Confidence distributions and a unifying framework for meta-analysis

Journal of the American Statistical Association

Volumn 106, Issue 493, 2011, Pages 320-333

  Xie, Minge ^a   Singh, Kesar ^a   Strawderman, William E ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Combination of p values; Fixed effects model; Random effects model; Robust methods

Indexed keywords

EID: 79954486112     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/jasa.2011.tm09803     Document Type: Article

References (37)

1. Dempster, A. P. (2008), "The Dempster-Shafer Calculus for Statisticians," International Journal of Approximate Reasoning, 48, 365-377. [321]
2. Efron, B. (1993), "Bayes and Likelihood Calculations From Confidence Intervals," Biometrika, 80, 3-26. [320,322,325,329,331]
3. Efron, B. (1996), "Empirical Bayes Methods for Combining Likelihoods," Journal of the American Statistical Association, 91, 538-550. [321,328,329]
4. Efron, B. (1998), "R. A. Fisher in the 21st Century," Statistical Science, 13, 95-122. [320,324,331]
5. Fisher, R. A. (1930), "Inverse Probability," Proceedings of the Cambridge Philosophical Society, 26, 528-535. [331]
6. Efron, B. (1932), Statistical Methods for Research Workers (4th ed.), Edinburgh, Scotland: Oliver & Boyd. [322]
7. Efron, B. (1973), Statistical Methods and Scientific Inference (3rd ed.), New York: Hafner Press. [320]
8. Fraser, D. A. S. (1991), "Statistical Inference: Likelihood to Significance," Journal of the American Statistical Association, 86, 258-265. [320,322, 323]
9. Hannig, J. (2009), "On Generalized Fiducial Inference," Statistica Sinica, 19, 491-544. [321]
10. Hedges, L. V., and Olkin, I. (1985), Statistical Methods for Meta-Analysis, New York: Academic Press. [320]
11. Hu, F., and Zidek, J. V. (2002), "The Weighted Likelihood," Canadian Journal of Statistics, 30, 347-371. [327]
12. Huber, P. J. (1964), "Robust Estimation of a Location Parameter," Annals of Mathematical Statistics, 35, 73-101. [326,332]
13. Lawless, F., and Fredette, M. (2005), "Frequentist Prediction Intervals and Predictive Distributions," Biometrika, 92 (3), 529-542. [320,331]
14. Lehmann, E. L. (1993), "The Fisher, Neyman-Pearson Theories of Testing Hypotheses: One Theory or Two?" Journal of the American Statistical Association, 88, 1242-1249. [331]
15. Lehmann, E. L. (1998), Elements of Large-Sample Theory, New York: SpringerVerlag. [331]
16. Littell, R. C., and Folks, J. L. (1973), "Asymptotic Optimality of Fisher's Method of Combining Independent Tests. II," Journal of the American Statistical Association, 68, 193-194. [322]
17. Marden, J. I. (1991), "Sensitive and Sturdy p-Values," The Annals of Statistics, 19, 918-934. [322,323]
18. Martin, R., Zhang, J., and Liu, C. (2010), "Dempster-Shafer Theory and Statistical Inference With Weak Beliefs," Statistical Science, 25, 72-87. [321]
19. Neyman, J. (1941), "Fiducial Argument and the Theory of Confidence Intervals," Biometrika, 32, 128-150. [331]
20. Normand S.-L. (1999), "Meta-Analysis: Formulating, Evaluating, Combining, and Reporting," Statistics in Medicine, 18, 321-359. [321-324,328,330]
21. Parzen, E. (2005), "All Statistical Methods, Parameter Confidence Quantiles," in Noether Award Lecture at the Joint Statistical Meeting, Minneapolis, MN, U.S.A., August 7-11, 2005. [320]
22. Preiss, R. W., Gayle, B. M., Burrell, N., Allen, M., and Bryant, J. (2006), Mass Media Effects Research: Advances Through Meta-Analysis, New York: Springer-Verlag. [320]
23. Schulze, R. (2004), Meta-Analysis: A Comparison of Approaches, Cambridge, MA: Hogrefe & Huber. [320]
24. Schweder, T. (2003), "Abundance Estimation From Multiple Photo Surveys: Confidence Distributions and Reduced Likelihoods for Bowhead Whales off Alaska," Biometrics, 59, 974-983. [320,331]
25. Schweder, T., and Hjort, N. L. (2002), "Confidence and Likelihood," Scandinavian Journal of Statistics, 29, 309-332. [320,330,331]
26. Schweder, T., and Hjort, N. L. (2003), "Frequentist Analogues of Priors and Posteriors," in Econometrics and the Philosophy of Economics, ed. B. P. Stigum, Princeton, NJ: Princeton University Press, pp. 285-317. [320]
27. Singh, K., Xie, M., and Strawderman, W. E. (2005), "Combining Information From Independent Sources Through Confidence Distributions," The Annals of Statistics, 33, 159-183. [320-322,324-326,330,331]
28. Singh, K., Xie, M., and Strawderman, W. E (2007), "Confidence Distribution (CD)-Distribution Estimator of a Parameter," in Complex Datasets and Inverse Problems. IMS Lecture Notes-Monograph Series, Vol. 54, eds. R. Liu et al., Beachwood, OH: Institute of Mathematical Statistics, pp. 132-150. [320,322,323,325,331,332]
29. Stangl, D. K., and Berry, D. A. (2000), Meta-Analysis in Medicine and Health Policy, New York: Springer-Verlag. [320]
30. Stouffer, S. A., Suchman, E. A., DeVinney, L. C., Star, S. A., and Williams, R. M., Jr. (1949), Adjustment During Army Life, Princeton, NJ: Princeton University Press. [322]
31. Sutton, A. J., and Higgins, J. P. T. (2008), "Recent Developments in Meta-Analysis," Statistics in Medicine, 27, 625-650. [320,323]
32. Sweeting, M. J., Sutton, A. J., and Lambert, P. C. (2004), "What to Add to Nothing? Use and Avoidance of Continuity Corrections in Meta-Analysis of Sparse Data," Statistics in Medicine, 23, 1351-1375. [329]
33. Tian, L., Wang, R., Cai, T., and Wei, L. J. (2010), "The Highest Confidence Density Region and Its Usage for Joint Inferences About Constrained Parameters," Biometrics, to appear. DOI: 10.1111/j.1541-0420.2010.01486.x. [320,331]
34. Wang, X., and Zidek, J. V. (2005), "Selecting Likelihood Weights by Cross-Validation," The Annals Statistics, 33, 463-501. [327]
35. Whitehead, A. (2002), Meta-Analysis of Controlled Clinical Trials, London: Wiley. [320]
36. Xie, M., Liu, R. Y., Damaraju, C. V., and Olson, W. H. (2009), "Incorporating Expert Opinions With Information From Binomial Clinical Trials," technical report, Rutgers University, Dept. of Statistics. [320,331]
37. Yang, G., and Xie, M. (2010), "Gmeta: Meta-Analysis via a Unified Frame-work Under Confidence Distribution," R package, available at http://stat.rutgers.edu/home/mxie/packages/gmetaRpackage/. [330]