Maximum likelihood estimation based on Newton-Raphson iteration for the bivariate random effects model in test accuracy meta-analysis.

Abstract:

: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.

journal_name

Stat Methods Med Res

authors

Willis BH,Baragilly M,Coomar D

doi

10.1177/0962280219853602

subject

Has Abstract

pub_date

2020-04-01 00:00:00

pages

1197-1211

issue

4

eissn

0962-2802

issn

1477-0334

journal_volume

29

pub_type

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