Meta-analysis of Binary Data Using Profile Likelihood (Hardback) book cover

Meta-analysis of Binary Data Using Profile Likelihood

By Dankmar Bohning, Sasivimol Rattanasiri, Ronny Kuhnert

© 2008 – Chapman and Hall/CRC

208 pages | 54 B/W Illus.

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Hardback: 9781584886303
pub: 2008-03-27
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Providing reliable information on an intervention effect, meta-analysis is a powerful statistical tool for analyzing and combining results from individual studies. Meta-Analysis of Binary Data Using Profile Likelihood focuses on the analysis and modeling of a meta-analysis with individually pooled data (MAIPD). It presents a unifying approach to modeling a treatment effect in a meta-analysis of clinical trials with binary outcomes.

After illustrating the meta-analytic situation of an MAIPD with several examples, the authors introduce the profile likelihood model and extend it to cope with unobserved heterogeneity. They describe elements of log-linear modeling, ways for finding the profile maximum likelihood estimator, and alternative approaches to the profile likelihood method. The authors also discuss how to model covariate information and unobserved heterogeneity simultaneously and use the profile likelihood method to estimate odds ratios. The final chapters look at quantifying heterogeneity in an MAIPD and show how meta-analysis can be applied to the surveillance of scrapie.

Containing new developments not available in the current literature, along with easy-to-follow inferences and algorithms, this book enables clinicians to efficiently analyze MAIPDs.


"The book is very focused on the methods the authors have developed for meta-analysis. It includes a lot of technical details for solving likelihood equations. The advanced key method is based on nonparametric mixing distributions and the question how many mixing components do we have is the crucial one. … A positive aspect is the development of the software tool. The software CAMAP can be downloaded with no costs from the website: …"

ISCB News #49, June 2010

"The authors have succeeded in demonstrating recent developments and the utility of statistical tools for MAIPD-type meta-analysis. … a strong background in mathematics is not needed. The material that is covered in this book can be a part of an advanced biostatistics course. The book should be accessible and useful to graduate students in biostatistics and biostatisticians working in theory as well as in applied areas. The book is well worth recommending for purchase by a library."

Journal of the Royal Statistical Society, Series A, 2010, 173

"I enjoyed reading this book. Having worked with commonly used tools of meta-analysis, I learned a new set of tools and options. The writing is clear and easy to follow. … this is a good book that assumes only a basic knowledge of metaanalysis. Students new to the subject should find it easy to follow while old hands will find interesting new research areas. I would recommend it to anyone interested in the field."

—Rafael Perera, Journal of the American Statistical Association, June 2010

"I recommend the book as a supplement for a graduate-level course in meta-analysis and for readers seeking an alternative approach to analyze MAIPD or multicenter clinical trial studies, specifically when the outcome variable is the occurrence of rare events."

—Taye H. Hamza, Statistics in Medicine, 2009

"The text contains many real-world examples which add to the usefulness of the book. … The balance between statistical theory and practical applications with CAMAP make the text suitable for private study and research."

—C.M. O’Brien, International Statistical Review, 2009

"I am not aware of a more complete source for this topic. The authors’ presentation of the core ideas behind the derivation and use of PML estimates is accessible to anyone familiar with standard likelihood-based estimation. The many good examples facilitate intelligent application of these ideas, and the described software makes implementation simple."

—Eloise Kaizar, Biometrics, June 2009

Table of Contents


The occurrence of meta-analytic studies with binary outcome

Meta-analytic and multicenter studies

Center or study effect


Some examples of MAIPDs

Choice of effect measure

The Basic Model


Estimation of relative risk in meta-analytic studies using the profile likelihood

The profile likelihood under effect homogeneity

Reliable construction of the profile MLE

A fast converging sequence

Inference under effect homogeneity

Modeling Unobserved Heterogeneity

Unobserved covariate and the marginal profile likelihood

Concavity, the gradient function, and the PNMLE

The PNMLE via the EM algorithm

The EMGFU for the profile likelihood mixture

Likelihood ratio testing and model evaluation

Classification of centers

A reanalysis on the effect of beta-blocker after myocardial infarction

Modeling Covariate Information

Classical methods

Profile likelihood method

Applications of the model


Alternative Approaches

Approximate likelihood model

Multilevel model

Comparing profile and approximate likelihood

Analysis for the MAIPD on selective tract decontamination

Simulation study

Discussion of this comparison

Binomial profile likelihood

Incorporating Covariate Information and Unobserved Heterogeneity

The model for observed and unobserved covariates

Application of the model

Simplification of the model for observed and unobserved covariates

Working with CAMAP

Getting started with CAMAP

Analysis of modeling


Estimation of Odds Ratio Using the Profile Likelihood

Profile likelihood under effect homogeneity

Modeling covariate information

Quantification of Heterogeneity in an MAIPD

The problem

The profile likelihood as binomial likelihood

The unconditional variance and its estimation

Testing for heterogeneity in an MAIPD

An analysis of the amount of heterogeneity in MAIPDs: a case study

A simulation study comparing the new estimate and the DerSimonian–Laird estimate of heterogeneity variance

Scrapie in Europe: A Multicountry Surveillance Study as an MAIPD

The problem

The data on scrapie surveillance without covariates

Analysis and results

The data with covariate information on representativeness


Derivatives of the binomial profile likelihood

The lower bound procedure for an objective function with a bounded Hesse matrix

Connection between the profile likelihood odds ratio estimation and the Mantel–Haenszel estimator



About the Series

Chapman & Hall/CRC Interdisciplinary Statistics

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General