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Doing Meta-Analysis with R: A Hands-On Guide

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Abstract

This book serves as an accessible introduction into how meta-analyses can be conducted in R. Essential steps for meta-analysis are covered, including pooling of outcome measures, forest plots, heterogeneity diagnostics, subgroup analyses, meta-regression, methods to control for publication bias, risk of bias assessments and plotting tools. Advanced, but highly relevant topics such as network meta-analysis, multi-/three-level meta-analyses, Bayesian meta-analysis approaches, SEM meta-analysis are also covered. The programming and statistical background covered in the book are kept at a non-expert level. A print version of this book has been published with Chapman & Hall/CRC Press (Taylor & Francis). The complete book can be accessed online: https://bookdown.org/MathiasHarrer/Doing_Meta_Analysis_in_R/.
Doing Meta-Analysis
with R
A Hands-On Guide
Mathias Harrer
Pim Cuijpers
Toshi A. Furukawa
David D. Ebert
First edition published 2022
by CRC Press
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and by CRC Press
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© 2022 Mathias Harrer, Pim Cuijpers, Toshi A. Furukawa, David D. Ebert
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Library of Congress Cataloging-in-Publication Data
Names: Harrer, Mathias, author.
Title: Doing meta-analysis with R : a hands-on guide / Mathias Harrer [and
three others].
Description: First edition. | Boca Raton : CRC Press, 2022. | Includes
bibliographical references and index.
Identifiers: LCCN 2021017096 (print) | LCCN 2021017097 (ebook) | ISBN
9780367610074 (hardback) | ISBN 9780367619770 (paperback) | ISBN
9780367619770 (ebook)
Subjects: LCSH: Meta-analysis. | R (Computer program language)
Classification: LCC R853.M48 H37 2022 (print) | LCC R853.M48 (ebook) |
DDC 610.727--dc23
LC record available at https://lccn.loc.gov/2021017096
LC ebook record available at https://lccn.loc.gov/2021017097
ISBN: 9780367610074 (hbk)
ISBN: 9780367619770 (pbk)
ISBN: 9781003107347 (ebk)
DOI: 10.1201/9781003107347
Typeset in Alegreya
by KnowledgeWorks Global Ltd.
Dear colleague,
As of September 2021, a fully revised and extended version of “Doing Meta-Analysis with R A
Hands-On Guide” has been published with CRC Press/Chapman & Hall (Taylor & Francis). A
physical copy of the book can be purchased, for example, via the Routledge Online Shop.
Unfortunately, it is therefore not possible to provide an openly accessible PDF Version of the
guide on the Internet any longer.
We strongly believe that everyone should have access to academic publications, regardless of
their background or financial resources. Thus, we are very grateful that CRC allows us to
maintain a full online version of the guide, which you can find here. On this website, the entire
contents of book can be accessed for free. The online version even contains some additional
content which did not make it into the printed version.
You are still free to use and adapt contents of the book, for example for your own teaching. If
you need more or other material for yourself or your students, feel free to contact Mathias
(mathias.harrer@fau.de).
We hope you are not too disappointed that the PDF ends here, and that you find reading the
guide useful, either in its printed form or on the web.
Kind regards,
Mathias, Pim, Toshi, David
June 2021
↗ Open Online Version
... By comprehensively integrating the results of previous studies, meta-analysis can expand the sample size and statistical power to further improve the effect size estimate, and examine variability between studies (14). A systematic review can synthesize the scientific evidence obtained through a meta-analysis and summarize the evidence for risk factors (15). Therefore, systematic reviews and meta-analyses of prior research could provide deeper insights by collecting and summarizing information on the prevalence, seroprevalence, and risk factors of swIAV in domestic pigs. ...
... The meta-analysis was conducted with the "meta, " "metafor, " "dmetar, " and "ggcorrplot" packages in the software R version 4.1.2 (R Studio version 1.4) (15,(22)(23)(24)(25)(26). Random effects models with 95% CIs were used to analyze the data, considering the variation between the studies. ...
... The subgroup analysis guided the selection of covariates for inclusion in the meta-regression model, which was developed using a combinatorial approach (15,32). Multicollinearity was measured between covariates to verify whether the regression assumption was satisfied (33). ...
Article
Full-text available
The past and current burden of swine influenza A viruses (swIAV) must be estimated since pigs act as mixing vessels and are considered a potential source of newly emerging IAV variants. The objective of this systematic review and meta-analysis was to integrate data on the prevalence and seroprevalence of swIAV in South Korean domestic pigs and evaluate important risk factors that influence these outcomes. Eight databases were searched for studies that evaluated the prevalence and seroprevalence of swIAV in South Korean pigs using a specified search string; twenty-seven eligible studies were identified after application of a set of pre-determined inclusion criteria by three authors. The reported prevalence and seroprevalence were pooled separately in proportions between 0 and 1, using a random-effect meta-analysis. To identify and quantify potential sources of heterogeneity, subgroup, and meta-regression analyses were conducted using covariates (publication type, swIAV subtype, growth stage of pigs, sampling region, publication year, sampling season, facility, detection method, sample type, and sample size). The overall prevalence and seroprevalence in domestic pigs were 0.05 [95% confidence intervals (CIs): 0.05–0.12] and 0.35 (95% CIs: 0.14–0.63), respectively. To identify the impact of covariates on effect size, a suitable meta-regression model was determined using predictor importance estimates with corrected Akaike information criterion values. Consequently, the best-fit model included two covariates, publication year and sample size, which were significantly associated with high heterogeneity in the subgroup analysis. Furthermore, data visualization depicted a significant non-linear association between swIAV prevalence and seroprevalence and specific growth stages of pigs. These findings suggest that the periodic monitoring of pigs at different growth stages in large farms may help to establish the status of swIAV-spread across species in the region, and thereby minimize pandemic risk.
... The number of participants (with and without childhood trauma) within the treatment and, if applicable, control group, mean depression severity before and after treatment with corresponding SDs, and the depression severity correlation before and after treatment 24 were used to calculate effect sizes (Hedges' g small effect 0·2, moderate effect 0·5, and large effect 0·8). 25 Syntheses were done using the random-effects models with the Sidik-Jonkman estimator and the Hartung-Knapp-Sidik-Jonkman method because of anticipated heterogeneity among studies. 26 First, we determined whether individuals with childhood trauma had more severe depression than those without childhood trauma before depression treatment using all eligible studies. This was done by pooling effect sizes indicating the difference at baseline between individuals with and without childhood trauma. ...
... 27 Potential outlier studies were identified by the 95% CI of the effect size not overlapping with the 95% CI of the pooled effect size and observed in the Baujat plot for heterogeneity of individual studies. 26 The extent of heterogeneity among the studies in all analyses was assessed by Higgin's I² statistic with corresponding 95% CIs, grouped as low (25%), moderate (50%), or high (75%) heterogeneity. 28 Publication bias was investigated by doing an Egger's test to determine significant bias captured by asymmetry of the funnel plot 29 and Duval and Tweedie's trim-and-fill procedure, 30 which imputes missing studies (effects) until the funnel plot is symmetrical, thereby estimating the corrected effect size after publication bias has been taken into account. ...
... Exclusion of two outlier studies resulted in similar outcomes (g=0·200, 0·148-0·253; p<0·0001; Baujat plots in the appendix pp [18][19][20][21]. No significant publication bias was observed (Egger t=-1·48; p=0·14), but a trim-and-fill procedure added nine studies and increased the effect size to g=0·235 (95% CI 0·172-0·298; p<0·0001; funnel plots in the appendix pp [22][23][24][25][26][27][28]. The findings remained consistent with the initial baseline analysis, showing significantly increased depression severity in individuals with childhood trauma. ...
Article
Background Childhood trauma is a common and potent risk factor for developing major depressive disorder in adulthood, associated with earlier onset, more chronic or recurrent symptoms, and greater probability of having comorbidities. Some studies indicate that evidence-based pharmacotherapies and psychotherapies for adult depression might be less efficacious in patients with a history of childhood trauma than patients without childhood trauma, but findings are inconsistent. Therefore, we examined whether individuals with major depressive disorder, including chronic forms of depression, and a reported history of childhood trauma, had more severe depressive symptoms before treatment, had more unfavourable treatment outcomes following active treatments, and were less likely to benefit from active treatments relative to a control condition, compared with individuals with depression without childhood trauma. Methods We did a comprehensive meta-analysis (PROSPERO CRD42020220139). Study selection combined the search of bibliographical databases (PubMed, PsycINFO, and Embase) from Nov 21, 2013, to March 16, 2020, and full-text randomised clinical trials (RCTs) identified from several sources (1966 up to 2016–19) to identify articles in English. RCTs and open trials comparing the efficacy or effectiveness of evidence-based pharmacotherapy, psychotherapy, or combination intervention for adult patients with depressive disorders and the presence or absence of childhood trauma were included. Two independent researchers extracted study characteristics. Group data for effect-size calculations were requested from study authors. The primary outcome was depression severity change from baseline to the end of the acute treatment phase, expressed as standardised effect size (Hedges' g). Meta-analyses were done using random-effects models. Findings From 10 505 publications, 54 trials met the inclusion criteria, of which 29 (20 RCTs and nine open trials) contributed data of a maximum of 6830 participants (age range 18–85 years, male and female individuals and specific ethnicity data unavailable). More than half (4268 [62%] of 6830) of patients with major depressive disorder reported a history of childhood trauma. Despite having more severe depression at baseline (g=0·202, 95% CI 0·145 to 0·258, I²=0%), patients with childhood trauma benefitted from active treatment similarly to patients without childhood trauma history (treatment effect difference between groups g=0·016, –0·094 to 0·125, I²=44·3%), with no significant difference in active treatment effects (vs control condition) between individuals with and without childhood trauma (childhood trauma g=0·605, 0·294 to 0·916, I²=58·0%; no childhood trauma g=0·178, –0·195 to 0·552, I²=67·5%; between-group difference p=0·051), and similar dropout rates (risk ratio 1·063, 0·945 to 1·195, I²=0%). Findings did not significantly differ by childhood trauma type, study design, depression diagnosis, assessment method of childhood trauma, study quality, year, or treatment type or length, but differed by country (North American studies showed larger treatment effects for patients with childhood trauma; false discovery rate corrected p=0·0080). Most studies had a moderate to high risk of bias (21 [72%] of 29), but the sensitivity analysis in low-bias studies yielded similar findings to when all studies were included. Interpretation Contrary to previous studies, we found evidence that the symptoms of patients with major depressive disorder and childhood trauma significantly improve after pharmacological and psychotherapeutic treatments, notwithstanding their higher severity of depressive symptoms. Evidence-based psychotherapy and pharmacotherapy should be offered to patients with major depressive disorder regardless of childhood trauma status. Funding None.
... Statistical significance was taken to be p < 0.05, with a Forest plot used to visualize the distribution of the SVI means from the different studies included. Meta-analysis was conducted using R-Studio [20], following the methods recommended in [21]. ...
... The checklist has been used widely because of its sub-scale divisions, which provides an opportunity to assess the profile of the weaknesses and the strengths of each methodological issue. Articles were rated on the scale of very good (26)(27)(28), good (20)(21)(22)(23)(24)(25), fair (15)(16)(17)(18)(19), and poor (≤14) [24]. ...
Article
Full-text available
The aim of this systematic literature review was to determine whether social vulnerability is associated with frailty in older people. Databases were searched for literature from January 2001 to March 2022. Hand searches of reference lists of the selected articles were also used to identify other relevant studies. Studies that met the inclusion criteria were selected. Two independent reviewers assessed the methodological quality using an established tool. Eleven eligible studies from Canada, Europe, USA, Tanzania, Mexico, and China were selected. The level of social vulnerability measured by the Social Vulnerability Index (SVI) from a meta-analysis was 0.300 (95% CI: 0.242, 0.358), with the highest SVI in Tanzania (0.49), while the lowest level of SVI was reported in China (0.15). The highest frailty level of 0.32 was observed in both Tanzania and Europe, with the lowest frailty reported in a USA study from Hawaii (0.15). In all studies, social vulnerability was a significant predictor of mortality for both sexes at subsequent data collection points. The association between SVI and frailty was high in Tanzania (r = 0.81), with other studies reporting stronger correlations for females compared to males, but at small to moderate levels. In one study, an increase of 1SD in SVI was linked to a 20% increase in frailty score at a subsequent evaluation. Additional study is warranted to determine a potential causality between social vulnerability and frailty.
... Hartung-Knapp adjustments were employed to adjust for confidence intervals by controlling for heterogeneity arising from between-study estimations. 28 The random effects model was used regardless of heterogeneity scores. 29 Analyses were only conducted when sufficient data could be extracted for the outcome of interest and publication bias was not conducted due to lack of a suitable assessment tool for single-arm meta-analyses. ...
Article
Full-text available
Background There is a growing number of trials examining the effectiveness of pharmacotherapies for obesity, however, little is known about placebo and nocebo effect in these trials. Hence, we sought to examine the effect of placebo in obesity trials, to better understand the potential factors affecting clinical endpoints in them. Methods Medline, Embase, and Cochrane CENTRAL were searched for articles examining weight-loss RCTs examining patients with overweight or obesity in placebo-controlled arms from inception till 25 June 2022. This paper was registered online with PROSPERO (CRD42022302482). A single arm meta-analysis of proportions was used to estimate the primary outcomes, ≥5%, ≥10%, and ≥15% total weight loss – and the adverse effects that patients experienced during the trial. A meta-analysis of means was used to estimate the pooled mean differences of the secondary outcomes including, body weight measurements, lipid levels, glycemic indices, and blood pressure over time. Findings A total of 63 papers involving 20,454 patients and 69 trials were included. The proportion of patients that had ≥5%, ≥10%, and ≥15% weight loss was 20·4% (CI:16·1% to 25·0%), 8·3% (CI:6·1% to 10·9%), and 6·2% (CI:3·8% to 9·7%), respectively. Analysis by duration of trials showed stepwise increase in proportion of patients with ≥5% and ≥10% weight loss with increasing duration of study. Analysis of secondary outcomes found modest improvement in all analyses. The pooled average rate of overall AEs, serious AEs, and discontinuation was 73·7% (CI:68·0% to 79·0%), 3·4% (CI:2·4% to 4·5%), and 5·2% (CI:4·0% to 6·5%), respectively. In psychiatric complications, the pooled rates of anxiety and depression were 2·7% (CI:1·8% to 3·7%) and 2·5 (CI:1·7% to 3·3%). Interpretation Our meta-analysis of placebo-treated participants in weight-loss RCTs indicate a significant placebo and nocebo effect. These findings are important to quantify their effect and may inform the design of future RCTs.
... 19.4289, p < .0001). Because the total number of studies is 36 which is above K > 9 we conducted 302 subgroup analysis (Harrer et al., 2021). As seen in power we performed power analysis by using the "metapower" package (Griffin, 2020). ...
Article
Full-text available
Background: Studies conducted in the health sector have determined a positive relationship between job satisfaction and work engagement. However, this paper reveals that this relationship turns into a negative or non-significant relationship during the Covid-19 pandemic. We explore the reasons for inconsistency in research findings in this critical period through a meta-analysis. Methods: This study was conducted according to the PRISMA guidelines and PICO framework. Online databases including Web of Science, Scopus, PubMed, ProQuest, Google Scholar, and additional records from other databases were searched without any time limitation, and all studies published in English that reported the correlation between work engagement and job satisfaction were included in the analysis. In total, 36 individual correlation coefficients were synthesized. R statistical language was used to analyze the data. Result: A total of 36 studies with a sample size of 16,087 were synthesized. The overall effect size was found as r = 0.57 (95% CI [0.50−0.64]). While the moderating effect of national culture was not statistically significant, presence of Covid-19 as the significant moderator explained 37.08% of effect size heterogeneity. Such that the presence of Covid-19 has transformed the positive relationship between work engagement and job satisfaction into a negative but statistically nonsignificant relationship. Conclusion: This study empirically challenges the existing assumptions about the positive link between work engagement and job satisfaction. The results of the research can be a guide for managers and policymakers. Specifically, based on these results, different mechanisms can be put in place to support work engagement and, in turn, job satisfaction in the Covid-19 process.
... [7][8][9][10] In addition, applying a Bayesian framework in metaanalysis allows to model the heterogeneity estimation directly and to estimate pooled effects more precisely, especially when the number of studies included in the analysis is small. 11 Furthermore, Bayesian analysis can produce a full posterior distribution for both the effect estimate and heterogeneity and provide the capability of testing for tailored hypotheses assessing, for instance, if the estimate is smaller or larger than a specified interesting threshold. 12,13 We hypothesize that the intervention effect on the posterior probability distribution will lay outside a predefined region of practical equivalence. ...
Article
Background: Using the frequentist approach, a recent meta–analysis of three randomized clinical trials in patients undergoing intraoperative ventilation during general anesthesia for major surgery failed to show the benefit of ventilation that uses high positive end–expiratory pressure with recruitment maneuvers when compared to ventilation that uses low positive end–expiratory pressure without recruitment maneuvers. Methods: We designed a protocol for a Bayesian analysis using the pooled dataset. The multilevel Bayesian logistic model will use the individual patient data. Prior distributions will be prespecified to represent a varying level of skepticism for the effect estimate. The primary endpoint will be a composite of postoperative pulmonary complications (PPC) within the first seven postoperative days, which reflects the primary endpoint of the original studies. We preset a range of practical equivalence to assess the futility of the intervention with an interval of odds ratio (OR) between 0.9 and 1.1 and assess how much of the 95% of highest density interval (HDI) falls between the region of practical equivalence. Ethics and dissemination: The used data derive from approved studies that were published in recent years. The findings of this current analysis will be reported in a new manuscript, drafted by the writing committee on behalf of the three research groups. All investigators listed in the original trials will serve as collaborative authors.
Preprint
Full-text available
Background: The use of open-label placebos (OLPs) has been shown to be effective in clinical trials. We conducted a systematic review and meta-analysis to examine whether OLPs are effective in experimental studies with non-clinical populations. Methods: We searched five electronic databases on April 15, 2021. We conducted separate analyses for self-reported and objective outcomes and examined whether the level of suggestiveness of the instructions influenced the effectiveness of OLPs. Results: Of 3,573 identified records, 20 studies comprising 1,201 participants were included. We found a significant effect of OLPs for self-reported outcomes (SMD=0.43; 95% CI=0.28, 0.58; I²=7.2%) but not for objective outcomes (SMD=-0.02; 95% CI=-0.25, 0.21; I²=43.6%). The level of suggestiveness of the instructions influenced the effectiveness of OLPs for objective outcomes (p=.02), but not for self-reported outcomes. Discussion: OLPs appear to be effective when examined in experimental studies. However, the small number of studies highlights the need for further research.
Article
Objective: Our study aims to evaluate the effectiveness of mastoid obliteration compared to the canal wall up (CWU) technique in cholesteatoma surgery based on the systematic review of the literature and the meta-analysis of the data. Methods: The systematic search was performed in four major databases (MEDLINE, Web of Science, Embase, and CENTRAL) on October 14, 2021. Studies comparing the CWU technique and mastoid obliteration were included. The exclusion criteria were less than 12 months follow-up, congenital cholesteatoma, indefinite description of the surgical method, and animal studies. The protocol was registered on Prospero (registration number: CRD42021282485). The risk of bias was evaluated with the ROBINS-I tool. Residual and recurrent disease proportions as primary outcomes, quality of life, ear discharge, infection rates, hearing results, and operation time as secondary outcomes were analyzed. In the quantitative synthesis, the random effect model was used, and heterogeneity was identified. Results: A total of 11 articles with 2077 operations' data were found eligible. All the identified studies were retrospective cohorts. The odds of pooled residual and recurrent disease proportion were significantly lower in the obliteration group compared to CWU (OR = 0.45, CI:0.28;0.80, p = 0.014). However, when separated, the proportion of ears with recurrent (OR = 0.41, CI:0.11;1.57, p = 0.140) or residual (OR = 0.59, CI:0.23, 1.50, p = 0.207) disease did not show a significant difference, even though the odds were quite similar. The qualitative synthesis identified no significant difference in the secondary outcomes, but obliteration elongated the operation time. Conclusion: Mastoid obliteration significantly decreased the proportion of residual and recurrent cholesteatoma in pooled analyses compared to the CWU technique with low-quality of data. Level of evidence: NA Laryngoscope, 2022.
Article
Full-text available
Cognitive resources contribute to balance control. There is evidence that mental fatigue reduces cognitive resources and impairs balance performance, particularly in older adults and when balance tasks are complex, for example when trying to walk or stand while concurrently performing a secondary cognitive task. We conducted a systematic literature search in PubMed (MEDLINE), Web of Science and Google Scholar to identify eligible studies and performed a random effects meta-analysis to quantify the effects of experimentally induced mental fatigue on balance performance in healthy adults. Subgroup analyses were computed for age (healthy young vs. healthy older adults) and balance task complexity (balance tasks with high complexity vs. balance tasks with low complexity) to examine the moderating effects of these factors on fatigue-mediated balance performance. We identified 7 eligible studies with 9 study groups and 206 participants. Analysis revealed that performing a prolonged cognitive task had a small but significant effect (SMDwm = −0.38) on subsequent balance performance in healthy young and older adults. However, age- and task-related differences in balance responses to fatigue could not be confirmed statistically. Overall, aggregation of the available literature indicates that mental fatigue generally reduces balance in healthy adults. However, interactions between cognitive resource reduction, aging and balance task complexity remain elusive.
Article
OBJECTIVE Several growth-preserving surgical techniques are employed in the management of early-onset scoliosis (EOS). The authors’ objective was to compare the use of traditional growing rods (TGRs), magnetically controlled growing rods (MCGRs), Shilla growth guidance techniques, and vertically expanding prosthetic titanium ribs (VEPTRs) for the management of EOS. METHODS A systematic review of electronic databases, including Ovid MEDLINE and Cochrane, was performed. Outcomes of interest included correction of Cobb angle, T1–S1 distance, and complication rate, including alignment, hardware failure and infection, and planned and unplanned reoperation rates. The percent changes and 95% CIs were pooled across studies using random-effects meta-analysis. RESULTS A total of 67 studies were identified, which included 2021 patients. Of these, 1169 (57.8%) patients underwent operations with TGR, 178 (8.8%) Shilla growth guidance system, 448 (22.2%) MCGR, and 226 (11.1%) VEPTR system. The mean ± SD age of the cohort was 6.9 ± 1.2 years. The authors found that the Shilla technique provided the most significant improvement in coronal Cobb angle immediately after surgery (mean [95% CI] 64.2° [61.4°–67.2°]), whereas VEPTR (27.6% [22.7%–33.6%]) and TGR (45% [42.5%–48.5%]) performed significantly worse. VEPTR also performed significantly worse than the other techniques at final follow-up. The techniques also provided comparable gains in T1–S1 height immediately postoperatively (mean [95% CI] 10.5% [9.0%–12.0%]); however, TGR performed better at final follow-up (21.3% [18.6%–24.1%]). Complications were not significantly different among the patients who underwent the Shilla, TGR, MCGR, and VEPTR techniques, except for the rate of infections. The TGR technique had the lowest rate of unplanned reoperations (mean [95% CI] 15% [10%–23%] vs 24% [19%–29%]) but the highest number of planned reoperations per patient (5.31 [4.83–5.82]). The overall certainty was also low, with a high risk of bias across studies. CONCLUSIONS This analysis suggested that the Shilla technique was associated with a greater early coronal Cobb angle correction, whereas use of VEPTR was associated with a lower correction rate at any time point. TGR offered the most significant height gain at final follow-up. The complication rates were comparable across all surgical techniques. The optimal surgical approach should be tailored to individual patients, taking into consideration the strengths and limitations of each option.
Article
Full-text available
The objective of this study is to describe the general approaches to network meta-analysis that are available for quantitative data synthesis using R software. We conducted a network meta-analysis using two approaches: Bayesian and frequentist methods. The corresponding R packages were "gemtc" for the Bayesian approach and "netmeta" for the frequentist approach. In estimating a network meta-analysis model using a Bayesian framework, the "rjags" package is a common tool. "rjags" implements Markov chain Monte Carlo simulation with a graphical output. The estimated overall effect sizes, test for heterogeneity, moderator effects, and publication bias were reported using R software. The authors focus on two flexible models, Bayesian and frequentist, to determine overall effect sizes in network meta-analysis. This study focused on the practical methods of network meta-analysis rather than theoretical concepts, making the material easy to understand for Korean researchers who did not major in statistics. The authors hope that this study will help many Korean researchers to perform network meta-analyses and conduct related research more easily with R software.
Article
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We introduce the statistical concept known as likelihood and discuss how it underlies common Frequentist and Bayesian statistical methods. This article is suitable for researchers interested in understanding the basis of their statistical tools, and is also ideal for teachers to use in their classrooms to introduce the topic to students at a conceptual level.
Book
Cambridge Core - Statistics for Life Sciences, Medicine and Health - Foundations of Agnostic Statistics - by Peter M. Aronow
Article
Journals tend to publish only statistically significant evidence, creating a scientific record that markedly overstates the size of effects. We provide a new tool that corrects for this bias without requiring access to nonsignificant results. It capitalizes on the fact that the distribution of significant p values, p-curve, is a function of the true underlying effect. Researchers armed only with sample sizes and test results of the published findings can correct for publication bias. We validate the technique with simulations and by reanalyzing data from the Many-Labs Replication project. We demonstrate that p-curve can arrive at conclusions opposite that of existing tools by reanalyzing the meta-analysis of the “choice overload” literature.