Index: Viechtbauer 2010 - Conducting Meta-Analyses in R with the metafor Package

Viechtbauer 2010 - Conducting Meta-Analyses in R with the metafor Package

Routing Summary

This folder fully captures Viechtbauer (2010), Conducting Meta-Analyses in R with the metafor Package (J. Stat. Softw. 36(3)): fixed, random and mixed-effects meta-analysis models, ${\tau }^2$ estimators, the Q-test, $I^2$/$H^2$, meta-regression, Knapp-Hartung, likelihood-ratio and permutation tests, diagnostics, funnel/forest/radial/Q-Q plots, trim and fill, cumulative meta-analysis, BLUPs and the 13-study BCG vaccine example. It also gives formal statements of DerSimonian-Laird (1986) and Higgins-Thompson (2002). 10 notes.

• Need the paper on one page, headline BCG numbers, or the section-to-note map? → Viechtbauer 2010 - Conducting Meta-Analyses in R with the metafor Package - Overview
• Need the model equations (random, mixed, fixed targets) and the conditional versus unconditional inference distinction? → Viechtbauer 2010 - Fixed, Random and Mixed-Effects Models
• Need DerSimonian-Laird, Cochran’s Q, I-squared, H-squared, the seven ${\tau }^2$ estimators, truncation and Fisher scoring? → Viechtbauer 2010 - tau2 Estimators, Q-Test and Heterogeneity Statistics
• Need effect-size formulas (RR, OR, RD, SMD, Fisher z, logit…) and zero-cell handling? → Viechtbauer 2010 - Effect Size Measures and escalc
• Need rma() syntax, moderators, omnibus test, categorical coding, Knapp-Hartung? → Viechtbauer 2010 - Fitting Models with rma, Moderators and Knapp-Hartung
• Need the full BCG analysis with tables and a Python reproduction? → Viechtbauer 2010 - BCG Vaccine Worked Example
• Need residuals, Cook’s distance, leave-one-out, forest/funnel/radial/Q-Q plots, or Table 1 (API map)? → Viechtbauer 2010 - Residuals, Influence Diagnostics and Plots
• Need publication-bias tests, trim and fill, or cumulative meta-analysis? → Viechtbauer 2010 - Publication Bias, Trim-and-Fill and Cumulative Meta-Analysis
• Need LRT, permutation tests, BLUP shrinkage or fit statistics? → Viechtbauer 2010 - LRT, Permutation Tests, BLUPs and Model Fit
• Need assumptions and caveats, validation, the package comparison (Table 2), Mantel-Haenszel/Peto, or the reference map? → Viechtbauer 2010 - Technical Details, Validation and Package Comparison

Concept Map

Concept	Note	Type	Depends On	Key Result
Observed-effect model $y_i={\theta }_i+e_i$	Viechtbauer 2010 - Fixed, Random and Mixed-Effects Models	definition	Hierarchical Models	known $v_i$, normal errors
Random- and mixed-effects models	Viechtbauer 2010 - Fixed, Random and Mixed-Effects Models	definition	observed-effect model	${\theta }_i=\mu +u_i$ / meta-regression
Fixed vs random inference	Viechtbauer 2010 - Fixed, Random and Mixed-Effects Models	theorem	models	FE is conditional, not homogeneity
Cochran’s Q	Viechtbauer 2010 - tau2 Estimators, Q-Test and Heterogeneity Statistics	definition	FE weights	$Q\sim {\chi }_{k-1}^2$ under ${\tau }^2=0$
DerSimonian-Laird estimator	Viechtbauer 2010 - tau2 Estimators, Q-Test and Heterogeneity Statistics	theorem	Q	$(Q-(k-1))/(\sum w-\sum w^2/\sum w)$
$H^2$, $I^2$	Viechtbauer 2010 - tau2 Estimators, Q-Test and Heterogeneity Statistics	definition	${\tau }^2$	BCG 92.22%, 12.86
Outcome measures	Viechtbauer 2010 - Effect Size Measures and escalc	concept	none	RR, OR, RD, SMD, ZCOR, PLO…
rma.uni, omnibus test	Viechtbauer 2010 - Fitting Models with rma, Moderators and Knapp-Hartung	definition	models	$Q_M$, btt
Knapp-Hartung	Viechtbauer 2010 - Fitting Models with rma, Moderators and Knapp-Hartung	definition	rma.uni	$s^2(X^{\top }WX{)}^{-1}$, $t_{k-p}$
BCG example	Viechtbauer 2010 - BCG Vaccine Worked Example	example	all above	RR 0.49; latitude explains 65-88%
Residuals, influence	Viechtbauer 2010 - Residuals, Influence Diagnostics and Plots	concept	BCG	studies 7, 13 outliers; 4 influential
Asymmetry tests, trim and fill	Viechtbauer 2010 - Publication Bias, Trim-and-Fill and Cumulative Meta-Analysis	definition	funnel plot	4 missing studies; effect stays significant
Cumulative meta-analysis	Viechtbauer 2010 - Publication Bias, Trim-and-Fill and Cumulative Meta-Analysis	definition	RE model	drift reflects latitude
LRT for moderators	Viechtbauer 2010 - LRT, Permutation Tests, BLUPs and Model Fit	theorem	ML fits	LRT 9.96, $p=0.0016$
Permutation test	Viechtbauer 2010 - LRT, Permutation Tests, BLUPs and Model Fit	definition	Wald tests	$p=0.0015$ exact (RE)
BLUP shrinkage	Viechtbauer 2010 - LRT, Permutation Tests, BLUPs and Model Fit	definition	RE model	${\lambda }_i{y}_i+(1-{\lambda }_i)\hat{\mu }$
Model assumptions	Viechtbauer 2010 - Technical Details, Validation and Package Comparison	theorem	all	known $v_i$, plug-in ${\tau }^2$, normality, independence

Notes

• Viechtbauer 2010 - Conducting Meta-Analyses in R with the metafor Package - Overview — CONTAINS: research question, contribution, headline BCG numbers, full Source Map (all sections, Tables 1-2, Figures 1-11 → notes).
• Viechtbauer 2010 - Fixed, Random and Mixed-Effects Models — CONTAINS: Eq. (1)-(5); definitions of the three models; theorem on conditional vs unconditional inference; BCG interpretation.
• Viechtbauer 2010 - tau2 Estimators, Q-Test and Heterogeneity Statistics — CONTAINS: estimator table (HS, HE, DL, SJ, ML, REML, EB); Cochran’s Q; DL theorem with proof of $E[Q]$; Higgins-Thompson $H^2$, $I^2$; Fisher scoring and truncation; BCG check; Python.
• Viechtbauer 2010 - Effect Size Measures and escalc — CONTAINS: all escalc measures with formulas, zero-cell options, formula interface, trial-1 hand computation.
• Viechtbauer 2010 - Fitting Models with rma, Moderators and Knapp-Hartung — CONTAINS: rma.uni signature, moderator specification, omnibus test, categorical coding, Knapp-Hartung definition and verified example, Python meta-regression.
• Viechtbauer 2010 - BCG Vaccine Worked Example — CONTAINS: 13-study data table, RE and mixed model outputs, predictions by latitude, categorical moderator, KH, Type I simulation, Python reproduction.
• Viechtbauer 2010 - Residuals, Influence Diagnostics and Plots — CONTAINS: Table 1 (function map), standardized residuals, influence measures, leave-one-out table, forest/funnel/radial/Q-Q plots.
• Viechtbauer 2010 - Publication Bias, Trim-and-Fill and Cumulative Meta-Analysis — CONTAINS: rank/regression asymmetry tests, trim and fill, cumulative forest plot, copas pointer, BCG results.
• Viechtbauer 2010 - LRT, Permutation Tests, BLUPs and Model Fit — CONTAINS: fit statistics, LRT theorem and BCG example, permutation test definition and results, BLUP definition and values, exact sign-permutation Python.
• Viechtbauer 2010 - Technical Details, Validation and Package Comparison — CONTAINS: introduction context, four assumptions, validation, Table 2 comparison, Mantel-Haenszel/Peto, reference map.

Sources

• Viechtbauer W (2010). Conducting Meta-Analyses in R with the metafor Package. Journal of Statistical Software 36(3), 1-48. PDF: Viechtbauer 2010 - Conducting Meta-Analyses in R with the metafor Package

See Also

• Roever 2020 - Bayesian Random-Effects Meta-Analysis with bayesmeta - Overview, IntHout 2014 - HKSJ vs DerSimonian-Laird Random-Effects Meta-Analysis - Overview
• Hierarchical Models, Partial Pooling as Multiple Comparisons Correction