Bayesian Meta-Analysis with Weakly Informative Prior Distributions

doi: 10.5005/jp/books/10519 Hardy, R. J., & Thompson, S. G. (1998). Detecting and describing heterogeneity in meta-analysis. Statistics in Medicine, 17 (8), 841–856. doi: 10.1002/(SICI)1097-0258(19980430)17:8<841:: AID-SIM781>3.0.CO;2-D Harrell, F. E., & Shih, Y. C. T. (2001). Using full probability models to compute probabilities of actual interest to decision makers. International journal of technology assessment in health care, 17 (1), 17–26. doi: 10.1017/S0266462301104034 Harris, A. L., & Robinson, K. (2007). Schooling Behaviors or Prior Skills ? , 80, 139–157. Heck, D. W., Gronau, Q. F., & Wagenmakers, E.-J. (2017). metaBMA: Bayesian Model Averaging for Random and Fixed Effects Meta-Analysis. Retrieved from https://cran.r -project.org/package=metaBMA Hedges, L. V., & Vevea, J. L. (1998). Fixedand random-effects models in meta-analysis. Psychological Methods, 3(4), 486–504. Retrieved from http://personal.psc .isr.umich.edu/yuxie-web/files/pubs/ Articles/Hedges_Vevea1998.pdfhttp:// doi.apa.org/getdoi.cfm?doi=10.1037/ 1082-989X.3.4.486 doi: 10.1037/1082-989X.3.4.486 Higgins, J., & Spiegelhalter, D. (2002). Being sceptical about metaanalyses: a Bayesian perspective on magnesium trials in myocardial infarction. International journal of epidemiology, 31(1), 96–104. doi: 10.1093/ije/31.1.96 Higgins, J., & Thompson, S. (2002). Quantifying heterogeneity in meta analysis. Statistics in Medicine, 21(11), 1539–1558. Retrieved from http://onlinelibrary .wiley.com/doi/10.1002/sim.1186/full Hoffman, M., & Gelman, A. (2014). The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research, 15(1), 30. Hoijtink, H., van Kooten, P., & Hulsker, K. (2016). Bayes Factors Have Frequency Properties—This Should Not Be Ignored: A Rejoinder to Morey, Wagenmakers, and Rouder. Multivariate Behavioral Research, 51(1), 20–22. Retrieved from http://dx.doi.org/10.1080/00273171 .2015.1071705 doi: 10.1080/00273171.2015.1071705 Hunter, J. E., & Schmidt, F. L. (2000). Fixed Effects vs. Random Effects Meta-Analysis Models: Implications for Cumulative Research Knowledge. International Journal of Selection and Assessment, 8(4), 275–292. Retrieved from https://www.biz.uiowa.edu/ faculty/fschmidt/meta-analysis/ Hunter_Schmidt_2000_rev.pdfhttp:// doi.wiley.com/10.1111/1468-2389.00156 doi: 10.1111/1468-2389.00156 Hunter, J. E., & Schmidt, F. L. (2004). Methods of Meta-Analysis: Correcting Error and Bias in Research Findings. Thousand Oaks: SAGE Publications. Kenny, D. A., & Judd, C. M. (2017). The Unappreciated Heterogeneity of Effect Sizes: Implications for Power, Precision, Planning of Research, and Replication. Retrieved from http://davidakenny.net/doc/KJ17R.pdf Klein, R. A., Ratliff, K. A., Vianello, M., Adams, R. B., Bahník, �., Bernstein, M. J., ... Nosek, B. A. (2014). Investigating variation in replicability: A ”many labs” replication project. Social Psychology, 45(3), 142–152. doi: 10.1027/1864-9335/ a000178 Kolenikov, S., & Bollen, K. A. (2012). Testing Negative Error Variances: Is a Heywood Case a Symptom of Misspecification? (Vol. 40) (No. 1). doi: 10.1177/0049124112442138 Kruschke, J. K. (2013). Bayesian estimation supersedes the t test. Journal of Experimental Psychology: General, 142(2), 573–603. Retrieved from http://doi.apa.org/ getdoi.cfm?doi=10.1037/a0029146 doi: 10 .1037/a0029146 Kullback, S., & Leibler, R. A. (1951). On information and sufficiency. The Annals of Mathematical Statistics. Retrieved from http://www.jstor.org/ stable/10.2307/2236703%5Cnpapers2:// publication/uuid/A65B3271-44DC-42DC

[1]  D. A. Kenny,et al.  The unappreciated heterogeneity of effect sizes: Implications for power, precision, planning of research, and replication. , 2019, Psychological methods.

[2]  B. Schmeichel,et al.  Ego Depletion Reduces Attention Control: Evidence From Two High-Powered Preregistered Experiments , 2018, Personality & social psychology bulletin.

[3]  Julian P T Higgins,et al.  A re‐evaluation of fixed effect(s) meta‐analysis , 2018 .

[4]  Gang Chen,et al.  Handling Multiplicity in Neuroimaging Through Bayesian Lenses with Multilevel Modeling , 2017, Neuroinformatics.

[5]  Donald R. Williams,et al.  Intranasal Oxytocin May Improve High-Level Social Cognition in Schizophrenia, But Not Social Cognition or Neurocognition in General: A Multilevel Bayesian Meta-analysis , 2017, Schizophrenia bulletin.

[6]  Sander Greenland,et al.  Invited Commentary: The Need for Cognitive Science in Methodology , 2017, American journal of epidemiology.

[7]  Donald R. Williams,et al.  Bayes Factors From Pooled Data Are No Substitute for Bayesian Meta-Analysis: Commentary on Scheibehenne, Jamil, and Wagenmakers (2016) , 2017, Psychological science.

[8]  Eric-Jan Wagenmakers,et al.  UvA-DARE ( Digital Academic Repository ) Estimates of Between-Study Heterogeneity for 705 Meta-Analyses Reported in Psychological Bulletin From 1990 – 2013 , 2017 .

[9]  Sarah Depaoli,et al.  Improving Transparency and Replication in Bayesian Statistics: The WAMBS-Checklist , 2017, Psychological methods.

[10]  Annamaria Guolo,et al.  Random-effects meta-analysis: the number of studies matters , 2017, Statistical methods in medical research.

[11]  R. V. Aert,et al.  Bayesian evaluation of effect size after replicating an original study , 2017 .

[12]  James T. Thorson,et al.  Faster estimation of Bayesian models in ecology using Hamiltonian Monte Carlo , 2017 .

[13]  Donald R. Williams,et al.  Effects of intranasal oxytocin on symptoms of schizophrenia: A multivariate Bayesian meta-analysis , 2017, Psychoneuroendocrinology.

[14]  Michael Betancourt,et al.  A Conceptual Introduction to Hamiltonian Monte Carlo , 2017, 1701.02434.

[15]  Tim Friede,et al.  Meta‐analysis of few small studies in orphan diseases , 2016, Research synthesis methods.

[16]  Sander Greenland,et al.  Remove, rather than redefine, statistical significance , 2017, Nature Human Behaviour.

[17]  A. Gelman,et al.  The prior can generally only be understood in the context of the likelihood , 2017 .

[18]  David J. Spiegelhalter,et al.  Implementing informative priors for heterogeneity in meta‐analysis using meta‐regression and pseudo data , 2016, Statistics in medicine.

[19]  Daniel McNeish,et al.  On Using Bayesian Methods to Address Small Sample Problems , 2016 .

[20]  Eric-Jan Wagenmakers,et al.  Bayesian Evidence Synthesis Can Reconcile Seemingly Inconsistent Results , 2016, Psychological science.

[21]  Bayes Factors Have Frequency Properties—This Should Not Be Ignored: A Rejoinder to Morey, Wagenmakers, and Rouder , 2016, Multivariate behavioral research.

[22]  Richard McElreath,et al.  Statistical Rethinking: A Bayesian Course with Examples in R and Stan , 2015 .

[23]  Sarah Depaoli,et al.  A Bayesian Approach to Multilevel Structural Equation Modeling With Continuous and Dichotomous Outcomes , 2015 .

[24]  Rebecca M. Turner,et al.  Predictive distributions were developed for the extent of heterogeneity in meta-analyses of continuous outcome data , 2015, Journal of clinical epidemiology.

[25]  J. Carlin,et al.  Beyond Power Calculations , 2014, Perspectives on psychological science : a journal of the Association for Psychological Science.

[26]  Yichuan Zhang,et al.  Semi-Separable Hamiltonian Monte Carlo for Inference in Bayesian Hierarchical Models , 2014, NIPS.

[27]  Reginald B. Adams,et al.  Investigating Variation in Replicability: A “Many Labs” Replication Project , 2014 .

[28]  Sander Greenland,et al.  Maximum likelihood, profile likelihood, and penalized likelihood: a primer. , 2014, American journal of epidemiology.

[29]  Andrew Gelman,et al.  The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo , 2011, J. Mach. Learn. Res..

[30]  D. Bates,et al.  fitting linear mixed effects models using lme 4 arxiv , 2014 .

[31]  Sophia Rabe-Hesketh,et al.  Avoiding zero between‐study variance estimates in random‐effects meta‐analysis , 2013, Statistics in medicine.

[32]  J. Kruschke Bayesian estimation supersedes the t test. , 2013, Journal of experimental psychology. General.

[33]  Sander Greenland,et al.  Living with P Values: Resurrecting a Bayesian Perspective on Frequentist Statistics , 2013, Epidemiology.

[34]  Simon G Thompson,et al.  Predicting the extent of heterogeneity in meta-analysis, using empirical data from the Cochrane Database of Systematic Reviews , 2012, International journal of epidemiology.

[35]  Eleanor M Pullenayegum,et al.  An informed reference prior for between‐study heterogeneity in meta‐analyses of binary outcomes , 2011, Statistics in medicine.

[36]  James G. Scott,et al.  On the half-cauchy prior for a global scale parameter , 2011, 1104.4937.

[37]  A. Gelman Bayesian Statistical Pragmatism , 2011, 1106.3220.

[38]  A B Haidich,et al.  Meta-analysis in medical research. , 2010, Hippokratia.

[39]  Wolfgang Viechtbauer,et al.  Conducting Meta-Analyses in R with the metafor Package , 2010 .

[40]  Tihomir Asparouhov,et al.  Bayesian Analysis of Latent Variable Models using Mplus , 2010 .

[41]  Andrea M Hussong,et al.  Integrative data analysis: the simultaneous analysis of multiple data sets. , 2009, Psychological methods.

[42]  In-Sue Oh,et al.  Fixed- versus random-effects models in meta-analysis: model properties and an empirical comparison of differences in results. , 2009, The British journal of mathematical and statistical psychology.

[43]  Stephen W. Raudenbush,et al.  Analyzing effect sizes: Random-effects models. , 2009 .

[44]  Andrew Gelman,et al.  Why We (Usually) Don't Have to Worry About Multiple Comparisons , 2009, 0907.2478.

[45]  M. G. Pittau,et al.  A weakly informative default prior distribution for logistic and other regression models , 2008, 0901.4011.

[46]  G. Casella,et al.  The Bayesian Lasso , 2008 .

[47]  F. Schmidt Meta-Analysis , 2008 .

[48]  Christian P. Robert,et al.  The Bayesian choice : from decision-theoretic foundations to computational implementation , 2007 .

[49]  Kurex Sidik,et al.  A comparison of heterogeneity variance estimators in combining results of studies , 2007, Statistics in medicine.

[50]  D. V. Dyk,et al.  Transformed and parameter-expanded Gibbs samplers for multilevel linear and generalized linear models , 2007 .

[51]  Donald B. Rubin,et al.  Validation of Software for Bayesian Models Using Posterior Quantiles , 2006 .

[52]  Michael Goldstein,et al.  Subjective Bayesian Analysis: Principles and Practice , 2006 .

[53]  J. Berger The case for objective Bayesian analysis , 2006 .

[54]  J. A. Boer,et al.  Evidence-based guidelines for the pharmacological treatment of anxiety disorders: recommendations from the British Association for Psychopharmacology , 2005, Journal of psychopharmacology.

[55]  David R. Jones,et al.  How vague is vague? A simulation study of the impact of the use of vague prior distributions in MCMC using WinBUGS , 2005, Statistics in medicine.

[56]  Kurex Sidik,et al.  Simple heterogeneity variance estimation for meta‐analysis , 2005 .

[57]  A. Gelman Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) , 2004 .

[58]  J. Berger Could Fisher, Jeffreys and Neyman Have Agreed on Testing? , 2003 .

[59]  S. Thompson,et al.  Quantifying heterogeneity in a meta‐analysis , 2002, Statistics in medicine.

[60]  David J Spiegelhalter,et al.  Being sceptical about meta-analyses: a Bayesian perspective on magnesium trials in myocardial infarction. , 2002, International journal of epidemiology.

[61]  Sarah E. Brockwell,et al.  A comparison of statistical methods for meta‐analysis , 2001, Statistics in medicine.

[62]  F. Harrell,et al.  USING FULL PROBABILITY MODELS TO COMPUTE PROBABILITIES OF ACTUAL INTEREST TO DECISION MAKERS , 2001, International Journal of Technology Assessment in Health Care.

[63]  K R Abrams,et al.  Bayesian methods in meta-analysis and evidence synthesis. , 2001, Statistical methods in medical research.

[64]  John E. Hunter,et al.  Fixed Effects vs. Random Effects Meta‐Analysis Models: Implications for Cumulative Research Knowledge , 2000 .

[65]  Sigrún Andradóttir,et al.  Applying Bayesian ideas in simulation , 2000, Simul. Pract. Theory.

[66]  Francis Tuerlinckx,et al.  Type S error rates for classical and Bayesian single and multiple comparison procedures , 2000, Comput. Stat..

[67]  R. Overton,et al.  A comparison of fixed-effects and mixed (random-effects) models for meta-analysis tests of moderator , 1998 .

[68]  S. Thompson,et al.  Detecting and describing heterogeneity in meta-analysis. , 1998, Statistics in medicine.

[69]  A. van Knippenberg,et al.  The relation between perception and behavior, or how to win a game of trivial pursuit. , 1998, Journal of personality and social psychology.

[70]  Jack L. Vevea,et al.  Fixed- and random-effects models in meta-analysis. , 1998 .

[71]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[72]  H. Jones Introduction to Meta-Analysis , 2010 .

[73]  Charles E. McCulloch Fixed and Random Effects and Best Prediction , 1994 .

[74]  Frank L. Schmidt,et al.  What do data really mean? Research findings, meta-analysis, and cumulative knowledge in psychology. , 1992 .

[75]  J. Berger Statistical Decision Theory and Bayesian Analysis , 1988 .

[76]  N. Laird,et al.  Meta-analysis in clinical trials. , 1986, Controlled clinical trials.

[77]  D. Rubin Bayesianly Justifiable and Relevant Frequency Calculations for the Applied Statistician , 1984 .

[78]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[79]  B. McShane Abandon Statistical Significance Forthcoming in The American Statistician , 2022 .