Sensitivity analysis for publication bias in meta-analysis of sparse data based on exact likelihood

Kavli Affiliate: Yi Zhou

| First 5 Authors: Taojun Hu, Yi Zhou, Sattoshi Hattori, ,

| Summary:

Meta-analysis is a powerful tool to synthesize findings from multiple
studies. The normal-normal random-effects model is widely used accounting for
between-study heterogeneity. However, meta-analysis of sparse data, which may
arise when the event rate is low for binary or count outcomes, poses a
challenge to the normal-normal random-effects model in the accuracy and
stability in inference since the normal approximation in the within-study
likelihood may not be good. To reduce bias arising from data sparsity, the
generalized linear mixed model can be used by replacing the approximate normal
within-study likelihood with an exact likelihood. Publication bias is one of
the most serious threats in meta-analysis. Several objective sensitivity
analysis methods for evaluating potential impacts of selective publication are
available for the normal-normal random-effects model. We propose a sensitivity
analysis method by extending the likelihood-based sensitivity analysis with the
$t$-statistic selection function of Copas to several generalized linear
mixed-effects models. Through applications of our proposed method to several
real-world meta-analyses and simulation studies, the proposed method was proven
to outperform the likelihood-based sensitivity analysis based on the
normal-normal model. The proposed method would give a useful guidance to
address publication bias in meta-analysis of sparse data.

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