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Maximum likelihood estimation based on Newton–Raphson iteration for the bivariate random effects model in test accuracy meta-analysis
A bivariate generalised linear mixed model is often used for meta-analysis of test accuracy studies. The model is complex and requires five parameters to be estimated. As there is no closed form for the likelihood function for the model, maximum likelihood estimates for the parameters have to be obt...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
SAGE Publications
2019
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7221455/ https://www.ncbi.nlm.nih.gov/pubmed/31184270 http://dx.doi.org/10.1177/0962280219853602 |
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author | Willis, Brian H Baragilly, Mohammed Coomar, Dyuti |
author_facet | Willis, Brian H Baragilly, Mohammed Coomar, Dyuti |
author_sort | Willis, Brian H |
collection | PubMed |
description | A bivariate generalised linear mixed model is often used for meta-analysis of test accuracy studies. The model is complex and requires five parameters to be estimated. As there is no closed form for the likelihood function for the model, maximum likelihood estimates for the parameters have to be obtained numerically. Although generic functions have emerged which may estimate the parameters in these models, they remain opaque to many. From first principles we demonstrate how the maximum likelihood estimates for the parameters may be obtained using two methods based on Newton–Raphson iteration. The first uses the profile likelihood and the second uses the Observed Fisher Information. As convergence may depend on the proximity of the initial estimates to the global maximum, each algorithm includes a method for obtaining robust initial estimates. A simulation study was used to evaluate the algorithms and compare their performance with the generic generalised linear mixed model function glmer from the lme4 package in R before applying them to two meta-analyses from the literature. In general, the two algorithms had higher convergence rates and coverage probabilities than glmer. Based on its performance characteristics the method of profiling is recommended for fitting the bivariate generalised linear mixed model for meta-analysis. |
format | Online Article Text |
id | pubmed-7221455 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | SAGE Publications |
record_format | MEDLINE/PubMed |
spelling | pubmed-72214552020-06-02 Maximum likelihood estimation based on Newton–Raphson iteration for the bivariate random effects model in test accuracy meta-analysis Willis, Brian H Baragilly, Mohammed Coomar, Dyuti Stat Methods Med Res Articles A bivariate generalised linear mixed model is often used for meta-analysis of test accuracy studies. The model is complex and requires five parameters to be estimated. As there is no closed form for the likelihood function for the model, maximum likelihood estimates for the parameters have to be obtained numerically. Although generic functions have emerged which may estimate the parameters in these models, they remain opaque to many. From first principles we demonstrate how the maximum likelihood estimates for the parameters may be obtained using two methods based on Newton–Raphson iteration. The first uses the profile likelihood and the second uses the Observed Fisher Information. As convergence may depend on the proximity of the initial estimates to the global maximum, each algorithm includes a method for obtaining robust initial estimates. A simulation study was used to evaluate the algorithms and compare their performance with the generic generalised linear mixed model function glmer from the lme4 package in R before applying them to two meta-analyses from the literature. In general, the two algorithms had higher convergence rates and coverage probabilities than glmer. Based on its performance characteristics the method of profiling is recommended for fitting the bivariate generalised linear mixed model for meta-analysis. SAGE Publications 2019-06-11 2020-04 /pmc/articles/PMC7221455/ /pubmed/31184270 http://dx.doi.org/10.1177/0962280219853602 Text en © The Author(s) 2019 http://creativecommons.org/licenses/by/4.0/ This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://www.creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/open-access-at-sage). |
spellingShingle | Articles Willis, Brian H Baragilly, Mohammed Coomar, Dyuti Maximum likelihood estimation based on Newton–Raphson iteration for the bivariate random effects model in test accuracy meta-analysis |
title | Maximum likelihood estimation based on Newton–Raphson iteration for
the bivariate random effects model in test accuracy
meta-analysis |
title_full | Maximum likelihood estimation based on Newton–Raphson iteration for
the bivariate random effects model in test accuracy
meta-analysis |
title_fullStr | Maximum likelihood estimation based on Newton–Raphson iteration for
the bivariate random effects model in test accuracy
meta-analysis |
title_full_unstemmed | Maximum likelihood estimation based on Newton–Raphson iteration for
the bivariate random effects model in test accuracy
meta-analysis |
title_short | Maximum likelihood estimation based on Newton–Raphson iteration for
the bivariate random effects model in test accuracy
meta-analysis |
title_sort | maximum likelihood estimation based on newton–raphson iteration for
the bivariate random effects model in test accuracy
meta-analysis |
topic | Articles |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7221455/ https://www.ncbi.nlm.nih.gov/pubmed/31184270 http://dx.doi.org/10.1177/0962280219853602 |
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