Methods for Assessing Distributional Assumptions in Individual Participant Data Meta-Analysis of Diagnostic Tests
Abstract
Meta-analysis of diagnostic test accuracy (DTA) studies is commonly based on bivariate generalized linear mixed models (GLMMs) that assume normally distributed study-specific random effects. In practice, this distributional assumption is rarely examined, particularly in individual participant data meta-analysis (IPDMA), where empirical Bayes (EB) estimates exhibit heterogeneous precision across studies. Applying standard multivariate normality tests to such estimates can therefore lead to misleading inference. We propose a weighted extension of the Henze-Zirkler (HZ) test to assess bivariate normality of random effects, accounting for study-specific precision via inverse-variance weighting. To obtain valid finite-sample inference, we develop a parametric bootstrap calibration procedure. Extensive simulation studies showed that the classical HZ test applied to EB estimates can exhibit substantial Type I error inflation, whereas the proposed weighted procedures maintain nominal error rates while retaining power to detect departures from normality. The proposed method provides a practical, statistically principled diagnostic tool for assessing random-effects distributional assumptions in hierarchical models, with particular relevance to IPDMA of DTA studies. Although motivated by IPDMA, the proposed approach also extends to aggregate-data diagnostic test accuracy meta-analysis based on study-level 2-by-2 tables.
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BibTeX
@misc{bedada2026methods,
title = {{Methods for Assessing Distributional Assumptions in Individual Participant Data Meta-Analysis of Diagnostic Tests}},
author = {Diribsa T. Bedada and Zelalem F. Negeri},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03333},
eprint = {2611.03333},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03333},
}
RIS
TY - UNPB
TI - Methods for Assessing Distributional Assumptions in Individual Participant Data Meta-Analysis of Diagnostic Tests
AU - Diribsa T. Bedada
AU - Zelalem F. Negeri
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03333
UR - https://arxiv.org/abs/2611.03333
AB - Meta-analysis of diagnostic test accuracy (DTA) studies is commonly based on bivariate generalized linear mixed models (GLMMs) that assume normally distributed study-specific random effects. In practice, this distributional assumption is rarely examined, particularly in individual participant data meta-analysis (IPDMA), where empirical Bayes (EB) estimates exhibit heterogeneous precision across studies. Applying standard multivariate normality tests to such estimates can therefore lead to misleading inference. We propose a weighted extension of the Henze-Zirkler (HZ) test to assess bivariate normality of random effects, accounting for study-specific precision via inverse-variance weighting. To obtain valid finite-sample inference, we develop a parametric bootstrap calibration procedure. Extensive simulation studies showed that the classical HZ test applied to EB estimates can exhibit substantial Type I error inflation, whereas the proposed weighted procedures maintain nominal error rates while retaining power to detect departures from normality. The proposed method provides a practical, statistically principled diagnostic tool for assessing random-effects distributional assumptions in hierarchical models, with particular relevance to IPDMA of DTA studies. Although motivated by IPDMA, the proposed approach also extends to aggregate-data diagnostic test accuracy meta-analysis based on study-level 2-by-2 tables.
ER -