Avoiding zero between-study variance estimates in random-effects meta-analysis

Statistics in Medicine

Volumn 32, Issue 23, 2013, Pages 4071-4089

  Chung, Yeojin ^a   Rabe Hesketh, Sophia ^b   Choi, In Hee ^b  

^a Kookmin University   (South Korea)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Bayesian posterior mode; Penalized maximum likelihood; Random effects meta analysis; Variance estimation

Indexed keywords

ANTICOAGULANT THERAPY; ARTICLE; BAYES THEOREM; CEREBROVASCULAR ACCIDENT; CONTROLLED STUDY; CORRELATION COEFFICIENT; DEPRESSION; EXERCISE; GENERALIZED LEAST SQUARES ESTIMATOR; INTERMETHOD COMPARISON; MARKOV CHAIN MONTE CARLO; META REGRESSION MODEL; RANDOM EFFECTS META ANALYSIS; REGRESSION ANALYSIS; SIMULATION; STANDARD DEVIATION; STATISTICAL ANALYSIS; STATISTICAL CONCEPTS; STATISTICAL DISTRIBUTION; UNWEIGHTED METHOD OF MOMENT ESTIMATOR; COMPUTER SIMULATION; HUMAN; META ANALYSIS (TOPIC); PSYCHOLOGY; STATISTICAL MODEL; STROKE;

ANTITHROMBOCYTIC AGENT; DIPYRIDAMOLE;

BAYES THEOREM; COMPUTER SIMULATION; DEPRESSION; DIPYRIDAMOLE; EXERCISE; HUMANS; LIKELIHOOD FUNCTIONS; META-ANALYSIS AS TOPIC; PLATELET AGGREGATION INHIBITORS; REGRESSION ANALYSIS; STROKE;

EID: 84884702463     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.5821     Document Type: Article

References (62)

1. DerSimonian R, Laird N. Meta-analysis in clinical trials. Controlled Clinical Trials 1986; 7(3):177-188.
2. National Research Council. Combining Information: Statistical Issues and Opportunities for Research. National Academic Press: Washington, DC, 1992.
3. Mosteller F, Colditz GA. Understanding research synthesis (meta-analysis). Annual Review of Public Health 1996; 17(1):1-23.
4. Higgins JPT, Thompson SG, Spiegelhalter DJ. A re-evaluation of random-effects meta-analysis. Journal of the Royal Statistical Society, Series A 2009; 172(1):137-159.
5. Borenstein M, Hedges L, Higgins J, Rothstein H. Introduction to Meta-analysis. Wiley: Chichester, 2009.
6. Thompson SG. Why sources of heterogeneity in meta-analysis should be investigated. British Medical Journal 1994; 309(6965):1351-1355.
7. Glasziou PP, Sanders SL. Investigating causes of heterogeneity in systematic reviews. Statistics in Medicine 2002; 21(11):1503-1511.
8. Raudenbush SW, Bryk AS. Empirical Bayes meta-analysis. Journal of Educational Statistics 1985; 10(2):75-98.
9. Hedges LV. Commentary. Statistics in Medicine 1987; 6(3):381-385.
10. Berkey CS, Hoaglin DC, Mosteller F, Colditz GA. A random-effects regression model for meta-analysis. Statistics in Medicine 1995; 14(4):395-411.
11. Brockwell SE, Gordon IR. A comparison of statistical methods for meta-analysis. Statistics in Medicine 2001; 20(6):825-840.
12. Sánchez-Meca J, Marín-Martínez F. Confidence intervals for the overall effect size in random-effects meta-analysis. Psychological Methods 2008; 13(1):31-48.
13. Draper D. Assessment and propagation of model uncertainty. Journal of the Royal Statistical Society, Series B 1995; 57(1):45-97.
14. Engels EA, Schmid CH, Terrin N, Olkin I, Lau J. Heterogeneity and statistical significance in meta-analysis: an empirical study of 125 meta-analyses. Statistics in Medicine 2000; 19(13):1707-1728.
15. Curcio D, Verde P. Comment on: Efficacy and safety of tigecycline: A systematic review and meta-analysis. Journal of Antimicrobial Chemotherapy 2011; 66(12):2893-2895.
16. Hardy R, Thompson S. Detecting and describing heterogeneity in meta-analysis. Statistics in Medicine 1998; 17(8):841-856.
17. Overton R. A comparison of fixed-effects and mixed (random-effects) models for meta-analysis tests of moderator variable effects. Psychological Methods 1998; 3(3):354.
18. Viechtbauer W. Bias and efficiency of meta-analytic variance estimators in the random-effects model. Journal of Educational and Behavioral Statistics 2005; 30(3):261-293.
19. Higgins JPT, Whitehead A. Borrowing strength from external trials in meta-analysis. Statistics in Medicine 1996; 15(24):2733-2749.
20. Longford NT. On estimating standard errors in multilevel analysis. Journal of the Royal Statistical Society, Series D 2000; 49(3):389-398.
21. Chung Y, Rabe-Hesketh S, Dorie V, Gelman A, Liu J. A non-degenerate penalized likelihood estimator for variance parameters in multilevel models. Psychometrika 2013: In press, DOI: 10.1007/s11336-013-9328-2.
22. Lawlor D, Hopker S. The effectiveness of exercise as an intervention in the management of depression: Systematic review and meta-regression analysis of randomised controlled trials. British Medical Journal 2001; 322: 1-8.
23. Higgins J, Thompson S. Controlling the risk of spurious findings from meta-regression. Statistics in Medicine 2004; 23(11):1663-1682.
24. Patterson HD, Thompson R. Recovery of inter-block information when block sizes are unequal. Biometrika 1971; 58(3):545-554.
25. Kontopantelis E, Reeves D. metaan: Random-effects meta-analysis. The Stata Journal 2010; 10(3):395-407.
26. Harbord R, Higgins JPT. Meta-regression in Stata. The Stata Journal 2008; 8(4):493-519.
27. Antithrombotic Trialists' Collaboration. Collaborative meta-analysis of randomised trials of antiplatelet therapy for prevention of death, myocardial infarction, and stroke in high risk patients. BMJ 2002; 324(7329):71-86.
28. Hedges LV. A random effects model for effect sizes. Psychological Bulletin 1983; 93(2):388-395.
29. Rao C. Linear Statistical Inference and Its Applications, (Second Edition), Wiley: New York, 1973.
30. Demidenko E. Mixed Models: Theory and Applications. Wiley: Hoboken, NJ, 2004.
31. Morris C. Parametric empirical Bayes inference-theory and applications. Journal of the American Statistical Association 1983; 78(381):47-55.
32. Viechtbauer W. Conducting meta-analyses in R with the metafor package. Journal of Statistical Software 2010; 36(10):1-48.
33. Hardy R, Thompson SG. A likelihood approach to meta-analysis with random effects. Statistics in Medicine 1996; 15(6):619-629.
34. Efron B, Hinkley D. Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information. Biometrika 1978; 65(3):457-483.
35. Fisher R. Theory of statistical estimation. Mathematical Proceedings of the Cambridge Philosophical Society 1925; 22(5):700-725.
36. Pawitan Y. In All Likelihood: Statistical Modelling and Inference Using Likelihood. Oxford University Press: Oxford, 2001.
37. Lambert P, Sutton A, Burton P, Abrams K, Jones D. How vague is vague? a simulation study of the impact of the use of vague prior distributions in mcmc using winbugs. Statistics in Medicine 2005; 24(15):2401-2428.
38. Pauler DK, Wakefield JC. Modeling and implementation issues in Bayesian meta-analysis. In Meta-Analysis in Medicine and Health Policy. Stangl DK, Berry DA (eds), Marcel Dekker, Inc: New York, 2000.
39. Abrams K, Sanso B. Approximate Bayesian inference for random effects meta-analysis. Statistics in Medicine 1998; 17(2):201-218.
40. Higgins J, Whitehead A. Borrowing strength from external trials in a meta-analysis. Statistics in Medicine 1996; 15(24):2733-2749.
41. Sutton A, Abrams K. Bayesian methods in meta-analysis and evidence synthesis. Statistical Methods in Medical Research 2001; 10(4):277-303.
42. Spiegelhalter D, Abrams K, Myles J. Bayesian Approaches to Clinical Trials and Health-Care Evaluation. Wiley: New York, 2004.
43. Galindo-Garre F, Vermunt J, Bergsma W. Bayesian posterior mode estimation of logit parameters with small samples. Sociological Methods & Research 2004; 33(1):88-117.
44. Maris E. Estimating multiple classification latent class models. Psychometrika 1999; 64(2):187-212.
45. Galindo-Garre F, Vermunt J. Avoiding boundary estimates in latent class analysis by Bayesian posterior mode estimation. Behaviormetrika 2006; 33(1):43-59.
46. Swaminathan H, Gifford JA. Bayesian estimation in the two-parameter logistic model. Psychometrika 1985; 50(3):349-364.
47. Mislevy RJ. Bayes modal estimation in item response models. Psychometrika 1986; 51(2):177-195.
48. Tsutakawa RK, Lin HY. Bayesian estimation of item response curves. Psychometrika 1986; 51(2):251-267.
49. Berger J. The case for objective Bayesian analysis. Bayesian Analysis 2006; 1(3):385-402.
50. Fay RE, Herriot RA. Estimates of income for small places: An application of James-Stein procedures to census data. Journal of the American Statistical Association 1979; 74(366):269-277.
51. Morris C. Mixed model prediction and small area estimation (with discussions). Test 2006; 15(1):72-76.
52. Li H, Lahiri P. An adjusted maximum likelihood method for solving small area estimation problems. Journal of Multivariate Analysis 2010; 101(4):882-892.
53. Morris C, Tang R. Estimating random effects via adjustment for density maximization. Statistical Science 2011; 26(2):271-287.
54. Rabe-Hesketh S, Skrondal A, Pickles A. Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects. Journal of Econometrics 2005; 128(2):301-323.
55. Rabe-Hesketh S, Skrondal A. Multilevel and Longitudinal Modeling Using Stata, (Third Edition), Stata Press: College Station, 2012.
56. Higgins JPT, Thompson SG. Quantifying heterogeneity in a meta-analysis. Statistics in Medicine 2002; 21(11):1539-1558.
57. Lunn DJ, Thomas A, Best N, Spiegelhalter D. WinBUGS - a Bayesian modelling framework: concepts, structure, and extensibility. Statistics and Computing. 2000; 10:325-337.
58. Lunn D, Jackson C, Best N, Thomas A, Spiegelhalter D. The Bugs Book. Chapman & Hall/CRC Press: Boca Raton, FL, 2012.
59. Crainiceanu C, Ruppert D. Likelihood ratio tests in linear mixed models with one variance component. Journal of the Royal Statistical Society, Series B 2004; 66(1):165-185.
60. Sidik K, Jonkman JN. A comparison of heterogeneity variance estimators in combining results of studies. Statistics in Medicine 2007; 26(9):1964-1981.
61. Sánchez-Meca J, Marín-Martínez F. Confidence intervals for the overall effect size in random-effects meta-analysis. Psychological Methods 2008; 13(1):31-48.
62. Hartung J, Knapp G. On tests of the overall treatment effect in meta-analysis with normally distributed responses. Statistics in Medicine 2001; 20(12):1771-1782.