A Robust Method for Genome‐Wide Association Meta‐Analysis With the Application to Circulating Insulin‐Like Growth Factor I Concentrations

Genome‐wide association studies (GWAS) offer an excellent opportunity to identify the genetic variants underlying complex human diseases. Successful utilization of this approach requires a large sample size to identify single nucleotide polymorphisms (SNPs) with subtle effects. Meta‐analysis is a cost‐efficient means to achieve large sample size by combining data from multiple independent GWAS; however, results from studies performed on different populations can be variable due to various reasons, including varied linkage equilibrium structures as well as gene‐gene and gene‐environment interactions. Nevertheless, one should expect effects of the SNP are more similar between similar populations than those between populations with quite different genetic and environmental backgrounds. Prior information on populations of GWAS is often not considered in current meta‐analysis methods, rendering such analyses less optimal for the detecting association. This article describes a test that improves meta‐analysis to incorporate variable heterogeneity among populations. The proposed method is remarkably simple in computation and hence can be performed in a rapid fashion in the setting of GWAS. Simulation results demonstrate the validity and higher power of the proposed method over conventional methods in the presence of heterogeneity. As a demonstration, we applied the test to real GWAS data to identify SNPs associated with circulating insulin‐like growth factor I concentrations.     

Improved score statistics for meta‐analysis in single‐variant and gene‐level association studies

Meta‐analysis is now an essential tool for genetic association studies, allowing them to combine large studies and greatly accelerating the pace of genetic discovery. Although the standard meta‐analysis methods perform equivalently as the more cumbersome joint analysis under ideal settings, they result in substantial power loss under unbalanced settings with various case–control ratios. Here, we investigate the power loss problem by the standard meta‐analysis methods for unbalanced studies, and further propose novel meta‐analysis methods performing equivalently to the joint analysis under both balanced and unbalanced settings. We derive improved meta‐score‐statistics that can accurately approximate the joint‐score‐statistics with combined individual‐level data, for both linear and logistic regression models, with and without covariates. In addition, we propose a novel approach to adjust for population stratification by correcting for known population structures through minor allele frequencies. In the simulated gene‐level association studies under unbalanced settings, our method recovered up to 85% power loss caused by the standard methods. We further showed the power gain of our methods in gene‐level tests with 26 unbalanced studies of age‐related macular degeneration . In addition, we took the meta‐analysis of three unbalanced studies of type 2 diabetes as an example to discuss the challenges of meta‐analyzing multi‐ethnic samples. In summary, our improved meta‐score‐statistics with corrections for population stratification can be used to construct both single‐variant and gene‐level association studies, providing a useful framework for ensuring well‐powered, convenient, cross‐study analyses.     

Meta‐analysis using individual participant data: one‐stage and two‐stage approaches,and why they may differ

Meta‐analysis using individual participant data (IPD) obtains and synthesises the raw, participant‐level data from a set of relevant studies. The IPD approach is becoming an increasingly popular tool as an alternative to traditional aggregate data meta‐analysis, especially as it avoids reliance on published results and provides an opportunity to investigate individual‐level interactions, such as treatment‐effect modifiers. There are two statistical approaches for conducting an IPD meta‐analysis: one‐stage and two‐stage. The one‐stage approach analyses the IPD from all studies simultaneously, for example, in a hierarchical regression model with random effects. The two‐stage approach derives aggregate data (such as effect estimates) in each study separately and then combines these in a traditional meta‐analysis model. There have been numerous comparisons of the one‐stage and two‐stage approaches via theoretical consideration, simulation and empirical examples, yet there remains confusion regarding when each approach should be adopted, and indeed why they may differ. In this tutorial paper, we outline the key statistical methods for one‐stage and two‐stage IPD meta‐analyses, and provide 10 key reasons why they may produce different summary results. We explain that most differences arise because of different modelling assumptions, rather than the choice of one‐stage or two‐stage itself. We illustrate the concepts with recently published IPD meta‐analyses, summarise key statistical software and provide recommendations for future IPD meta‐analyses. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.     

Predictive distributions for between‐study heterogeneity and simple methods for their application in Bayesian meta‐analysis

Numerous meta‐analyses in healthcare research combine results from only a small number of studies, for which the variance representing between‐study heterogeneity is estimated imprecisely. A Bayesian approach to estimation allows external evidence on the expected magnitude of heterogeneity to be incorporated. The aim of this paper is to provide tools that improve the accessibility of Bayesian meta‐analysis. We present two methods for implementing Bayesian meta‐analysis, using numerical integration and importance sampling techniques. Based on 14 886 binary outcome meta‐analyses in the Cochrane Database of Systematic Reviews, we derive a novel set of predictive distributions for the degree of heterogeneity expected in 80 settings depending on the outcomes assessed and comparisons made. These can be used as prior distributions for heterogeneity in future meta‐analyses. The two methods are implemented in R, for which code is provided. Both methods produce equivalent results to standard but more complex Markov chain Monte Carlo approaches. The priors are derived as log‐normal distributions for the between‐study variance, applicable to meta‐analyses of binary outcomes on the log odds‐ratio scale. The methods are applied to two example meta‐analyses, incorporating the relevant predictive distributions as prior distributions for between‐study heterogeneity. We have provided resources to facilitate Bayesian meta‐analysis, in a form accessible to applied researchers, which allow relevant prior information on the degree of heterogeneity to be incorporated. © 2014 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.     

Meta‐STEPP: subpopulation treatment effect pattern plot for individual patient data meta‐analysis

We have developed a method, called Meta‐STEPP (subpopulation treatment effect pattern plot for meta‐analysis), to explore treatment effect heterogeneity across covariate values in the meta‐analysis setting for time‐to‐event data when the covariate of interest is continuous. Meta‐STEPP forms overlapping subpopulations from individual patient data containing similar numbers of events with increasing covariate values, estimates subpopulation treatment effects using standard fixed‐effects meta‐analysis methodology, displays the estimated subpopulation treatment effect as a function of the covariate values, and provides a statistical test to detect possibly complex treatment‐covariate interactions. Simulation studies show that this test has adequate type‐I error rate recovery as well as power when reasonable window sizes are chosen. When applied to eight breast cancer trials, Meta‐STEPP suggests that chemotherapy is less effective for tumors with high estrogen receptor expression compared with those with low expression. Copyright © 2016 John Wiley & Sons, Ltd.     

A Bayesian approach to sequential meta‐analysis

As evidence accumulates within a meta‐analysis, it is desirable to determine when the results could be considered conclusive to guide systematic review updates and future trial designs. Adapting sequential testing methodology from clinical trials for application to pooled meta‐analytic effect size estimates appears well suited for this objective. In this paper, we describe a Bayesian sequential meta‐analysis method, in which an informative heterogeneity prior is employed and stopping rule criteria are applied directly to the posterior distribution for the treatment effect parameter. Using simulation studies, we examine how well this approach performs under different parameter combinations by monitoring the proportion of sequential meta‐analyses that reach incorrect conclusions (to yield error rates), the number of studies required to reach conclusion, and the resulting parameter estimates. By adjusting the stopping rule thresholds, the overall error rates can be controlled within the target levels and are no higher than those of alternative frequentist and semi‐Bayes methods for the majority of the simulation scenarios. To illustrate the potential application of this method, we consider two contrasting meta‐analyses using data from the Cochrane Library and compare the results of employing different sequential methods while examining the effect of the heterogeneity prior in the proposed Bayesian approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Imputation aware meta‐analysis of genome‐wide association studies

Genome‐wide association studies have recently identified many new loci associated with human complex diseases. These newly discovered variants typically have weak effects requiring studies with large numbers of individuals to achieve the statistical power necessary to identify them. Likely, there exist even more associated variants, which remain to be found if even larger association studies can be assembled. Meta‐analysis provides a straightforward means of increasing study sample sizes without collecting new samples by combining existing data sets. One obstacle to combining studies is that they are often performed on platforms with different marker sets. Current studies overcome this issue by imputing genotypes missing from each of the studies and then performing standard meta‐analysis techniques. We show that this approach may result in a loss of power since errors in imputation are not accounted for. We present a new method for performing meta‐analysis over imputed single nucleotide polymorphisms, show that it is optimal with respect to power, and discuss practical implementation issues. Through simulation experiments, we show that our imputation aware meta‐analysis approach outperforms or matches standard meta‐analysis approaches. Genet. Epidemiol. 34: 537–542, 2010. © 2010 Wiley‐Liss, Inc.     

Implementing informative priors for heterogeneity in meta‐analysis using meta‐regression and pseudo data

Many meta‐analyses combine results from only a small number of studies, a situation in which the between‐study variance is imprecisely estimated when standard methods are applied. Bayesian meta‐analysis allows incorporation of external evidence on heterogeneity, providing the potential for more robust inference on the effect size of interest. We present a method for performing Bayesian meta‐analysis using data augmentation, in which we represent an informative conjugate prior for between‐study variance by pseudo data and use meta‐regression for estimation. To assist in this, we derive predictive inverse‐gamma distributions for the between‐study variance expected in future meta‐analyses. These may serve as priors for heterogeneity in new meta‐analyses. In a simulation study, we compare approximate Bayesian methods using meta‐regression and pseudo data against fully Bayesian approaches based on importance sampling techniques and Markov chain Monte Carlo (MCMC). We compare the frequentist properties of these Bayesian methods with those of the commonly used frequentist DerSimonian and Laird procedure. The method is implemented in standard statistical software and provides a less complex alternative to standard MCMC approaches. An importance sampling approach produces almost identical results to standard MCMC approaches, and results obtained through meta‐regression and pseudo data are very similar. On average, data augmentation provides closer results to MCMC, if implemented using restricted maximum likelihood estimation rather than DerSimonian and Laird or maximum likelihood estimation. The methods are applied to real datasets, and an extension to network meta‐analysis is described. The proposed method facilitates Bayesian meta‐analysis in a way that is accessible to applied researchers. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.     

Meta‐analysis approaches to combine multiple gene set enrichment studies

In the field of gene set enrichment analysis (GSEA), meta‐analysis has been used to integrate information from multiple studies to present a reliable summarization of the expanding volume of individual biomedical research, as well as improve the power of detecting essential gene sets involved in complex human diseases. However, existing methods, Meta‐Analysis for Pathway Enrichment (MAPE), may be subject to power loss because of (1) using gross summary statistics for combining end results from component studies and (2) using enrichment scores whose distributions depend on the set sizes. In this paper, we adapt meta‐analysis approaches recently developed for genome‐wide association studies, which are based on fixed effect and random effects (RE) models, to integrate multiple GSEA studies. We further develop a mixed strategy via adaptive testing for choosing RE versus FE models to achieve greater statistical efficiency as well as flexibility. In addition, a size‐adjusted enrichment score based on a one‐sided Kolmogorov‐Smirnov statistic is proposed to formally account for varying set sizes when testing multiple gene sets. Our methods tend to have much better performance than the MAPE methods and can be applied to both discrete and continuous phenotypes. Specifically, the performance of the adaptive testing method seems to be the most stable in general situations.     

Multivariate meta‐analysis for non‐linear and other multi‐parameter associations

In this paper, we formalize the application of multivariate meta‐analysis and meta‐regression to synthesize estimates of multi‐parameter associations obtained from different studies. This modelling approach extends the standard two‐stage analysis used to combine results across different sub‐groups or populations. The most straightforward application is for the meta‐analysis of non‐linear relationships, described for example by regression coefficients of splines or other functions, but the methodology easily generalizes to any setting where complex associations are described by multiple correlated parameters. The modelling framework of multivariate meta‐analysis is implemented in the package mvmeta within the statistical environment R . As an illustrative example, we propose a two‐stage analysis for investigating the non‐linear exposure–response relationship between temperature and non‐accidental mortality using time‐series data from multiple cities. Multivariate meta‐analysis represents a useful analytical tool for studying complex associations through a two‐stage procedure. Copyright © 2012 John Wiley & Sons, Ltd.     

The use of imputed values in the meta‐analysis of genome‐wide association studies

In genome‐wide association studies (GWAS), it is a common practice to impute the genotypes of untyped single nucleotide polymorphism (SNP) by exploiting the linkage disequilibrium structure among SNPs. The use of imputed genotypes improves genome coverage and makes it possible to perform meta‐analysis combining results from studies genotyped on different platforms. A popular way of using imputed data is the “expectation‐substitution” method, which treats the imputed dosage as if it were the true genotype. In current practice, the estimates given by the expectation‐substitution method are usually combined using inverse variance weighting (IVM) scheme in meta‐analysis. However, the IVM is not optimal as the estimates given by the expectation‐substitution method are generally biased. The optimal weight is, in fact, proportional to the inverse variance and the expected value of the effect size estimates. We show both theoretically and numerically that the bias of the estimates is very small under practical conditions of low effect sizes in GWAS. This finding validates the use of the expectation‐substitution method, and shows the inverse variance is a good approximation of the optimal weight. Through simulation, we compared the power of the IVM method with several methods including the optimal weight, the regular z‐score meta‐analysis and a recently proposed “imputation aware” meta‐analysis method (Zaitlen and Eskin [2010] Genet Epidemiol 34:537–542). Our results show that the performance of the inverse variance weight is always indistinguishable from the optimal weight and similar to or better than the other two methods. Genet. Epidemiol. 2011. © 2011 Wiley Periodicals, Inc. 35:597‐605, 2011     

An Empirical Comparison of Meta‐analysis and Mega‐analysis of Individual Participant Data for Identifying Gene‐Environment Interactions

For analysis of the main effects of SNPs, meta‐analysis of summary results from individual studies has been shown to provide comparable results as “mega‐analysis” that jointly analyzes the pooled participant data from the available studies. This fact revolutionized the genetic analysis of complex traits through large GWAS consortia. Investigations of gene‐environment (G×E) interactions are on the rise since they can potentially explain a part of the missing heritability and identify individuals at high risk for disease. However, for analysis of gene‐environment interactions, it is not known whether these methods yield comparable results. In this empirical study, we report that the results from both methods were largely consistent for all four tests; the standard 1 degree of freedom (df) test of main effect only, the 1 df test of the main effect (in the presence of interaction effect), the 1 df test of the interaction effect, and the joint 2 df test of main and interaction effects. They provided similar effect size and standard error estimates, leading to comparable P‐values. The genomic inflation factors and the number of SNPs with various thresholds were also comparable between the two approaches. Mega‐analysis is not always feasible especially in very large and diverse consortia since pooling of raw data may be limited by the terms of the informed consent. Our study illustrates that meta‐analysis can be an effective approach also for identifying interactions. To our knowledge, this is the first report investigating meta‐versus mega‐analyses for interactions.     

Sample size calculation for meta‐epidemiological studies

Meta‐epidemiological studies are used to compare treatment effect estimates between randomized clinical trials with and without a characteristic of interest. To our knowledge, there is presently nothing to help researchers to a priori specify the required number of meta‐analyses to be included in a meta‐epidemiological study. We derived a theoretical power function and sample size formula in the framework of a hierarchical model that allows for variation in the impact of the characteristic between trials within a meta‐analysis and between meta‐analyses. A simulation study revealed that the theoretical function overestimated power (because of the assumption of equal weights for each trial within and between meta‐analyses). We also propose a simulation approach that allows for relaxing the constraints used in the theoretical approach and is more accurate. We illustrate that the two variables that mostly influence power are the number of trials per meta‐analysis and the proportion of trials with the characteristic of interest. We derived a closed‐form power function and sample size formula for estimating the impact of trial characteristics in meta‐epidemiological studies. Our analytical results can be used as a ‘rule of thumb’ for sample size calculation for a meta‐epidemiologic study. A more accurate sample size can be derived with a simulation study. Copyright © 2015 John Wiley & Sons, Ltd.     

General Framework for Meta‐Analysis of Haplotype Association Tests

For complex traits, most associated single nucleotide variants (SNV) discovered to date have a small effect, and detection of association is only possible with large sample sizes. Because of patient confidentiality concerns, it is often not possible to pool genetic data from multiple cohorts, and meta‐analysis has emerged as the method of choice to combine results from multiple studies. Many meta‐analysis methods are available for single SNV analyses. As new approaches allow the capture of low frequency and rare genetic variation, it is of interest to jointly consider multiple variants to improve power. However, for the analysis of haplotypes formed by multiple SNVs, meta‐analysis remains a challenge, because different haplotypes may be observed across studies. We propose a two‐stage meta‐analysis approach to combine haplotype analysis results. In the first stage, each cohort estimate haplotype effect sizes in a regression framework, accounting for relatedness among observations if appropriate. For the second stage, we use a multivariate generalized least square meta‐analysis approach to combine haplotype effect estimates from multiple cohorts. Haplotype‐specific association tests and a global test of independence between haplotypes and traits are obtained within our framework. We demonstrate through simulation studies that we control the type‐I error rate, and our approach is more powerful than inverse variance weighted meta‐analysis of single SNV analysis when haplotype effects are present. We replicate a published haplotype association between fasting glucose‐associated locus (G6PC2) and fasting glucose in seven studies from the Cohorts for Heart and Aging Research in Genomic Epidemiology Consortium and we provide more precise haplotype effect estimates.     

Testing moderation in network meta‐analysis with individual participant data

Meta‐analytic methods for combining data from multiple intervention trials are commonly used to estimate the effectiveness of an intervention. They can also be extended to study comparative effectiveness, testing which of several alternative interventions is expected to have the strongest effect. This often requires network meta‐analysis (NMA), which combines trials involving direct comparison of two interventions within the same trial and indirect comparisons across trials. In this paper, we extend existing network methods for main effects to examining moderator effects, allowing for tests of whether intervention effects vary for different populations or when employed in different contexts. In addition, we study how the use of individual participant data may increase the sensitivity of NMA for detecting moderator effects, as compared with aggregate data NMA that employs study‐level effect sizes in a meta‐regression framework. A new NMA diagram is proposed. We also develop a generalized multilevel model for NMA that takes into account within‐trial and between‐trial heterogeneity and can include participant‐level covariates. Within this framework, we present definitions of homogeneity and consistency across trials. A simulation study based on this model is used to assess effects on power to detect both main and moderator effects. Results show that power to detect moderation is substantially greater when applied to individual participant data as compared with study‐level effects. We illustrate the use of this method by applying it to data from a classroom‐based randomized study that involved two sub‐trials, each comparing interventions that were contrasted with separate control groups. Copyright © 2016 John Wiley & Sons, Ltd.     

The Role of Environmental Heterogeneity in Meta‐Analysis of Gene–Environment Interactions With Quantitative Traits

With challenges in data harmonization and environmental heterogeneity across various data sources, meta‐analysis of gene–environment interaction studies can often involve subtle statistical issues. In this paper, we study the effect of environmental covariate heterogeneity (within and between cohorts) on two approaches for fixed‐effect meta‐analysis: the standard inverse‐variance weighted meta‐analysis and a meta‐regression approach. Akin to the results in Simmonds and Higgins ( 2007 ), we obtain analytic efficiency results for both methods under certain assumptions. The relative efficiency of the two methods depends on the ratio of within versus between cohort variability of the environmental covariate. We propose to use an adaptively weighted estimator (AWE), between meta‐analysis and meta‐regression, for the interaction parameter. The AWE retains full efficiency of the joint analysis using individual level data under certain natural assumptions. Lin and Zeng (2010a, b) showed that a multivariate inverse‐variance weighted estimator retains full efficiency as joint analysis using individual level data, if the estimates with full covariance matrices for all the common parameters are pooled across all studies. We show consistency of our work with Lin and Zeng (2010a, b). Without sacrificing much efficiency, the AWE uses only univariate summary statistics from each study, and bypasses issues with sharing individual level data or full covariance matrices across studies. We compare the performance of the methods both analytically and numerically. The methods are illustrated through meta‐analysis of interaction between Single Nucleotide Polymorphisms in FTO gene and body mass index on high‐density lipoprotein cholesterol data from a set of eight studies of type 2 diabetes.     

Neither fixed nor random: weighted least squares meta‐analysis

This study challenges two core conventional meta‐analysis methods: fixed effect and random effects. We show how and explain why an unrestricted weighted least squares estimator is superior to conventional random‐effects meta‐analysis when there is publication (or small‐sample) bias and better than a fixed‐effect weighted average if there is heterogeneity. Statistical theory and simulations of effect sizes, log odds ratios and regression coefficients demonstrate that this unrestricted weighted least squares estimator provides satisfactory estimates and confidence intervals that are comparable to random effects when there is no publication (or small‐sample) bias and identical to fixed‐effect meta‐analysis when there is no heterogeneity. When there is publication selection bias, the unrestricted weighted least squares approach dominates random effects; when there is excess heterogeneity, it is clearly superior to fixed‐effect meta‐analysis. In practical applications, an unrestricted weighted least squares weighted average will often provide superior estimates to both conventional fixed and random effects. Copyright © 2015 John Wiley & Sons, Ltd.     

Avoiding zero between‐study variance estimates in random‐effects meta‐analysis

Fixed‐effects meta‐analysis has been criticized because the assumption of homogeneity is often unrealistic and can result in underestimation of parameter uncertainty. Random‐effects meta‐analysis and meta‐regression are therefore typically used to accommodate explained and unexplained between‐study variability. However, it is not unusual to obtain a boundary estimate of zero for the (residual) between‐study standard deviation, resulting in fixed‐effects estimates of the other parameters and their standard errors. To avoid such boundary estimates, we suggest using Bayes modal (BM) estimation with a gamma prior on the between‐study standard deviation. When no prior information is available regarding the magnitude of the between‐study standard deviation, a weakly informative default prior can be used (with shape parameter 2 and rate parameter close to 0) that produces positive estimates but does not overrule the data, leading to only a small decrease in the log likelihood from its maximum. We review the most commonly used estimation methods for meta‐analysis and meta‐regression including classical and Bayesian methods and apply these methods, as well as our BM estimator, to real datasets. We then perform simulations to compare BM estimation with the other methods and find that BM estimation performs well by (i) avoiding boundary estimates; (ii) having smaller root mean squared error for the between‐study standard deviation; and (iii) better coverage for the overall effects than the other methods when the true model has at least a small or moderate amount of unexplained heterogeneity. Copyright © 2013 John Wiley & Sons, Ltd.     

Handling incomplete correlated continuous and binary outcomes in meta‐analysis of individual participant data

Meta‐analysis of individual participant data (IPD) is increasingly utilised to improve the estimation of treatment effects, particularly among different participant subgroups. An important concern in IPD meta‐analysis relates to partially or completely missing outcomes for some studies, a problem exacerbated when interest is on multiple discrete and continuous outcomes. When leveraging information from incomplete correlated outcomes across studies, the fully observed outcomes may provide important information about the incompleteness of the other outcomes. In this paper, we compare two models for handling incomplete continuous and binary outcomes in IPD meta‐analysis: a joint hierarchical model and a sequence of full conditional mixed models. We illustrate how these approaches incorporate the correlation across the multiple outcomes and the between‐study heterogeneity when addressing the missing data. Simulations characterise the performance of the methods across a range of scenarios which differ according to the proportion and type of missingness, strength of correlation between outcomes and the number of studies. The joint model provided confidence interval coverage consistently closer to nominal levels and lower mean squared error compared with the fully conditional approach across the scenarios considered. Methods are illustrated in a meta‐analysis of randomised controlled trials comparing the effectiveness of implantable cardioverter‐defibrillator devices alone to implantable cardioverter‐defibrillator combined with cardiac resynchronisation therapy for treating patients with chronic heart failure. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.     

Meta‐analysis of studies of a specific delivery mode for a modified‐carbohydrate diet

Background: Obesity is highly prevalent throughout the world. Although modified‐carbohydrate diets (MCDs) comprise one popular approach, questions remain about their utility for weight loss. The objective of the present study was to conduct a meta‐analysis of randomised controlled trials (RCTs) of a specific MCD compared with various control diets on weight loss. Methods: Data from four RCTs (three obtained from the sponsor and one indentified through literature searches) were included. Intent‐to‐treat analyses were conducted using multiple imputation to handle missing data, where possible. Because inter‐study heterogeneity was demonstrated with fixed‐effects meta‐analysis, a random‐effects meta‐analysis also was conducted. Results: When considered separately, all four studies showed greater reduction in body weight with the MCD compared to control diets at 12‐week follow‐up; the results at 24 weeks (available for three of the studies) were not as consistent. Results for body mass index (BMI) were similar. Greater reductions in waist circumference with the MCD were seen at either time point in only one study. When fixed‐effects meta‐analysis was applied, significantly greater reductions in weight, BMI and waist circumference with the MCD at both 12 weeks (1.66 kg, 0.53 kg m^–2 and 1.02 cm, respectively) and 24 weeks (1.20 kg, 0.43 kg m^–2 and 0.69 cm, respectively) were evident. Random‐effects meta‐analysis revealed similar results; however, the 24‐week difference for a reduction in waist circumference was no longer statistically significant. Conclusions: Meta‐analysis of individual RCT results demonstrated consistent benefits of this MCD compared to control diets on weight loss up to 24 weeks and waist circumference up to 12 weeks.