforms and saddlepoint methods and meld them with data analysis and statistical methods.” I recommend this book for readers who have a serious interest in these methods.

This 250-page book is composed of nine chapters and an appendix. Chapter 1, “Multistate Models and Flowgraph Models,” poses the problem, and identifies the scope of the book, in about ten pages. Chapter 2, “Flowgraph Models,” is 30 pages long, and introduces flowgraph models in which series, parallel, feedback loop, recurrent events, convolution, competing risks, and finite mixture distribution are discussed, with ample examples, including cancer progression and engineering hydraulic pumps. Chapter 3, “Inversion of Flowgraph Moment Generating Functions,” is 30 pages long, and connects flowgraph analysis with a density function, survivor function, reliability function, and hazard function, with ample examples including some Maple and R coding. This involves moment generating functions, saddlepoint approximation, and saddlepoint programs. Chapter 4, “Censored Data Histograms,” is about 20 pages long, and introduces histograms !for censored data. Chapter 5, “Bayesian Prediction for Flowgraph Models,” is about 40 pages long, and introduces computing Bayesian predictive densities, cumulative distribution functions, survivor functions, and hazard functions for flowgraph models. Diverse examples used in this chapter involve cancer progression, kidney disease, HIV transfusion, a reversible illness death model, hydraulic pumps, and parts testing. Chapter 6, “Computation Implementation of Flowgraph Models,” is about ten pages of mostly code, showing flowgraph computations using Maple, R, and C. Code for censored data histograms, saddlepoint approximation, Bayesian analysis, and maximum likelihood analysis are given. I have not personally tested this code, but a visual inspection showed that the author had not extensively documented the programs, which is usually the case in this type of programming. Chapter 7, “Semi-Markov Processes,” is about 40 pages long, and introdu!ces applications of flowgraph models for analyzing data from semi-Markov processes. The ample examples in this chapter include birth and death processes, HIV progression, retinopathy, construction engineering, and bone marrow transplants. Chapter 8, “Incomplete Data,” is about 20 pages long, and introduces strategies for incomplete data beyond the usual censoring, with examples including kidney disease, Alzheimer’s related dementia, and retinopathy. The last chapter, “Flowgraph Models for Queuing Systems,” is about 45 pages long, and introduces flowgraph model applications for queueing systems. The appendix is on moment generating functions.

In conclusion, this book is not just for reading, but is for using and applying. Methods are explained comprehensively, with extensive examples. I am sure that data analysts would find valuable examples here for their own applications.

Reviewer:  M. M. Tanik Review #: CR131352 (0604-0353)
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Graph Algorithms (G.2.2 ... )
 
 
State Diagrams (D.2.2 ... )
 
 
Statistical Computing (G.3 ... )
 
 
Design Tools and Techniques (D.2.2 )
 
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