ABSTRACT
BACKGROUND: Studies included in a meta-analysis are often heterogeneous. The traditional random-effects models assume their true effects to follow a normal distribution, while it is unclear if this critical assumption is practical. Violations of this between-study normality assumption could lead to problematic meta-analytical conclusions. We aimed to empirically examine if this assumption is valid in published meta-analyses. METHODS: In this cross-sectional study, we collected meta-analyses available in the Cochrane Library with at least 10 studies and with between-study variance estimates > 0. For each extracted meta-analysis, we performed the Shapiro-Wilk (SW) test to quantitatively assess the between-study normality assumption. For binary outcomes, we assessed between-study normality for odds ratios (ORs), relative risks (RRs), and risk differences (RDs). Subgroup analyses based on sample sizes and event rates were used to rule out the potential confounders. In addition, we obtained the quantile-quantile (Q-Q) plot of study-specific standardized residuals for visually assessing between-study normality. RESULTS: Based on 4234 eligible meta-analyses with binary outcomes and 3433 with non-binary outcomes, the proportion of meta-analyses that had statistically significant non-normality varied from 15.1 to 26.2%. RDs and non-binary outcomes led to more frequent non-normality issues than ORs and RRs. For binary outcomes, the between-study non-normality was more frequently found in meta-analyses with larger sample sizes and event rates away from 0 and 100%. The agreements of assessing the normality between two independent researchers based on Q-Q plots were fair or moderate. CONCLUSIONS: The between-study normality assumption is commonly violated in Cochrane meta-analyses. This assumption should be routinely assessed when performing a meta-analysis. When it may not hold, alternative meta-analysis methods that do not make this assumption should be considered.
Subject(s)
Cross-Sectional Studies , Humans , Sample Size , Odds RatioABSTRACT
Bayesian methods are an important set of tools for performing meta-analyses. They avoid some potentially unrealistic assumptions that are required by conventional frequentist methods. More importantly, meta-analysts can incorporate prior information from many sources, including experts' opinions and prior meta-analyses. Nevertheless, Bayesian methods are used less frequently than conventional frequentist methods, primarily because of the need for nontrivial statistical coding, while frequentist approaches can be implemented via many user-friendly software packages. This article aims at providing a practical review of implementations for Bayesian meta-analyses with various prior distributions. We present Bayesian methods for meta-analyses with the focus on odds ratio for binary outcomes. We summarize various commonly used prior distribution choices for the between-studies heterogeneity variance, a critical parameter in meta-analyses. They include the inverse-gamma, uniform, and half-normal distributions, as well as evidence-based informative log-normal priors. Five real-world examples are presented to illustrate their performance. We provide all of the statistical code for future use by practitioners. Under certain circumstances, Bayesian methods can produce markedly different results from those by frequentist methods, including a change in decision on statistical significance. When data information is limited, the choice of priors may have a large impact on meta-analytic results, in which case sensitivity analyses are recommended. Moreover, the algorithm for implementing Bayesian analyses may not converge for extremely sparse data; caution is needed in interpreting respective results. As such, convergence should be routinely examined. When select statistical assumptions that are made by conventional frequentist methods are violated, Bayesian methods provide a reliable alternative to perform a meta-analysis.
