Empirical Bayes models of Poisson clinical trials and sample size determination

Pharmaceutical Statistics

Volumn 9, Issue 2, 2010, Pages 133-141

  Zaslavsky, Boris G ^a  

^a CENTER FOR DRUG EVALUATION AND RESEARCH   (United States)

Author keywords

Gamma distribution; Maximum likelihood; Negative binomial distribution; Poisson distribution; WinBUGS

Indexed keywords

ARTICLE; BAYES THEOREM; BINOMIAL DISTRIBUTION; MONTE CARLO METHOD; POISSON DISTRIBUTION; SAMPLE SIZE; CLINICAL TRIAL (TOPIC); CONFIDENCE INTERVAL; HUMAN; MARKOV CHAIN; STATISTICAL MODEL; STATISTICS AND NUMERICAL DATA;

BAYES THEOREM; CLINICAL TRIALS AS TOPIC; CONFIDENCE INTERVALS; HUMANS; LIKELIHOOD FUNCTIONS; MARKOV CHAINS; MODELS, STATISTICAL; MONTE CARLO METHOD; SAMPLE SIZE;

EID: 77954629685     PISSN: 15391604     EISSN: 15391612     Source Type: Journal    
DOI: 10.1002/pst.383     Document Type: Article

References (21)

1. Carlin BP, Louis TA. Bayes and empirical Bayes methods for data analysis. Chapman & Hall/CRC: Boca Raton, London, New York, Washington, DC, 2000.
2. Lehmann EL, Casella G. Theory of point estimation. Springer: New York, Berlin, Heildelberg, 1998.
3. Maritz JS. Empirical bayes estimation for the Poisson distribution. Biometrika 1969; 56:349-359.
4. Wessa P. Free statistics software, Office for Research Development and Education, version 1.1.21. Available at: http://www.wessa.net/.
5. Demidenko E. Mixed models theory and application. Wiley: New Jersey, 2004.
6. SAS/STAT User's Guide, version 8. SAS Institute: Cary, NC, 1999.
7. GLIMMIX Procedure in SAS. Available at: http://support.sas.com/rnd/app/ da/glimmix.html.
8. GLMM procedure in S-PLUS. Available at: www.insightful.com/products/ splus/s7-features.asp.
9. Spiegelhalter D, Thomas A, Best N, Lunn D. WinBUGS User Manual. Available at: www.mrc-bsu.cam.ac.uk/bugs.
10. Sazama K. Reports of 355 transfusion-associated deaths: 1976 through 1985. Transfusion 1990; 30: 583-590.
11. High R. SAS program NLMIXED. Available at: http://www.uoregon.edu/ ~robinh/gnmd11-negbin.txt.
12. Grunkemeier GL, MacCulloch JD, Naftel DC. Sample size requiements for evaluaing heart valve with constant risk events. Journal of Heart Valve Disease 1994; 3:53-58.
13. Zacks S. Introduction to reliability analysis. Probability models and statistical analysis. Springer-Verlag: New York, 1992.
14. Bain LJ. Statistical analysis of reliability and life-testing models. Marcel Dekker: New York, 1978.
15. Dempster AP, Laird NM, Rubin DB. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B 1977; 39(1):1-38.
16. Wu CFJ. On the convergence properties of the em algorithm. The Annals of Statistics 1983; 11(1): 95-103.
17. Minka TP. Available at: http://research.microsoft.com/~minka/papers/ minka-gamma.pdf.
18. Hung HMJ, Wang SJ, Tsong Y et al. Some fundamental issues with non-inferiority testing in active controlled trials. Statistics in Medicine 2003; 22:213-225.
19. Handbook of Mathematical Functions, p. 253. Available at: http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP?Res5150&Page5253.
20. Zou KH, Resnic FS, Gogate AS et al. Efficient Bayesian sample size calculation for designing a clinical trial with multi-cluster outcome data. Biometrical Journal 2003; 45:826-836.
21. Gradshteyn IS, Ryzhik IM. Tables of integrals, series, and products. (6th edn). Academic Press: New York 2000.