A Simplification and Implementation of Random-effects Meta-analyses Based on the Exact Distribution of Cochran’s Q

Preuß, M.; Ziegler, Andreas

doi:10.3414/me13-01-0073

Cited by 8 publications

(10 citation statements)

References 21 publications

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“…Rhttp://www.r‐project.org/ Packages: bayesmeta , blme , boot , BRugs , Mad , mada , meta , gemtc , metafor , metagen , metaLik , metamisc , metaplus , metaSEM , metatest , metaxa , mvmeta , mvtmeta , netmeta ) R2WinBUGS , rjugs , rmeta …”

Section: Resultsmentioning

confidence: 99%

“…Alternative estimators could also be used, in principle, when using this method, provided that their distribution, and so the expected weights used by the method, can be evaluated. The variance of

{\overset{truê}{μ}}_{RE}^{BT}

is estimated as

italicvar ((), {\hat{μ}}_{italicRE}^{italicBT}) = \frac{1}{{((), \sum w_{i, italicRE}^{BT})}^{2}} \sum {(w_{i, italicRE}^{BT})}^{2} ((), v_{i} + {\overset{truê}{τ}}^{2}) .

Assuming normality, a 95% CI can be obtained as

{\overset{truê}{μ}}_{RE}^{BT} \pm z_{0.975} \sqrt{italicvar ((), {\hat{μ}}_{italicRE}^{italicBT})},

Biggerstaff and Tweedie use an approximate distribution to obtain the expected weights, but this has been improved upon by Preuß and Ziegler who used the exact weights through the exact cumulative distribution function of Q , where

Q = {Q_{gen}|}_{({\overset{τ}{true}}^{2} = 0)} .

Biggerstaff and Tweedie provided the algorithm to implement the method in SAS.…”

Section: Resultsmentioning

confidence: 99%

“…The same study showed that when publication bias is present and for k > 10, HC improved coverage compared with WTz, HKSJ, PL, and BT methods and showed less bias than the fixed‐effect model. Also, the WTz and BT methods have comparable coverage probabilities with coverage below the nominal level, but coverage is increased for the exact weights …”

Section: Resultsmentioning

confidence: 99%

“…30 The same study showed that when publication bias is present and for k > 10, HC improved coverage compared with WTz, HKSJ, PL, and BT methods and showed less bias than the fixed-effect model. Also, the WTz and BT methods have comparable coverage probabilities with coverage below the nominal level, 54,122 but coverage is increased for the exact weights. 54 3.2.5 | Resampling methods (methods 11, 12, 13, and 14) Zeng and Lin 146 showed that the ZL CI outperforms both WTz and PL CIs for small k in terms of coverage.…”

Section: Hc and Bt (Methods 9 And 10)mentioning

confidence: 97%

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Methods to calculate uncertainty in the estimated overall effect size from a random‐effects meta‐analysis

Veroniki

Jackson

Bender

et al. 2018

Research Synthesis Methods

154

210

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Meta-analyses are an important tool within systematic reviews to estimate the overall effect size and its confidence interval for an outcome of interest. If heterogeneity between the results of the relevant studies is anticipated, then a random-effects model is often preferred for analysis. In this model, a prediction interval for the true effect in a new study also provides additional useful information. However, the DerSimonian and Laird method-frequently used as the default method for meta-analyses with random effects-has been long challenged due to its unfavorable statistical properties. Several alternative methods have been proposed that may have better statistical properties in specific scenarios. In this paper, we aim to provide a comprehensive overview of available methods for calculating point estimates, confidence intervals, and prediction intervals for the overall effect size under the random-effects model. We indicate whether some methods are preferable than others by considering the results of comparative simulation and real-life data studies.

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Section: Resultsmentioning

confidence: 99%

{\overset{truê}{μ}}_{RE}^{BT}

is estimated as

italicvar ((), {\hat{μ}}_{italicRE}^{italicBT}) = \frac{1}{{((), \sum w_{i, italicRE}^{BT})}^{2}} \sum {(w_{i, italicRE}^{BT})}^{2} ((), v_{i} + {\overset{truê}{τ}}^{2}) .

Assuming normality, a 95% CI can be obtained as

{\overset{truê}{μ}}_{RE}^{BT} \pm z_{0.975} \sqrt{italicvar ((), {\hat{μ}}_{italicRE}^{italicBT})},

Q = {Q_{gen}|}_{({\overset{τ}{true}}^{2} = 0)} .

Biggerstaff and Tweedie provided the algorithm to implement the method in SAS.…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Hc and Bt (Methods 9 And 10)mentioning

confidence: 97%

See 2 more Smart Citations

Methods to calculate uncertainty in the estimated overall effect size from a random‐effects meta‐analysis

Veroniki

Jackson

Bender

et al. 2018

Research Synthesis Methods

154

210

View full text Add to dashboard Cite

show abstract

“…They mention limitations associated with assuming that the

σ_{i}^{2}

are well‐estimated and can be replaced by study‐specific estimates, but they adopt that ‘standard approach’ throughout. In another paper whose title includes ‘the exact distribution of Cochran's Q ', Preuss and Ziegler build on the ‘exact’ cumulative distribution function of Cochran's Q derived by Biggerstaff and Jackson and use partial integration to avoid evaluating that CDF numerically in order to obtain a confidence interval for the between‐study variance in random‐effects meta‐analysis. Preuss and Ziegler (page 56) say, ‘In these derivations, we have made the conventional assumption that the within study variances are known.…”

Section: The Null Distribution Of Qmentioning

confidence: 99%

Misunderstandings about Q and ‘Cochran's Q test' in meta‐analysis

Hoaglin

2015

Statistics in Medicine

233

146

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Many meta-analyses report using 'Cochran's Q test' to assess heterogeneity of effect-size estimates from the individual studies. Some authors cite work by W. G. Cochran, without realizing that Cochran deliberately did not use Q itself to test for heterogeneity. Further, when heterogeneity is absent, the actual null distribution of Q is not the chi-squared distribution assumed for 'Cochran's Q test'. This paper reviews work by Cochran related to Q. It then discusses derivations of the asymptotic approximation for the null distribution of Q, as well as work that has derived finite-sample moments and corresponding approximations for the cases of specific measures of effect size. Those results complicate implementation and interpretation of the popular heterogeneity index I(2) . Also, it turns out that the test-based confidence intervals used with I(2) are based on a fallacious approach. Software that outputs Q and I(2) should use the appropriate reference value of Q for the particular measure of effect size and the current meta-analysis. Q is a key element of the popular DerSimonian-Laird procedure for random-effects meta-analysis, but the assumptions of that procedure and related procedures do not reflect the actual behavior of Q and may introduce bias. The DerSimonian-Laird procedure should be regarded as unreliable.

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Drug Efficacy in the Treatment of Antipsychotic-Induced Akathisia

Gerolymos,

Barazer,

Yon

et al. 2024

JAMA Netw Open

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ImportanceAntipsychotic-induced akathisia (AIA) occurs in 14% to 35% of patients treated with antipsychotics and is associated with increased suicide and decreased adherence in patients with schizophrenia. However, no comprehensive review and network meta-analysis has been conducted to compare the efficacy of treatments for AIA.ObjectiveTo compare the efficacy associated with AIA treatments.Data SourcesThree databases (MEDLINE, Web of Science, and Google Scholar) were systematically searched by multiple researchers for double-blind randomized clinical trials (RCTs) comparing active drugs for the treatment of AIA with placebo or another treatment between May 30 and June 18, 2023.Study SelectionSelected studies were RCTs that compared adjunctive drugs for AIA vs placebo or adjunctive treatment in patients treated with antipsychotics fulfilling the criteria for akathisia, RCTs with sample size of 10 patients or more, only trials in which no additional drugs were administered during the study, and RCTs that used a validated akathisia score. Trials with missing data for the main outcome (akathisia score at the end points) were excluded.Data Extraction and SynthesisData extraction and synthesis were performed, estimating standardized mean differences (SMDs) through pairwise and network meta-analysis with a random-effects model. The Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guideline was followed.Main Outcomes and MeasuresThe primary outcome was the severity of akathisia measured by a validated scale at the last available end point.ResultsFifteen trials involving 492 participants compared 10 treatments with placebo. Mirtazapine (15 mg/d for ≥5 days; SMD, −1.20; 95% CI, −1.83 to −0.58), biperiden (6 mg/d for ≥14 days; SMD, −1.01; 95% CI, −1.69 to −0.34), vitamin B6 (600-1200 mg/d for ≥5 days; SMD, −0.92; 95% CI, −1.57 to −0.26), trazodone (50 mg/d for ≥5 days; SMD, −0.84; 95% CI, −1.54 to −0.14), mianserin (15 mg/d for ≥5 days; SMD, −0.81; 95% CI, −1.44 to −0.19), and propranolol (20 mg/d for ≥6 days; SMD, −0.78; 95% CI, −1.35 to −0.22) were associated with greater efficacy than placebo, with low to moderate heterogeneity (I2 = 34.6%; 95% CI, 0.0%-71.1%). Cyproheptadine, clonazepam, zolmitriptan, and valproate did not yield significant effects. Eight trials were rated as having low risk of bias; 2, moderate risk; and 5, high risk. Sensitivity analyses generally confirmed the results for all drugs except for cyproheptadine and propranolol. No association between effect sizes and psychotic severity was found.Conclusions and RelevanceIn this systematic review and network meta-analysis, mirtazapine, biperiden, and vitamin B6 were associated with the greatest efficacy for AIA, with vitamin B6 having the best efficacy and tolerance profile. Trazodone, mianserin, and propranolol appeared as effective alternatives with slightly less favorable efficacy and tolerance profiles. These findings should assist prescribers in selecting an appropriate medication for treating AIA.

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A Simplification and Implementation of Random-effects Meta-analyses Based on the Exact Distribution of Cochran’s Q

Cited by 8 publications

References 21 publications

Methods to calculate uncertainty in the estimated overall effect size from a random‐effects meta‐analysis

Methods to calculate uncertainty in the estimated overall effect size from a random‐effects meta‐analysis

Misunderstandings about Q and ‘Cochran's Q test' in meta‐analysis

Drug Efficacy in the Treatment of Antipsychotic-Induced Akathisia

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