Meta-analysis methods for risk difference: A comparison of different models

Risk difference is a frequently-used effect measure for binary outcomes. In a meta-analysis, commonly-used methods to synthesize risk differences include: (1) the two-step methods that estimate study-specific risk differences first, then followed by the univariate common-effect model, fixed-effects model, or random-effects models; and (2) the one-step methods using bivariate random-effects models to estimate the summary risk difference from study-specific risks. These methods are expected to have similar performance when the number of studies is large and the event rate is not rare. However, studies with zero events are common in meta-analyses, and bias may occur with the conventional two-step methods from excluding zero-event studies or using an artificial continuity correction to zero events. In contrast, zero-event studies can be included and modeled by bivariate random-effects models in a single step. This article compares various methods to estimate risk differences in meta-analyses. Specifically, we present two case studies and three simulation studies to compare the performance of conventional two-step methods and bivariate random-effects models in the presence or absence of zero-event studies. In conclusion, we recommend researchers using bivariate random-effects models to estimate risk differences in meta-analyses, particularly in the presence of zero events.

Bayesian analysis on meta-analysis of case-control studies accounting for within-study correlation

In retrospective studies, odds ratio is often used as the measure of association. Under independent beta prior assumption, the exact posterior distribution of odds ratio given a single 2 × 2 table has been derived in the literature. However, independence between risks within the same study may be an oversimplified assumption because cases and controls in the same study are likely to share some common factors and thus to be correlated. Furthermore, in a meta-analysis of case-control studies, investigators usually have multiple 2 × 2 tables. In this article, we first extend the published results on a single 2 × 2 table to allow within study prior correlation while retaining the advantage of closed-form posterior formula, and then extend the results to multiple 2 × 2 tables and regression setting. The hyperparameters, including within study correlation, are estimated via an empirical Bayes approach. The overall odds ratio and the exact posterior distribution of the study-specific odds ratio are inferred based on the estimated hyperparameters. We conduct simulation studies to verify our exact posterior distribution formulas and investigate the finite sample properties of the inference for the overall odds ratio. The results are illustrated through a twin study for genetic heritability and a meta-analysis for the association between the N-acetyltransferase 2 (NAT2) acetylation status and colorectal cancer.

Meta-analysis of studies with bivariate binary outcomes: a marginal beta-binomial model approach

When conducting a meta-analysis of studies with bivariate binary outcomes, challenges arise when the within-study correlation and between-study heterogeneity should be taken into account. In this paper, we propose a marginal beta-binomial model for the meta-analysis of studies with binary outcomes. This model is based on the composite likelihood approach and has several attractive features compared with the existing models such as bivariate generalized linear mixed model (Chu and Cole, 2006) and Sarmanov beta-binomial model (Chen et al., 2012). The advantages of the proposed marginal model include modeling the probabilities in the original scale, not requiring any transformation of probabilities or any link function, having closed-form expression of likelihood function, and no constraints on the correlation parameter. More importantly, because the marginal beta-binomial model is only based on the marginal distributions, it does not suffer from potential misspecification of the joint distribution of bivariate study-specific probabilities. Such misspecification is difficult to detect and can lead to biased inference using currents methods. We compare the performance of the marginal beta-binomial model with the bivariate generalized linear mixed model and the Sarmanov beta-binomial model by simulation studies. Interestingly, the results show that the marginal beta-binomial model performs better than the Sarmanov beta-binomial model, whether or not the true model is Sarmanov beta-binomial, and the marginal beta-binomial model is more robust than the bivariate generalized linear mixed model under model misspecifications. Two meta-analyses of diagnostic accuracy studies and a meta-analysis of case-control studies are conducted for illustration.