Mike W.-L. Cheung

Outlier and influence diagnostics for meta-analysis.

The presence of outliers and influential cases may affect the validity and robustness of the conclusions from a meta-analysis. While researchers generally agree that it is necessary to examine outlier and influential case diagnostics when conducting a meta-analysis, limited studies have addressed how to obtain such diagnostic measures in the context of a meta-analysis. The present paper extends standard diagnostic procedures developed for linear regression analyses to the meta-analytic fixed- and random/mixed-effects models. Three examples are used to illustrate the usefulness of these procedures in various research settings. Issues related to these diagnostic procedures in meta-analysis are also discussed. Copyright

Comparison of Approaches to Constructing Confidence Intervals for Mediating Effects Using Structural Equation Models.

Abstract Mediators are variables that explain the association between an independent variable and a dependent variable. Structural equation modeling (SEM) is widely used to test models with mediating effects. This article illustrates how to construct confidence intervals (CIs) of the mediating effects for a variety of models in SEM. Specifically, mediating models with 1 mediator, 2 intermediate mediators, 2 specific mediators, and 1 mediator in 2 independent groups are illustrated. By using phantom variables (Rindskopf, 1984), a Wald CI, percentile bootstrap CI, bias-corrected bootstrap CI, and a likelihood-based CI on the mediating effect are easily constructed with some existing SEM packages, such as LISREL, M plus, and Mx. Monte Carlo simulation studies are used to compare the coverage probabilities of these CIs. The results show that the coverage probabilities of these CIs are comparable when the mediating effect is large or when the sample size is large. However, when the mediating effect and the sample size are both small, the bootstrap CI and likelihood-based CI are preferred over the Wald CI. Extensions of this SEM approach for future research are discussed.

A Model for Integrating Fixed-, Random-, and Mixed-effects Meta-analyses into Structural Equation Modeling

Meta-analysis and structural equation modeling (SEM) are two important statistical methods in the behavioral, social, and medical sciences. They are generally treated as two unrelated topics in the literature. The present article proposes a model to integrate fixed-, random-, and mixed-effects meta-analyses into the SEM framework. By applying an appropriate transformation on the data, studies in a meta-analysis can be analyzed as subjects in a structural equation model. This article also highlights some practical benefits of using the SEM approach to conduct a meta-analysis. Specifically, the SEM-based meta-analysis can be used to handle missing covariates, to quantify the heterogeneity of effect sizes, and to address the heterogeneity of effect sizes with mixture models. Examples are used to illustrate the equivalence between the conventional meta-analysis and the SEM-based meta-analysis. Future directions on and issues related to the SEM-based meta-analysis are discussed.

Modeling dependent effect sizes with three-level meta-analyses: a structural equation modeling approach.

Meta-analysis is an indispensable tool used to synthesize research findings in the social, educational, medical, management, and behavioral sciences. Most meta-analytic models assume independence among effect sizes. However, effect sizes can be dependent for various reasons. For example, studies might report multiple effect sizes on the same construct, and effect sizes reported by participants from the same cultural group are likely to be more similar than those reported by other cultural groups. This article reviews the problems and common methods to handle dependent effect sizes. The objective of this article is to demonstrate how 3-level meta-analyses can be used to model dependent effect sizes. The advantages of the structural equation modeling approach over the multilevel approach with regard to conducting a 3-level meta-analysis are discussed. This article also seeks to extend the key concepts of Q statistics, I2, and R2 from 2-level meta-analyses to 3-level meta-analyses. The proposed procedures are implemented using the open source metaSEM package for the R statistical environment. Two real data sets are used to illustrate these procedures. New research directions related to 3-level meta-analyses are discussed.

Prevalence of depressive symptoms in patients with chronic obstructive pulmonary disease: a systematic review, meta-analysis and meta-regression

OBJECTIVE This meta-analysis was aimed to evaluate the differences in aggregated prevalence of depressive symptoms among people with chronic obstructive pulmonary disease (COPD) as compared to controls without COPD and to determine underlying moderators to explain potential heterogeneity of prevalence. METHODS A meta-analysis of published work was performed using the random effect model. A total of eight studies were identified. We calculated the differences in prevalence proportion of depressive symptoms in patients with COPD versus controls. Meta-regression and subgroup analysis were performed to identify factors that may contribute to heterogeneity. RESULTS The prevalence proportion of depressive symptoms was found to be significantly higher (pooled odds ratio: 2.81; 95% CI: 1.69-4.66) among 39587 individuals with COPD as compared to 39,431 controls (24.6%, 95% CI: 20.0-28.6% vs. 11.7%, 95% CI: 9-15.1%). Meta-regression was conducted to account for the heterogeneity of the prevalence proportion, but moderators like mean age, gender, mean FEV(1) and proportion of current smokers among COPD patients were nonsignificant and could not explain heterogeneity in prevalence of depressive symptoms. Subgroup analyses showed no significant differences based on different methods of assessment of depressive symptoms and countries sampled. CONCLUSION This meta-analytical review identified higher prevalence of depressive symptoms among COPD patients, and meta-regression showed that demographic and clinical factors were not the determinants of heterogeneity in prevalence of depressive symptoms.

Evaluating Multilevel Models in Cross-Cultural Research An Illustration With Social Axioms

To assess how culture influences the behavior of people, multilevel models are an immediate choice for modeling the relationship at the levels of the individual and culture. The authors propose structural equation modeling (SEM) to test the universality of psychological processes at the individual and culture levels. Specifically, the structural equivalence of the measurement (where the instrument is measuring the same construct across countries) is first tested with meta-analytic SEM. If the measurement is structurally equivalent, cross-level equivalence (where the instrument is measuring similar constructs at different levels) will then be tested with multilevel SEM. A large data set on social axioms with 7,590 university students from 40 cultural groups was used to illustrate the procedures. The results showed that the structural equivalence of the social axioms was well supported at the individual level across 40 cultural groups, whereas the cross-level equivalence was partially supported. The superiority of the SEM approach and the theoretical meaning of its solution are discussed.

Applications of Multilevel Structural Equation Modeling to Cross-Cultural Research

Multilevel structural equation modeling (MSEM) has been proposed as an extension to structural equation modeling for analyzing data with nested structure. We have begun to see a few applications in cross-cultural research in which MSEM fits well as the statistical model. However, given that cross-cultural studies can only afford collecting data from a relatively small number of countries, the appropriateness of MSEM has been questioned. Using the data from the International Social Survey Program (1997; N = 15,244 from 27 countries), we first showed how Muth�ns MSEM procedure could be applied to a real data set on cross-cultural research. Given a small country-level sample size (27 countries) we then demonstrated that results on the individual level were quite stable even when using small individual-level sample sizes, whereas the group-level parameter estimates and their standard errors were affected unsystematically by varying individual-level sample sizes. Use of the findings for cross-cultural research and other areas with limited numbers of groups are discussed.

Global Trend of Survival and Damage of Systemic Lupus Erythematosus: Meta-Analysis and Meta-Regression of Observational Studies from the 1950s to 2000s

OBJECTIVE To assess systemically with meta-analysis the trend of survival and its determinants, which are hindering further improvement of survival of patients with systemic lupus erythematosus (SLE) over the past 5 decades. METHODS Retrospective, cross-sectional, and prospective observational studies addressing survival and damage in SLE patients published between 1 January 1950 and 31 July 2010 were identified in electronic databases. Using the random-effects model, effect size was calculated based on the logit of the overall 5- and 10-year survival rates. The pooled logit and its robust 95% confidence interval were transformed back into the 5- and 10-year survival rates, after adjusting for potential dependence on the data. Potential factors predicting the pooled survival rates were explored by meta-regression. RESULTS Seventy-seven studies involving 18,998 SLE patients were analyzed. Between the 1950s and the 2000s, their overall survival significantly increased, from 74.8% to 94.8% and 63.2% to 91.4% for the overall 5-year and 10-year survival, respectively (P < 0.001). The survival improvement, however, appeared to slow down between 1980 and 1990. Meta-regression revealed that neuropsychiatric and renal damage negatively affected the overall 5-year survival, whereas neuropsychiatric damage remained so for the 10-year survival for the past 50 years. Furthermore, the prevalence of neuropsychiatric damage has been significantly increasing over the past 5 decades. CONCLUSIONS For the past 50 years, damage involving the renal and neuropsychiatric systems has been negatively affecting survival of SLE patients. Early detection and aggressive management of renal and neuropsychiatric involvement may potentially improve further the survival of lupus patients.

metaSEM: an R package for meta-analysis using structural equation modeling

The metaSEM package provides functions to conduct univariate, multivariate, and three-level meta-analyses using a structural equation modeling (SEM) approach via the OpenMx package in the R statistical platform. It also implements the two-stage SEM approach to conducting fixed- and random-effects meta-analytic SEM on correlation or covariance matrices. This paper briefly outlines the theories and their implementations. It provides a summary on how meta-analyses can be formulated as structural equation models. The paper closes with a conclusion on several relevant topics to this SEM-based meta-analysis. Several examples are used to illustrate the procedures in the supplementary material.

Comparison of methods for constructing confidence intervals of standardized indirect effects.

Mediation models are often used as a means to explain the psychological mechanisms between an independent and a dependent variable in the behavioral and social sciences. A major limitation of the unstandardized indirect effect calculated from raw scores is that it cannot be interpreted as an effect-size measure. In contrast, the standardized indirect effect calculated from standardized scores can be a good candidate as a measure of effect size because it is scale invariant. In the present article, 11 methods for constructing the confidence intervals (CIs) of the standardized indirect effects were evaluated via a computer simulation. These included six Wald CIs, three bootstrap CIs, one likelihood-based CI, and the PRODCLIN CI. The results consistently showed that the percentile bootstrap, the bias-corrected bootstrap, and the likelihood-based approaches had the best coverage probability. Mplus, LISREL, and Mx syntax were included to facilitate the use of these preferred methods in applied settings. Future issues on the use of the standardized indirect effects are discussed.