Approximate confidence intervals for moment-based estimators of the between-study variance in random effects meta-analysis

Bayesian estimation and testing in random-effects meta-analysis of rare binary events allowing for flexible group variability

Rare binary events data arise frequently in medical research. Due to lack of statistical power in individual studies involving such data, meta-analysis has become an increasingly important tool for combining results from multiple independent studies. However, traditional meta-analysis methods often report severely biased estimates in such rare-event settings. Moreover, many rely on models assuming a pre-specified direction for variability between control and treatment groups for mathematical convenience, which may be violated in practice. Based on a flexible random-effects model that removes the assumption about the direction, we propose new Bayesian procedures for estimating and testing the overall treatment effect and inter-study heterogeneity. Our Markov chain Monte Carlo algorithm employs Pólya-Gamma augmentation so that all conditionals are known distributions, greatly facilitating computational efficiency. Our simulation shows that the proposed approach generally reports less biased and more stable estimates compared to existing methods. We further illustrate our approach using two real examples, one using rosiglitazone data from 56 studies and the other using stomach ulcers data from 41 studies.

Jackknife empirical likelihood confidence intervals for assessing heterogeneity in meta-analysis of rare binary event data

In meta-analysis, the heterogeneity of effect sizes across component studies is typically described by a variance parameter in a random-effects (Re) model. In the literature, methods for constructing confidence intervals (CIs) for the parameter often assume that study-level effect sizes are normally distributed. However, this assumption might be violated in practice, especially in meta-analysis of rare binary events. We propose to use jackknife empirical likelihood (JEL), a nonparametric approach that uses jackknife pseudo-values, to construct CIs for the heterogeneity parameter. To compute jackknife pseudo-values, we employ a moment-based estimator and consider two commonly used weighing schemes (i.e., equal and inverse variance weights). We prove that with each scheme, the resulting log empirical likelihood ratio follows a chi-square distribution asymptotically. We further examine the performance of the proposed JEL methods and compare them with existing CIs through simulation studies and data examples that focus on data of rare binary events. Our numerical results suggest that the JEL method with equal weights compares favorably to alternatives, especially when (observed) effect sizes are non-normal and the number of component studies is large. Thus, it is worth serious consideration in statistical inference.

Brucellosis in Iranian livestock: A meta-epidemiological study

Brucellosis is a widespread zoonotic disease affecting human and livestock health. This meta-epidemiological study is aiming to draw a comprehensive picture of the Brucella prevalence in Iranian livestock, trying to estimate most affected subgroups as well as the most appropriate methods and sampling conditions for brucellosis screening programs. A literature search was performed among data published between 1 January 1970 and July 2020. Different subgroups were compared according to animal species, gender, age, sampling season, sampling locations as well as the diagnostic method used for brucellosis screening. To determine heterogeneity of studies, Chi-squared test was used and a random effect model (REM) estimated the pooled prevalence among subgroups. A total of 45 publications, comprising 240 studies/data-reports, were evaluated. A significant increase in the number of studies was found over time (Coefficient = 0.151, p value < 0.001). The most studied species in Iran was cow (n = 75), followed by sheep (n = 63), goat (n = 45), camel (n = 40) and Buffalo (n = 16). The most identified Brucella species in livestock were Brucella melitensis (n = 50), Brucella abortus (n = 39), mix infection of B. melitensis and B. abortus (n = 11) and vaccine strain of B. melitensis Rev1 (n = 4). PCR-based tests were the most common applied diagnostic method (n = 140), while the highest prevalence rate of positive samples was obtained by indirect ELISA (69%). The prevalence of brucellosis was significantly higher in females (10.91%) compared to males (8.23%). The meta-epidemiological study of brucellosis in Iranian livestock would help to strengthen surveillance, control and prevention approaches to counter the spread of this zoonotic disease.

Ethnicity-Stratified Analysis of the Association between TNF-α Genetic Polymorphisms and Acute Kidney Injury: A Systematic Review and Meta-Analysis

Background

Several studies have reported conflicting findings regarding the association between tumor necrosis factor-alpha (TNF-α) genetic polymorphisms and acute kidney injury (AKI). Therefore, we performed this meta-analysis to further investigate whether TNF-α variants are related to AKI susceptibility.

Methods

A comprehensive search of observational studies on the association of TNF-α polymorphism with AKI susceptibility was conducted in the PubMed, Cochrane, and Embase databases through February 10, 2020. Pooled odds ratios (ORs) and 95% corresponding confidence intervals (95% CIs) were analyzed to evaluate the strength of the relationship.

Results

A total of 8 studies involving 6694 patients (2559 cases and 4135 controls) were included. Pooled analysis showed a trend of increased risk between the TNF-α rs1800629 variant and AKI (A vs. G: OR [95%CI] = 1.33 [0.98‐1.81]) among the overall population. Ethnicity-stratified analysis indicated that the TNF-α rs1800629 variant was a risk factor for Asians (OR [95%CI] = 1.93 [1.59‐2.35]) while it is not for Caucasians (OR [95%CI] = 1.04 [0.91‐1.20]). Additionally, we also found that TNF-α rs1799964 polymorphism was observed to have a significant relationship with AKI risk in Asian patients (C vs. T, OR [95%CI] = 1.26 [1.11‐1.43]).

Conclusions

The TNF rs1800629 polymorphism exhibited a trend toward AKI susceptibility with ethnic differences. The relationship was found to be significant among the Asian population, but not among those of Caucasian origin. Additionally, the TNF-α rs1799964 polymorphism was also related to a significantly increased risk of AKI in Asians.

The global epidemiology of Brucella infections in terrestrial wildlife: A meta-analysis

Brucellosis is a widespread zoonotic disease with serious consequences on human and animal health. Brucella infections were reported in many terrestrial wild animals, from subtropical and temperate regions to arctic regions. In many areas, the epidemiology of brucellosis in wildlife is closely associated with the occurrence of the disease in livestock. Some wild species may contribute to the re-introduction of Brucella infections in livestock (spillback), even in officially brucellosis-free (OBF) regions. Through meta-regression analysis, this study draws a global picture of the prevalence of Brucella spp. in terrestrial wild animals, trying to determine most affected subgroups as well as preferential sampling and screening methods. For this purpose, a literature search was carried out among publications published from 1983 to 2019. Different subgroups were compared according to animal species, feeding, gender, age as well as the method used for sampling and for brucellosis diagnostic. To determine heterogeneity of studies, chi-squared test was used and a random-effects model (REM) estimated the pooled prevalence among subgroups. A total of 68 publications, comprising 229 data reports/studies, were selected. The most-reported Brucella species in wildlife was Brucella abortus, and the highest prevalence rate was found in American bison, Bison bison (39.9%) followed by Alpine ibex, Capra ibex (33%). Serology was the most widely applied diagnostic approach (66%), while PCR appeared to be highly sensitive (36.62% of positive results). The gender of animals showed no significant association with the prevalence of brucellosis (p > .05). Blood samples and visceral organs constituted the great majority of specimen used for the detection of Brucella spp., while lymph nodes showed a high prevalence of positive samples (94.6%). The present study provides insight into the global epidemiology and enzootic potential of brucellosis in wild terrestrial animals worldwide, aiming at helping the appropriate authorities to strengthen prevention, surveillance and control strategies.

Statistical Methods for Quantifying Between-study Heterogeneity in Meta-analysis with Focus on Rare Binary Events

Meta-analysis, the statistical procedure for combining results from multiple independent studies, has been widely used in medical research to evaluate intervention efficacy and drug safety. In many practical situations, treatment effects vary notably among the collected studies, and the variation, often modeled by the between-study variance parameter τ 2, can greatly affect the inference of the overall effect size. In the past, comparative studies have been conducted for both point and interval estimation of τ 2. However, most are incomplete, only including a limited subset of existing methods, and some are outdated. Further, none of the studies covers descriptive measures for assessing the level of heterogeneity, nor are they focused on rare binary events that require special attention. We summarize by far the most comprehensive set including 11 descriptive measures, 23 estimators, and 16 confidence intervals. In addition to providing synthesized information, we further categorize these methods according to their key features. We then evaluate their performance based on simulation studies that examine various realistic scenarios for rare binary events, with an illustration using a data example of a gestational diabetes meta-analysis. We conclude that there is no uniformly "best" method. However, methods with consistently better performance do exist in the context of rare binary events, and we provide practical guidelines based on numerical evidences.

Contamination of milk and dairy products by Brucella species: A global systematic review and meta-analysis

Brucellosis is known as an influential zoonosis in different regions worldwide, with significant effects on the reproductive performance of livestock. Considering the high incidence of brucellosis in dairy products and further negative impacts on food safety, the present study was aimed to systematically investigate prevalence worldwide among published data regarding the identification of Brucella spp. in dairy products. In this regard, some databases, i.e., Scopus, PubMed, Embase, and Web of Science have been searched to retrieve all related articles regarding the incidence of Brucella contaminations in dairy products from 1 January 1983 to 1 April 2019. The prevalence of Brucella spp. in unpasteurized dairy products based on countries, WHO regions, and dairy product subgroups were evaluated and statistically compared. Based on the findings, the prevalence of Brucella spp. in dairy products increased while the GDP (C = 0.17, P-value < 0.001) and HDI (C = 0.19, P-value < 0.001) ranking decreased. Also, the highest prevalence of Brucella contamination in dairy products was noted in buffalo (25.91%) and goat (17.90%), respectively. The lowest and highest prevalence of Brucella spp. were observed in the Western Pacific (15.32%) and the Southeast Asia region (25.55%), respectively. Also, the rank order of WHO regions based on odds ratio (OR) was Southeast Asia region (2.84) > Eastern Mediterranean (2.41) > Region of America (1.65) > European Region (1.54) > Africa region (1.46) > Western Pacific (reference). The results of this study showed that decreasing poverty and an increase in the level of education in societies could reduce the prevalence of Brucella spp. in dairy products. The outcome of the current investigation can be used for the implementation of sustainable intervention and prevention strategies in affected regions.

Statistical properties of methods based on the Q-statistic for constructing a confidence interval for the between-study variance in meta-analysis

The effect sizes of studies included in a meta‐analysis do often not share a common true effect size due to differences in for instance the design of the studies. Estimates of this so‐called between‐study variance are usually imprecise. Hence, reporting a confidence interval together with a point estimate of the amount of between‐study variance facilitates interpretation of the meta‐analytic results. Two methods that are recommended to be used for creating such a confidence interval are the Q‐profile and generalized Q‐statistic method that both make use of the Q‐statistic. These methods are exact if the assumptions underlying the random‐effects model hold, but these assumptions are usually violated in practice such that confidence intervals of the methods are approximate rather than exact confidence intervals. We illustrate by means of two Monte‐Carlo simulation studies with odds ratio as effect size measure that coverage probabilities of both methods can be substantially below the nominal coverage rate in situations that are representative for meta‐analyses in practice. We also show that these too low coverage probabilities are caused by violations of the assumptions of the random‐effects model (ie, normal sampling distributions of the effect size measure and known sampling variances) and are especially prevalent if the sample sizes in the primary studies are small.

Contamination and Prevalence of Histamine in Canned Tuna from Iran: A Systematic Review, Meta-Analysis, and Health Risk Assessment

Histamine is one of the most important health issues associated with consumption of canned tuna because of possible allergic and anaphylactic reactions in consumers. Although the concentrations of histamine in tuna in Iran have been investigated in several studies, definitive conclusions are elusive. This study was undertaken as a systematic review and meta-analysis of the concentration and prevalence of histamine in Iranian canned tuna, and the related health risk was assessed. An extensive search of articles in the databases Scopus, PubMed, and Scientific Information Database resulted in 11 articles and a total of 693 samples for inclusion in this review. The minimum and maximum concentrations of histamine were determined as 8.59 ± 14.24 and 160.52 ± 87.59 mg kg⁻¹, respectively. The mean concentration was calculated as 77.86 mg kg⁻¹ (95% confidence interval [CI], 47.51 to 108.21 mg kg⁻¹), which was lower than the 200 mg kg⁻¹ recommended limit by the U.S. Food and Drug Administration (FDA). The mean prevalence of histamine was 9.19% (95%; CI, 6.88 to 11.5%). The 95% value of the target hazard quotient for adult consumers was calculated as 0.10. In all studies performed in Iran, the concentration of histamine in canned tuna was lower than FDA standard. Health risk assessment indicated low histamine risk (target hazard quotient < 1) for adults in Iran from consumption of canned tuna.

When should meta-analysis avoid making hidden normality assumptions?

Meta-analysis is a widely used statistical technique. The simplicity of the calculations required when performing conventional meta-analyses belies the parametric nature of the assumptions that justify them. In particular, the normal distribution is extensively, and often implicitly, assumed. Here, we review how the normal distribution is used in meta-analysis. We discuss when the normal distribution is likely to be adequate and also when it should be avoided. We discuss alternative and more advanced methods that make less use of the normal distribution. We conclude that statistical methods that make fewer normality assumptions should be considered more often in practice. In general, statisticians and applied analysts should understand the assumptions made by their statistical analyses. They should also be able to defend these assumptions. Our hope is that this article will foster a greater appreciation of the extent to which assumptions involving the normal distribution are made in statistical methods for meta-analysis. We also hope that this article will stimulate further discussion and methodological work.

The Hartung-Knapp modification for random-effects meta-analysis: A useful refinement but are there any residual concerns?

The modified method for random-effects meta-analysis, usually attributed to Hartung and Knapp and also proposed by Sidik and Jonkman, is easy to implement and is becoming advocated for general use. Here, we examine a range of potential concerns about the widespread adoption of this method. Motivated by these issues, a variety of different conventions can be adopted when using the modified method in practice. We describe and investigate the use of a variety of these conventions using a new taxonomy of meta-analysis datasets. We conclude that the Hartung and Knapp modification may be a suitable replacement for the standard method. Despite this, analysts who advocate the modified method should be ready to defend its use against the possible objections to it that we present. We further recommend that the results from more conventional approaches should be used as sensitivity analyses when using the modified method. It has previously been suggested that a common-effect analysis should be used for this purpose but we suggest amending this recommendation and argue that a standard random-effects analysis should be used instead.

Confidence intervals for the between-study variance in random-effects meta-analysis using generalised heterogeneity statistics: should we use unequal tails?

BACKGROUND

Confidence intervals for the between study variance are useful in random-effects meta-analyses because they quantify the uncertainty in the corresponding point estimates. Methods for calculating these confidence intervals have been developed that are based on inverting hypothesis tests using generalised heterogeneity statistics. Whilst, under the random effects model, these new methods furnish confidence intervals with the correct coverage, the resulting intervals are usually very wide, making them uninformative.

METHODS

We discuss a simple strategy for obtaining 95 % confidence intervals for the between-study variance with a markedly reduced width, whilst retaining the nominal coverage probability. Specifically, we consider the possibility of using methods based on generalised heterogeneity statistics with unequal tail probabilities, where the tail probability used to compute the upper bound is greater than 2.5 %. This idea is assessed using four real examples and a variety of simulation studies. Supporting analytical results are also obtained.

RESULTS

Our results provide evidence that using unequal tail probabilities can result in shorter 95 % confidence intervals for the between-study variance. We also show some further results for a real example that illustrates how shorter confidence intervals for the between-study variance can be useful when performing sensitivity analyses for the average effect, which is usually the parameter of primary interest.

CONCLUSIONS

We conclude that using unequal tail probabilities when computing 95 % confidence intervals for the between-study variance, when using methods based on generalised heterogeneity statistics, can result in shorter confidence intervals. We suggest that those who find the case for using unequal tail probabilities convincing should use the '1-4 % split', where greater tail probability is allocated to the upper confidence bound. The 'width-optimal' interval that we present deserves further investigation.

Approximate confidence intervals for moment-based estimators of the between-study variance in random effects meta-analysis

Moment‐based estimators of the between‐study variance are very popular when performing random effects meta‐analyses. This type of estimation has many advantages including computational and conceptual simplicity. Furthermore, by using these estimators in large samples, valid meta‐analyses can be performed without the assumption that the treatment effects follow a normal distribution. Recently proposed moment‐based confidence intervals for the between‐study variance are exact under the random effects model but are quite elaborate. Here, we present a much simpler method for calculating approximate confidence intervals of this type. This method uses variance‐stabilising transformations as its basis and can be used for a very wide variety of moment‐based estimators in both the random effects meta‐analysis and meta‐regression models. © 2015 The Authors. Research Synthesis Methods published by John Wiley & Sons, Ltd.