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**Empirical likelihood method in survival analysis.**
*(English)*
Zbl 1341.62031

Chapman & Hall/CRC Biostatistics Series. Boca Raton, FL: CRC Press (ISBN 978-1-4665-5492-4/hbk; 978-1-4665-5493-1/ebook). xvii, 202 p. (2016).

The interest in empirical likelihood methods has grown steadily during the last three decades, mainly because of the attraction of the combination of nonparametric and likelihood methods. This is particularly valid for the analysis of survival data, where almost total focus is on nonparametric or semiparametric methods: Kaplan-Meier and Nelson-Aalen estimators of distributions and Cox regression. The book fits well into this framework.

After an introduction to traditional survival analysis theory, the empirical likelihood approach is introduced, including treatment of right censored observations. The author underlines in the preface that the book only deals with right censored data, excluding for instance interval censored and left-truncated data. Especially, the exclusion of left truncation is disturbing (depending on application). Thus, the treatment of topics in survival analysis is fairly complete, following the typical path of books on survival analysis in general: One-sample estimation, two-sample and \(k\)-sample testing, and Cox regression. The empirical likelihood methods for accelerated failure time models are introduced, and the optimality of confidence regions derived from empirical likelihood is discussed. Each chapter ends with a set of exercises.

The presentation is to a large extent based on illustrations using a couple of R packages, emplik and ELYP by the author, and a few other packages, all available from CRAN, The Comprehensive R Archive Network. The reader can easily reproduce the analyses presented in the book with the aid of these packages and data sets found in R packages from CRAN.

After an introduction to traditional survival analysis theory, the empirical likelihood approach is introduced, including treatment of right censored observations. The author underlines in the preface that the book only deals with right censored data, excluding for instance interval censored and left-truncated data. Especially, the exclusion of left truncation is disturbing (depending on application). Thus, the treatment of topics in survival analysis is fairly complete, following the typical path of books on survival analysis in general: One-sample estimation, two-sample and \(k\)-sample testing, and Cox regression. The empirical likelihood methods for accelerated failure time models are introduced, and the optimality of confidence regions derived from empirical likelihood is discussed. Each chapter ends with a set of exercises.

The presentation is to a large extent based on illustrations using a couple of R packages, emplik and ELYP by the author, and a few other packages, all available from CRAN, The Comprehensive R Archive Network. The reader can easily reproduce the analyses presented in the book with the aid of these packages and data sets found in R packages from CRAN.

Reviewer: Göran Broström (Umea)

### MSC:

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

62N02 | Estimation in survival analysis and censored data |

62G05 | Nonparametric estimation |

62N01 | Censored data models |

62N05 | Reliability and life testing |