Random Effects Meta-Analysis of Contingency Tables with Complete and Partially Complete Data, with Application to COVID-19 Research

We present a random effects meta-analytic approach for analyzing exchangeable 2×2×2 tables of COVID-19 deaths classified by two comorbidities, for example, diabetes and hypertension. We take the marginal tables of comorbidities as multinomial with table-specific cell probabilities drawn from a Dirichlet distribution. Conditionally hereon, we model the death counts for cell in the 2×2 table of possible comorbidity combinations as independent binomial random variables. We allow for a randomly drawn normally distributed frailty to model the correlation of the death counts within the same study. For complete tables, this model can be fitted by standard statistical software. We propose an approximate maximum likelihood (ML) imputation procedure by which tables with missing entries can be completed enabling the use of the same standard procedures and giving a better estimate of model parameters than one would get by leaving partial tables out. The properties of the method are illustrated by simulations.