Estimating heterogeneity variance under sparsity

Abstract

Meta-analysis has become the gold standard in medical research analysis. The random effects model is generally the preferred method to conduct a meta-analysis, as it incorporates between-study heterogeneity - the variability between study estimates as a result of differences in study characteristics. Several methods to estimate the heterogeneity variance parameter in this model have been proposed, including the popular DerSimonian-Laird estimator, which has been shown to produce negatively biased estimates, performing well only in scenarios not seen in real-life data. Many medical meta-analyses are concerned with rare-event data, where event probabilities are so low that often a small number or zero events are observed in the studies. Examples of this include adverse drug reactions in a clinical trial or very rare diseases in epidemiological studies, where as few as 1 in 1000 people may be affected by the outcome of interest. In such cases, most pre-proposed heterogeneity variance estimators perform poorly, and standard analysis techniques can result in the incorrect estimation of overall treatment effect. In this thesis, we propose novel methods that we believe are appropriate for the estimation of heterogeneity variance in the case of rare-event data. These are based on generalised linear mixed models (GLMMs), and use the Poisson mixed regression model and the conditional logistic mixed regression model. We conducted a simulation study to compare our novel approaches with a selection of existing heterogeneity variance estimators for use in random-effect binary outcome meta-analyses. From the results of our simulation study, which agree with results given in previous studies, we found that our novel GLMM-based estimating methods outperform existing methods in terms of the estimation of heterogeneity variance and summary log-risk ratio. This is the case when study sample sizes in the meta-analysis are balanced or unbalanced, and thus we recommend them for use with rare-event data.

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Identifiers

ORCID for Susan Martin: orcid.org/0000-0001-8746-0947

ORCID for Dankmar Böhning: orcid.org/0000-0003-0638-7106

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