Meta -Analysis of binary data using profile likelihood

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.

Author Notes

Bohning, Dankmar; Rattanasiri, Sasivimol; Kuhnert, Ronny

Preface	p. xi
Abbreviations	p. xv
1 Introduction	p. 1
1.1 The occurrence of meta-analytic studies with binary outcome	p. 1
1.2 Meta-analytic and multicenter studies	p. 7
1.3 Center or study effect	p. 9
1.4 Sparsity	p. 10
1.5 Some examples of MAIPDs	p. 12
1.6 Choice of effect measure	p. 14
2 The basic model	p. 23
2.1 Likelihood	p. 23
2.2 Estimation of relative risk in meta-analytic studies using the profile likelihood	p. 24
2.3 The profile likelihood under effect homogeneity	p. 25
2.4 Reliable construction of the profile MLE	p. 28
2.5 A fast converging sequence	p. 29
2.6 Inference under effect homogeneity	p. 33
3 Modeling unobserved heterogeneity	p. 41
3.1 Unobserved covariate and the marginal profile likelihood	p. 42
3.2 Concavity, the gradient function and the PNMLE	p. 43
3.3 The PNMLE via the EM algorithm	p. 45
3.4 The EMGFU for the profile likelihood mixture	p. 46
3.5 Likelihood ratio testing and model evaluation	p. 47
3.6 Classification of centers	p. 48
3.7 A reanalysis on the effect of beta-blocker after myocardial infarction	p. 48
4 Modeling covariate information	p. 55
4.1 Classical methods	p. 55
4.2 Profile likelihood method	p. 59
4.3 Applications of the model	p. 62
4.4 Summary	p. 74
5 Alternative approaches	p. 75
5.1 Approximate likelihood model	p. 75
5.2 Multilevel model	p. 76
5.3 Comparing profile and approximate likelihood	p. 77
5.4 Analysis for the MAIPD on selective tract decontamination	p. 80
5.5 Simulation study	p. 82
5.6 Discussion of this comparison	p. 85
5.7 Binomial profile likelihood	p. 87
6 Incorporating covariate information and unobserved heterogeneity	p. 93
6.1 The model for observed and unobserved covariates	p. 93
6.2 Application of the model	p. 100
6.3 Simplification of the model for observed and unobserved covariates	p. 102
7 Working with CAMAP	p. 105
7.1 Getting started with CAMAP	p. 106
7.2 Analysis of modeling	p. 111
7.3 Conclusion	p. 121
8 Estimation of odds ratio using the profile likelihood	p. 123
8.1 Profile likelihood under effect homogeneity	p. 124
8.2 Modeling covariate information	p. 126
9 Quantification of heterogeneity in a MAIPD	p. 131
9.1 The problem	p. 131
9.2 The profile likelihood as binomial likelihood	p. 134
9.3 The unconditional variance and its estimation	p. 134
9.4 Testing for heterogeneity in a MAIPD	p. 140
9.5 An analysis of the amount of heterogeneity in MAIPDs: a case study	p. 143
9.6 A simulation study comparing the new estimate and the DerSimonian-Laird estimate of heterogeneity variance	p. 144
10 Scrapie in Europe: a multicountry surveillance study as a MAIPD	p. 149
10.1 The problem	p. 149
10.2 The data on scrapie surveillance without covariates	p. 151
10.3 Analysis and results	p. 152
10.4 The data with covariate information on representativeness	p. 153
A	p. 169
A.1 Derivatives of the binomial profile likelihood	p. 169
A.2 The lower bound procedure for an objective function with a bounded Hesse matrix	p. 170
A.3 Connection between the profile likelihood odds ratio estimation and the Mantel-Haenszel estimator	p. 172
Bibliography	p. 175
Author index	p. 183
Subject index	p. 186

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