A Method of Moments Estimator for Random Effect Multivariate Meta‐Analysis

Summary Meta‐analysis is a powerful approach to combine evidence from multiple studies to make inference about one or more parameters of interest, such as regression coefficients. The validity of the fixed effect model meta‐analysis depends on the underlying assumption that all studies in the meta‐analysis share the same effect size. In the presence of heterogeneity, the fixed effect model incorrectly ignores the between‐study variance and may yield false positive results. The random effect model takes into account both within‐study and between‐study variances. It is more conservative than the fixed effect model and should be favored in the presence of heterogeneity. In this paper, we develop a noniterative method of moments estimator for the between‐study covariance matrix in the random effect model multivariate meta‐analysis. To our knowledge, it is the first such method of moments estimator in the matrix form. We show that our estimator is a multivariate extension of DerSimonian and Laird’s univariate method of moments estimator, and it is invariant to linear transformations. In the simulation study, our method performs well when compared to existing random effect model multivariate meta‐analysis approaches. We also apply our method in the analysis of a real data example.     

Sexual selection and sperm quantity: meta‐analyses of strategic ejaculation

Multiple mating or group spawning leads to post‐copulatory sexual selection, which generally favours ejaculates that are more competitive under sperm competition. In four meta‐analyses we quantify the evidence that sperm competition (SC) favours greater sperm number using data from studies of strategic ejaculation. Differential investment into each ejaculate emerges at the individual level if males exhibit phenotypic plasticity in ejaculate properties in response to the likely risk and/or intensity of sperm competition after a given mating. Over the last twenty years, a series of theoretical models have been developed that predict how ejaculate size will be strategically adjusted in relation to: (a) the number of immediate rival males, with a distinction made between 0 versus 1 rival (‘risk’ of SC) and 1 versus several rivals (‘intensity’ of SC); (b) female mating status (virgin or previously mated); and (c) female phenotypic quality (e.g. female size or condition). Some well‐known studies have reported large adjustments in ejaculate size depending on the relevant social context and this has led to widespread acceptance of the claim that strategic sperm allocation occurs in response to each of these factors. It is necessary, however, to test each claim separately because it is easy to overlook studies with weak or negative findings. Compiling information on the variation in outcomes among species is potentially informative about the relevance of these assumptions in different taxa or mating systems. We found strong evidence that, on average, males transfer larger ejaculates to higher quality females. The effect of female mating status was less straightforward and depended on how ejaculate size was measured (i.e. use of proxy or direct measure). There is strong evidence that ejaculate size increased when males were exposed to a single rival, which is often described as a response to the risk of SC. There is, however, no evidence for the general prediction that ejaculate size decreases as the number of rivals increases from one to several males (i.e. in response to a higher intensity of SC which lowers the rate of return per sperm released). Our results highlight how meta‐analysis can reveal unintentional biases in narrative literature reviews. We note that several assumptions of theoretical models can alter an outcome's predicted direction in a given species (e.g. the effect of female mating status depends on whether there is first‐ or last‐male sperm priority). Many studies do not provide this background information and fail to make strong a priori predictions about the expected response of ejaculate size to manipulation of the mating context. Researchers should be explicit about which model they are testing to ensure that future meta‐analyses can better partition studies into different categories, or control for continuous moderator variables.     

Termite‐induced heterogeneity in African savanna vegetation: mechanisms and patterns

Objectives: To (1) assess the strength of evidence for the role of termites in vegetation heterogeneity in African savannas, and (2) identify the mechanisms by which termites induce such heterogeneity. Location: African savannas. Methods: We conducted a review of the literature, a meta‐analysis and qualitative systems analysis to identify mechanisms to explain the observed patterns. Results: The review provided evidence for termite‐induced heterogeneity in floristic composition and vegetation patterning in savannas across Africa. Termites induced vegetation heterogeneity directly or indirectly through their nest‐building and foraging activities, associated nutrient cycling and their interaction with mammalian herbivores and fire. The literature reviewed indicated that termite mounds essentially act as islands of fertility, which are responsible for ecosystem‐level spatial heterogeneity in savannas. This was supported by the meta‐analysis, which demonstrated that mounds of Ancistrotermes, Macrotermes, Odontotermes (family Macrotermitinae), Cubitermes (family Termitinae) and Trinervitermes (Nasutitermitinae) are significantly enriched in clay (75%), carbon (16%), total nitrogen (42%), calcium (232%), potassium (306%) and magnesium (154%) compared to the surrounding savanna soil. Conclusions: Termite activity is one of the major factors that induce vegetation patterning in African savannas. The implications of this are discussed and research questions for future studies and modelling efforts are indicated.     

A meta‐review of “lifestyle psychiatry”: the role of exercise,smoking, diet and sleep in the prevention and treatment of mental disorders

There is increasing academic and clinical interest in how “lifestyle factors” traditionally associated with physical health may also relate to mental health and psychological well‐being. In response, international and national health bodies are producing guidelines to address health behaviors in the prevention and treatment of mental illness. However, the current evidence for the causal role of lifestyle factors in the onset and prognosis of mental disorders is unclear. We performed a systematic meta‐review of the top‐tier evidence examining how physical activity, sleep, dietary patterns and tobacco smoking impact on the risk and treatment outcomes across a range of mental disorders. Results from 29 meta‐analyses of prospective/cohort studies, 12 Mendelian randomization studies, two meta‐reviews, and two meta‐analyses of randomized controlled trials were synthesized to generate overviews of the evidence for targeting each of the specific lifestyle factors in the prevention and treatment of depression, anxiety and stress‐related disorders, schizophrenia, bipolar disorder, and attention‐deficit/hyperactivity disorder. Standout findings include: a) convergent evidence indicating the use of physical activity in primary prevention and clinical treatment across a spectrum of mental disorders; b) emerging evidence implicating tobacco smoking as a causal factor in onset of both common and severe mental illness; c) the need to clearly establish causal relations between dietary patterns and risk of mental illness, and how diet should be best addressed within mental health care; and d) poor sleep as a risk factor for mental illness, although with further research required to understand the complex, bidirectional relations and the benefits of non‐pharmacological sleep‐focused interventions. The potentially shared neurobiological pathways between multiple lifestyle factors and mental health are discussed, along with directions for future research, and recommendations for the implementation of these findings at public health and clinical service levels.     

Meta‐analysis of genome‐wide association from genomic prediction models

Genome‐wide association (GWA) studies based on GBLUP models are a common practice in animal breeding. However, effect sizes of GWA tests are small, requiring larger sample sizes to enhance power of detection of rare variants. Because of difficulties in increasing sample size in animal populations, one alternative is to implement a meta‐analysis (MA), combining information and results from independent GWA studies. Although this methodology has been used widely in human genetics, implementation in animal breeding has been limited. Thus, we present methods to implement a MA of GWA, describing the proper approach to compute weights derived from multiple genomic evaluations based on animal‐centric GBLUP models. Application to real datasets shows that MA increases power of detection of associations in comparison with population‐level GWA, allowing for population structure and heterogeneity of variance components across populations to be accounted for. Another advantage of MA is that it does not require access to genotype data that is required for a joint analysis. Scripts related to the implementation of this approach, which consider the strength of association as well as the sign, are distributed and thus account for heterogeneity in association phase between QTL and SNPs. Thus, MA of GWA is an attractive alternative to summarizing results from multiple genomic studies, avoiding restrictions with genotype data sharing, definition of fixed effects and different scales of measurement of evaluated traits.     

Ignoring non‐English‐language studies may bias ecological meta‐analyses

Meta‐analysis plays a crucial role in syntheses of quantitative evidence in ecology and biodiversity conservation. The reliability of estimates in meta‐analyses strongly depends on unbiased sampling of primary studies. Although earlier studies have explored potential biases in ecological meta‐analyses, biases in reported statistical results and associated study characteristics published in different languages have never been tested in environmental sciences. We address this knowledge gap by systematically searching published meta‐analyses and comparing effect‐size estimates between English‐ and Japanese‐language studies included in existing meta‐analyses. Of the 40 published ecological meta‐analysis articles authored by those affiliated to Japanese institutions, we find that three meta‐analysis articles searched for studies in the two languages and involved sufficient numbers of English‐ and Japanese‐language studies, resulting in four eligible meta‐analyses (i.e., four meta‐analyses conducted in the three meta‐analysis articles). In two of the four, effect sizes differ significantly between the English‐ and Japanese‐language studies included in the meta‐analyses, causing considerable changes in overall mean effect sizes and even their direction when Japanese‐language studies are excluded. The observed differences in effect sizes are likely attributable to systematic differences in reported statistical results and associated study characteristics, particularly taxa and ecosystems, between English‐ and Japanese‐language studies. Despite being based on a small sample size, our findings suggest that ignoring non‐English‐language studies may bias outcomes of ecological meta‐analyses, due to systematic differences in study characteristics and effect‐size estimates between English‐ and non‐English languages. We provide a list of actions that meta‐analysts could take in the future to reduce the risk of language bias.     

Indirect comparisons: a review of reporting and methodological quality

Background

The indirect comparison of two interventions can be valuable in many situations. However, the quality of an indirect comparison will depend on several factors including the chosen methodology and validity of underlying assumptions. Published indirect comparisons are increasingly more common in the medical literature, but as yet, there are no published recommendations of how they should be reported. Our aim is to systematically review the quality of published indirect comparisons to add to existing empirical data suggesting that improvements can be made when reporting and applying indirect comparisons.

Methodology/Findings

Reviews applying statistical methods to indirectly compare the clinical effectiveness of two interventions using randomised controlled trials were eligible. We searched (1966–2008) Database of Abstracts and Reviews of Effects, The Cochrane library, and Medline. Full review publications were assessed for eligibility. Specific criteria to assess quality were developed and applied. Forty-three reviews were included. Adequate methodology was used to calculate the indirect comparison in 41 reviews. Nineteen reviews assessed the similarity assumption using sensitivity analysis, subgroup analysis, or meta-regression. Eleven reviews compared trial-level characteristics. Twenty-four reviews assessed statistical homogeneity. Twelve reviews investigated causes of heterogeneity. Seventeen reviews included direct and indirect evidence for the same comparison; six reviews assessed consistency. One review combined both evidence types. Twenty-five reviews urged caution in interpretation of results, and 24 reviews indicated when results were from indirect evidence by stating this term with the result.

Conclusions

This review shows that the underlying assumptions are not routinely explored or reported when undertaking indirect comparisons. We recommend, therefore, that the quality of indirect comparisons should be improved, in particular, by assessing assumptions and reporting the assessment methods applied. We propose that the quality criteria applied in this article may provide a basis to help review authors carry out indirect comparisons and to aid appropriate interpretation.     

The effects of sex hormones on immune function: a meta‐analysis

The effects of sex hormones on immune function have received much attention, especially following the proposal of the immunocompetence handicap hypothesis. Many studies, both experimental and correlational, have been conducted to test the relationship between immune function and the sex hormones testosterone in males and oestrogen in females. However, the results are mixed. We conducted four cross‐species meta‐analyses to investigate the relationship between sex hormones and immune function: (i) the effect of testosterone manipulation on immune function in males, (ii) the correlation between circulating testosterone level and immune function in males, (iii) the effect of oestrogen manipulation on immune function in females, and (iv) the correlation between circulating oestrogen level and immune function in females. The results from the experimental studies showed that testosterone had a medium‐sized immunosuppressive effect on immune function. The effect of oestrogen, on the other hand, depended on the immune measure used. Oestrogen suppressed cell‐mediated immune function while reducing parasite loads. The overall correlation (meta‐analytic relationship) between circulating sex hormone level and immune function was not statistically significant for either testosterone or oestrogen despite the power of meta‐analysis. These results suggest that correlational studies have limited value for testing the effects of sex hormones on immune function. We found little evidence of publication bias in the four data sets using indirect tests. There was a weak and positive relationship between year of publication and effect size for experimental studies of testosterone that became non‐significant after we controlled for castration and immune measure, suggesting that the temporal trend was due to changes in these moderators over time. Graphical analyses suggest that the temporal trend was due to an increased use of cytokine measures across time. We found substantial heterogeneity in effect sizes, except in correlational studies of testosterone, even after we accounted for the relevant random and fixed factors. In conclusion, our results provide good evidence that testosterone suppresses immune function and that the effect of oestrogen varies depending on the immune measure used.     

Publication bias in ecology and evolution: an empirical assessment using the 'trim and fill' method

Recent reviews of specific topics, such as the relationship between male attractiveness to females and fluctuating asymmetry or attractiveness and the expression of secondary sexual characters, suggest that publication bias might be a problem in ecology and evolution. In these cases, there is a significant negative correlation between the sample size of published studies and the magnitude or strength of the research findings (formally the ‘effect size’). If all studies that are conducted are equally likely to be published, irrespective of their findings, there should not be a directional relationship between effect size and sample size; only a decrease in the variance in effect size as sample size increases due to a reduction in sampling error. One interpretation of these reports of negative correlations is that studies with small sample sizes and weaker findings (smaller effect sizes) are less likely to be published. If the biological literature is systematically biased this could undermine the attempts of reviewers to summarise actual biology relationships by inflating estimates of average effect sizes. But how common is this problem? And does it really effect the general conclusions of literature reviews? Here, we examine data sets of effect sizes extracted from 40 peer‐reviewed, published meta‐analyses. We estimate how many studies are missing using the newly developed ‘trim and fill’ method. This method uses asymmetry in plots of effect size against sample size (‘funnel plots’) to detect ‘missing’ studies. For random‐effect models of meta‐analysis 38% (15/40) of data sets had a significant number of ‘missing’ studies. After correcting for potential publication bias, 21% (8/38) of weighted mean effects were no longer significantly greater than zero, and 15% (5/34) were no longer statistically robust when we used random‐effects models in a weighted meta‐analysis. The mean correlation between sample size and the magnitude of standardised effect size was also significantly negative (r_s=‐0.20, P < 0‐0001). Individual correlations were significantly negative (P < 0.10) in 35% (14/40) of cases. Publication bias may therefore effect the main conclusions of at least 15–21% of meta‐analyses. We suggest that future literature reviews assess the robustness of their main conclusions by correcting for potential publication bias using the ‘trim and fill’ method.     

Comparison of One‐Step and Two‐Step Meta‐Analysis Models Using Individual Patient Data

The problem of combining information from separate trials is a key consideration when performing a meta‐analysis or planning a multicentre trial. Although there is a considerable journal literature on meta‐analysis based on individual patient data (IPD), i.e. a one‐step IPD meta‐analysis, versus analysis based on summary data, i.e. a two‐step IPD meta‐analysis, recent articles in the medical literature indicate that there is still confusion and uncertainty as to the validity of an analysis based on aggregate data. In this study, we address one of the central statistical issues by considering the estimation of a linear function of the mean, based on linear models for summary data and for IPD. The summary data from a trial is assumed to comprise the best linear unbiased estimator, or maximum likelihood estimator of the parameter, along with its covariance matrix. The setup, which allows for the presence of random effects and covariates in the model, is quite general and includes many of the commonly employed models, for example, linear models with fixed treatment effects and fixed or random trial effects. For this general model, we derive a condition under which the one‐step and two‐step IPD meta‐analysis estimators coincide, extending earlier work considerably. The implications of this result for the specific models mentioned above are illustrated in detail, both theoretically and in terms of two real data sets, and the roles of balance and heterogeneity are highlighted. Our analysis also shows that when covariates are present, which is typically the case, the two estimators coincide only under extra simplifying assumptions, which are somewhat unrealistic in practice.     

The impact of pharmacological and non‐pharmacological interventions to improve physical health outcomes in people with schizophrenia: a meta‐review of meta‐analyses of randomized controlled trials

We summarized and compared meta‐analyses of pharmacological and non‐pharmacological interventions targeting physical health outcomes among people with schizophrenia spectrum disorders. Major databases were searched until June 1, 2018. Of 3,709 search engine hits, 27 meta‐analyses were included, representing 128 meta‐analyzed trials and 47,231 study participants. While meta‐analyses were generally of adequate or high quality, meta‐analyzed studies were less so. The most effective weight reduction interventions were individual lifestyle counseling (standardized mean difference, SMD=–0.98) and exercise interventions (SMD=–0.96), followed by psychoeducation (SMD=–0.77), aripiprazole augmentation (SMD=–0.73), topiramate (SMD=–0.72), d‐fenfluramine (SMD=–0.54) and metformin (SMD=–0.53). Regarding waist circumference reduction, aripiprazole augmentation (SMD=–1.10) and topiramate (SMD=–0.69) demonstrated the best evidence, followed by dietary interventions (SMD=–0.39). Dietary interventions were the only to significantly improve (diastolic) blood pressure (SMD=–0.39). Switching from olanzapine to quetiapine or aripiprazole (SMD=–0.71) and metformin (SMD=–0.65) demonstrated best efficacy for reducing glucose levels, followed by glucagon‐like peptide‐1 receptor agonists (SMD=–0.39), dietary interventions (SMD=–0.37) and aripiprazole augmentation (SMD=–0.34), whereas insulin resistance improved the most with metformin (SMD=–0.75) and rosiglitazone (SMD=–0.44). Topiramate had the greatest efficacy for triglycerides (SMD=–0.68) and low‐density lipoprotein (LDL)‐cholesterol (SMD=–0.80), whereas metformin had the greatest beneficial effects on total cholesterol (SMD=–0.51) and high‐density lipoprotein (HDL)‐cholesterol (SMD=0.45). Lifestyle interventions yielded small effects for triglycerides, total cholesterol and LDL‐cholesterol (SMD=–0.35 to –0.37). Only exercise interventions increased exercise capacity (SMD=1.81). Despite frequent physical comorbidities and premature mortality mainly due to these increased physical health risks, the current evidence for pharmacological and non‐pharmacological interventions in people with schizophrenia to prevent and treat these conditions is still limited and more larger trials are urgently needed.     

Effectiveness of programs for reducing the stigma associated with mental disorders. A meta‐analysis of randomized controlled trials

The stigma associated with mental disorders is a global public health problem. Programs to combat it must be informed by the best available evidence. To this end, a meta‐analysis was undertaken to investigate the effectiveness of existing programs. A systematic search of PubMed, PsycINFO and Cochrane databases yielded 34 relevant papers, comprising 33 randomized controlled trials. Twenty‐seven papers (26 trials) contained data that could be incorporated into a quantitative analysis. Of these trials, 19 targeted personal stigma or social distance (6,318 participants), six addressed perceived stigma (3,042 participants) and three self‐stigma (238 participants). Interventions targeting personal stigma or social distance yielded small but significant reductions in stigma across all mental disorders combined (d=0.28, 95% CI: 0.17‐0.39, p<0.001) as well as for depression (d=0.36, 95% CI: 0.10‐0.60, p<0.01), psychosis (d=0.20, 95% CI: 0.06‐0.34, p<0.01) and generic mental illness (d=0.30, 95% CI: 0.10‐0.50, p<0.01). Educational interventions were effective in reducing personal stigma (d=0.33, 95% CI: 0.19‐0.42, p<0.001) as were interventions incorporating consumer contact (d=0.47, 95% CI: 0.17‐0.78, p<0.001), although there were insufficient studies to demonstrate an effect for consumer contact alone. Internet programs were at least as effective in reducing personal stigma as face‐to‐face delivery. There was no evidence that stigma interventions were effective in reducing perceived or self‐stigma. In conclusion, there is an evidence base to inform the roll out of programs for improving personal stigma among members of the community. However, there is a need to investigate methods for improving the effectiveness of these programs and to develop interventions that are effective in reducing perceived and internalized stigma.     

Sample size recalculation in multicenter randomized controlled clinical trials based on noncomparative data

Many late-phase clinical trials recruit subjects at multiple study sites. This introduces a hierarchical structure into the data that can result in a power-loss compared to a more homogeneous single-center trial. Building on a recently proposed approach to sample size determination, we suggest a sample size recalculation procedure for multicenter trials with continuous endpoints. The procedure estimates nuisance parameters at interim from noncomparative data and recalculates the sample size required based on these estimates. In contrast to other sample size calculation methods for multicenter trials, our approach assumes a mixed effects model and does not rely on balanced data within centers. It is therefore advantageous, especially for sample size recalculation at interim. We illustrate the proposed methodology by a study evaluating a diabetes management system. Monte Carlo simulations are carried out to evaluate operation characteristics of the sample size recalculation procedure using comparative as well as noncomparative data, assessing their dependence on parameters such as between-center heterogeneity, residual variance of observations, treatment effect size and number of centers. We compare two different estimators for between-center heterogeneity, an unadjusted and a bias-adjusted estimator, both based on quadratic forms. The type 1 error probability as well as statistical power are close to their nominal levels for all parameter combinations considered in our simulation study for the proposed unadjusted estimator, whereas the adjusted estimator exhibits some type 1 error rate inflation. Overall, the sample size recalculation procedure can be recommended to mitigate risks arising from misspecified nuisance parameters at the planning stage.     

Efficacy Comparison of Six Chemotherapeutic Combinations for Osteosarcoma and Ewing's Sarcoma Treatment: A Network Meta‐Analysis

This study aimed to address the insufficiency of traditional meta‐analysis and provide improved guidelines for the clinical practice of osteosarcoma treatment. The heterogeneity of the fixed‐effect model was calculated, and when necessary, a random‐effect model was adopted. Furthermore, the direct and indirect evidence was pooled together and exhibited in the forest plot and slash table. The surface under the cumulative ranking curve (SUCRA) value was also measured to rank each intervention. Finally, heat plot was introduced to demonstrate the contribution of each intervention and the inconsistency between direct and indirect comparisons. This network meta‐analysis included 32 trials, involving a total of 5,626 subjects reported by 28 articles. All the treatments were classified into six chemotherapeutic combinations: dual agent with or without ifosfamide (IFO), multi‐agent with or without IFO, and dual agent or multi‐agent with IFO and etoposide. For the primary outcomes, both overall survival (OS) and event‐free survival (EFS) rates were considered. The multi‐agent integrated with IFO and etoposide showed an optimal performance for 5‐year OS, 10‐year OS, 3‐year EFS, 5‐year EFS, and 10‐year EFS when compared with placebo. The SUCRA value of this treatment was also the highest of these six interventions. However, multi‐drug with IFO alone had the highest SUCRA value of 0.652 and 0.516 when it came to relapse and lung‐metastasis. It was efficient to some extent, but no significant difference was observed in both outcomes. Chemotherapy, applied as induction or adjuvant treatment with radiation therapy or surgery, is able to increase the survival rate of patients, especially by combining multi‐drug with IFO and etoposide, which demonstrated the best performance in both OS and EFS. As for relapse and the lung‐metastasis, multiple agents with IFO alone seemed to have the optimal efficiency, although no significant difference was observed here. J. Cell. Biochem. 119: 250–259, 2018. © 2017 Wiley Periodicals, Inc.     

Lack of evidence to favor specific preventive interventions in psychosis: a network meta‐analysis

Preventing psychosis in patients at clinical high risk may be a promising avenue for pre‐emptively ameliorating outcomes of the most severe psychiatric disorder. However, information on how each preventive intervention fares against other currently available treatment options remains unavailable. The aim of the current study was to quantify the consistency and magnitude of effects of specific preventive interventions for psychosis, comparing different treatments in a network meta‐analysis. PsycINFO, Web of Science, Cochrane Central Register of Controlled Trials, and unpublished/grey literature were searched up to July 18, 2017, to identify randomized controlled trials conducted in individuals at clinical high risk for psychosis, comparing different types of intervention and reporting transition to psychosis. Two reviewers independently extracted data. Data were synthesized using network meta‐analyses. The primary outcome was transition to psychosis at different time points and the secondary outcome was treatment acceptability (dropout due to any cause). Effect sizes were reported as odds ratios and 95% confidence intervals (CIs). Sixteen studies (2,035 patients, 57% male, mean age 20.1 years) reported on risk of transition. The treatments tested were needs‐based interventions (NBI); omega‐3 + NBI; ziprasidone + NBI; olanzapine + NBI; aripiprazole + NBI; integrated psychological interventions; family therapy + NBI; D‐serine + NBI; cognitive behavioural therapy, French & Morrison protocol (CBT‐F) + NBI; CBT‐F + risperidone + NBI; and cognitive behavioural therapy, van der Gaag protocol (CBT‐V) + CBT‐F + NBI. The network meta‐analysis showed no evidence of significantly superior efficacy of any one intervention over the others at 6 and 12 months (insufficient data were available after 12 months). Similarly, there was no evidence for intervention differences in acceptability at either time point. Tests for inconsistency were non‐significant and sensitivity analyses controlling for different clustering of interventions and biases did not materially affect the interpretation of the results. In summary, this study indicates that, to date, there is no evidence that any specific intervention is particularly effective over the others in preventing transition to psychosis. Further experimental research is needed.     

Formalizing the definition of meta‐analysis in Molecular Ecology

Meta‐analysis, the statistical synthesis of pertinent literature to develop evidence‐based conclusions, is relatively new to the field of molecular ecology, with the first meta‐analysis published in the journal Molecular Ecology in 2003 (Slate & Phua 2003). The goal of this article is to formalize the definition of meta‐analysis for the authors, editors, reviewers and readers of Molecular Ecology by completing a review of the meta‐analyses previously published in this journal. We also provide a brief overview of the many components required for meta‐analysis with a more specific discussion of the issues related to the field of molecular ecology, including the use and statistical considerations of Wright's F_ST and its related analogues as effect sizes in meta‐analysis. We performed a literature review to identify articles published as ‘meta‐analyses’ in Molecular Ecology, which were then evaluated by at least two reviewers. We specifically targeted Molecular Ecology publications because as a flagship journal in this field, meta‐analyses published in Molecular Ecology have the potential to set the standard for meta‐analyses in other journals. We found that while many of these reviewed articles were strong meta‐analyses, others failed to follow standard meta‐analytical techniques. One of these unsatisfactory meta‐analyses was in fact a secondary analysis. Other studies attempted meta‐analyses but lacked the fundamental statistics that are considered necessary for an effective and powerful meta‐analysis. By drawing attention to the inconsistency of studies labelled as meta‐analyses, we emphasize the importance of understanding the components of traditional meta‐analyses to fully embrace the strengths of quantitative data synthesis in the field of molecular ecology.     

Plant species diversity and environmental heterogeneity: spatial scale and competing hypotheses

Questions: What is the observed relationship between plant species diversity and spatial environmental heterogeneity? Does the relationship scale predictably with sample plot size? What are the relative contributions to diversity patterns of variables linked to productivity or available energy compared to those corresponding to spatial heterogeneity? Methods: Observational and experimental studies that quantified relationships between plant species richness and within‐sample spatial environmental heterogeneity were reviewed. Effect size in experimental studies was quantified as the standardized mean difference between control (homogeneous) and heterogeneous treatments. For observational studies, effect sizes in individual studies were examined graphically across a gradient of plot size (focal scale). Relative contributions of variables representing spatial heterogeneity were compared to those representing available energy using a response ratio. Results: Forty‐one observational and 11 experimental studies quantified plant species diversity and spatial environmental heterogeneity. Observational studies reported positive species diversity‐spatial heterogeneity correlations at all points across a plot size gradient from ～1.0 × 10^?1 to ～1.0 × 10¹¹ m², although many studies reported spatial heterogeneity variables with no significant relationships to species diversity. The cross‐study effect size in experimental studies was not significantly different from zero. Available energy variables explained consistently more of the variance in species richness than spatial heterogeneity variables, especially at the smallest and largest plot sizes. Main conclusions: Species diversity was not related to spatial heterogeneity in a way predictable by plot size. Positive heterogeneity‐diversity relationships were common, confirming the importance of niche differentiation in species diversity patterns, but future studies examining a range of spatial scales in the same system are required to determine the role of dispersal and available energy in these patterns.     

Sample Size Requirements for Evaluation of Bridging Evidence

This paper addresses issues concerning methodologies on the sample size required for statistical evaluation of bridging evidence for a registration of pharmaceutical products in a new region. The bridging data can be either in the Complete Clinical Data Package (CCDP) generated during clinical drug development for submission to the original region or from a bridging study conducted in the new region after the pharmaceutical product was approved in the original region. When the data are in the CCDP, the randomized parallel dose‐response design stratified to the ethnic factors and region will generate internally valid data for evaluating similarity concurrently between the regions for assessment of the ability of extrapolation to the new region. Formula for sample size under this design is derived. The required sample size for evaluation of similarity between the regions can be at least four times as large as that needed for evaluation of treatment effects only. For a bridging study conducted in the new region in which the data of the foreign and new regions are not generated concurrently, a hierarchical model approach to incorporating the foreign bridging information into the data generated by the bridging study is suggested. The sample size required is evaluated. In general, the required sample size for the bridging trials in the new region is inversely proportional to equivalence limits, variability of primary endpoints, and the number of patients of the trials conducted in the original region.     

Letter to the Editor

Regarding Paper “Sample size determination in clinical trials with multiple co‐primary endpoints including mixed continuous and binary variables” by T. Sozu , T. Sugimoto , and T. Hamasaki Biometrical Journal (2012) 54 (5): 716–729 Article: http://dx.doi.org/10.1002/bimj.201100221 Authors' Reply: http://dx.doi.org/10.1002/bimj.201300032 This paper recently introduced a methodology for calculating the sample size in clinical trials with multiple mixed binary and continuous co‐primary endpoints modeled by the so‐called conditional grouped continuous model (CGCM). The purpose of this note is to clarify certain aspects of the methodology and propose an alternative approach based on latent means tests for the binary endpoints. We demonstrate that our approach is more powerful, yielding smaller sample sizes at powers comparable to those used in the paper.     

Bayesian design of noninferiority trials for medical devices using historical data

Summary We develop a new Bayesian approach of sample size determination (SSD) for the design of noninferiority clinical trials. We extend the fitting and sampling priors of Wang and Gelfand (2002, Statistical Science 17 , 193–208) to Bayesian SSD with a focus on controlling the type I error and power. Historical data are incorporated via a hierarchical modeling approach as well as the power prior approach of Ibrahim and Chen (2000, Statistical Science 15 , 46–60). Various properties of the proposed Bayesian SSD methodology are examined and a simulation‐based computational algorithm is developed. The proposed methodology is applied to the design of a noninferiority medical device clinical trial with historical data from previous trials.