The power prior: Theory and applications

Statistics in Medicine

Volumn 34, Issue 28, 2015, Pages 3724-3749

  Ibrahim, Joseph G ^a   Chen, Ming Hui ^b   Gwon, Yeongjin ^b   Chen, Fang ^c  

^a IL   (United States)

^b UNIVERSITY OF CONNECTICUT   (United States)

^c SAS INSTITUTE INC   (United States)

Author keywords

Bayesian design; Borrowing; Clinical trials; Discounting; Historical data; Informative prior

Indexed keywords

ARTICLE; BAYES THEOREM; LINEAR SYSTEM; LOGISTIC REGRESSION ANALYSIS; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MONTE CARLO METHOD; POWER PRIOR; SAMPLE SIZE; STATISTICAL ANALYSIS; STATISTICAL DISTRIBUTION; STATISTICAL MODEL; THEORY; VARIANCE; CLINICAL TRIAL (TOPIC); EPIDEMIOLOGY; METHODOLOGY; PROCEDURES; STATISTICS; STATISTICS AND NUMERICAL DATA;

BAYES THEOREM; CLINICAL TRIALS AS TOPIC; HISTORICALLY CONTROLLED STUDY; LINEAR MODELS; MODELS, STATISTICAL; RESEARCH DESIGN; STATISTICS AS TOPIC;

EID: 84961217468     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.6728     Document Type: Article

References (69)

1. Ibrahim JG, Chen MH. Power prior distributions for regression models. Statistical Science 2000; 15:46-60.
2. Berry DA. Bayesian methods in phase III trials. Drug Information Journal 1991; 25:345-368.
3. Eddy DM, Hasselblad V, Schachter R. Meta-analysis by the Confidence Profile Method: The Statistical Synthesis of Evidence. Academic Press: New York, 1992.
4. Berry DA, Hardwick J. Using historical controls in clinical trials: application to ECMO. Statistical Decision Theory and Related Topics 1993; 5:141-156.
5. Lin Z.. Statistical methods for combining historical controls with clinical trials data. Unpublished Doctorial Dissertation, Duke University, 1993.
6. Spiegelhalter DJ, Freedman LS, Parmar MKB. Bayesian approaches to randomised trials (with discussion). Journal of Royal Statistical Society, Series A 1994; 157:357-416.
7. Berry DA, Stangl DK. Bayesian Biostatistics. Marcel Dekker: New York, 1996.
8. Chen MH, Manatunga AK, Williams CJ. Heritability estimates from human twin data by incorporating historical prior information. Biometrics 1998; 54:1348-1362.
9. Ibrahim JG, Chen MH. Prior distributions and Bayesian computation for proportional hazards models. Sankhya, Series B 1998; 60:48-64.
10. Ibrahim JG, Ryan LM, Chen MH. Use of historical controls to adjust for covariates in trend tests for binary data. Journal of the American Statistical Association 1998; 93:1282-1293.
11. Chen MH, Ibrahim JG, Sinha D.. A new Bayesian model for survival data with a surviving fraction. Journal of the American Statistical Association 1999; 94:909-919.
12. Chen MH, Ibrahim JG, Yiannoutsos C.. Prior elicitation, variable selection and Bayesian computation for logistic regression models. Journal of the Royal Statistical Society, Series B 1999; 61:223-242.
13. Ibrahim JG, Chen MH, MacEachern SN. Bayesian variable selection for proportional hazards models. Canadian Journal of Statistics 1999; 27:701-717.
14. Chen MH, Ibrahim JG, Shao QM. Power prior distributions for generalized linear models. Journal of Statistical Planning and Inference 2000; 84:121-137.
15. Ibrahim JG, Chen MH, Sinha D. On optimality properties of the power prior. Journal of the American Statistical Association 2003; 98:204-213.
16. Chen MH, Ibrahim JG. The relationship between the power prior and hierarchical models. Bayesian Analysis 2006; 1:551-574.
17. De Santis F. Using historical data for Bayesian sample size determination. Journal of the Royal Statistical Society, Series A 2007; 170:95-113.
18. De Santis F. Power priors and their use in clinical trials. American Statistical Association 2006; 60:122-129.
19. Duan Y, Ye K, Smith EP. Evaluating water quality using power priors to incorporate historical information. Environmetrics 2006; 17:95-106.
20. Neelon B, O'Malley AJ, Margolis PA. Bayesian analysis using historical data with application to pediatric quality of care. ASA Proceedings of the Bayesian Statistical Sciences Section: Denver, CO, 2008; 2960-2967.
21. Chen MH, Ibrahim JG, Lam P, Yu A, Zhang Y. Bayesian design of non-inferiority trials for medical devices using historical data. Biometrics 2011; 67:1163-1170.
22. Hobbs BP, Carlin BP, Mandrekar SJ, Sargent DJ. Hierarchical commensurate and power prior models for adaptive incorporation of historical information in clinical trials. Biometrics 2011; 67:1047-1056.
23. Hobbs BP, Sargent DJ, Carlin BP. Commensurate priors for incorporating historical information in clinical trials using general and generalized linear models. Bayesian Analysis 2012; 7:639-674.
24. Ibrahim JG, Chen MH, Xia A, Liu T. Bayesian meta-experimental design: evaluating cardiovascular risk in new antidiabetic therapies to treat type 2 diabetes. Biometrics 2012; 68:578-586.
25. Spiegelhalter DJ, Abrams KR, Myles JP. Bayesian Approaches to Clinical Trials and Health-care Evaluation: Chichester, 2004.
26. Berry SM, Carlin PR, Lee JJ, Müller P. Bayesian Adaptive Methods for Clinical Trials. John Wiley & Sons: Boca Raton, 2012.
27. Zellner A. Optimal information processing and Bayes's theorem (with discussion). The American Statistician 1988; 42:278-284.
28. Zellner A. Information processing and Bayesian analysis. Journal of Econometrics 2002; 107:41-50.
29. Chen MH, Harrington DP, Ibrahim JG. Bayesian cure rate models for malignant melanoma: a case study of Eastern Cooperative Oncology Group Trial E1690. Applied Statistics 2002; 51:135-150.
30. Duan Y. A modified Bayesian power prior with applications in water quality evaluation. Unpublished Doctoral Dissertation, Virginia Polytechnic Institute and State University, 2005.
31. Chen MH, Ibrahim JG, Shao QM, Weiss RE. Prior elicitation for model selection and estimation in generalized linear mixed models. Journal of Statistical Planning and Inference 2003; 111:57-76.
32. Chen MH, Dey DK, Shao QM. Bayesian analysis of binary data using skewed logit models. Calcutta Statistical Association Bulletin 2001; 51:11-30.
33. Chen MH, Dey DK. A unified Bayesian analysis for correlated ordinal data models. Brazilian Journal of Probability and Statistics 2000; 14:87-111.
34. Chen MH. Bayesian analysis of correlated mixed categorical data by incorporating historical prior information. The Special Issue of Communications in Statistics: Theory and Methods 1998; 27:1341-1361.
35. Chen MH, Dey DK. Bayesian modeling of correlated binary responses via scale mixture of multivariate normal link functions. Sankhyā, Series A 1998; 60:322-343.
36. Chen MH, Dey DK. Variable selection for multivariate logistic regression models. Journal of Statistical Planning and Inference 2003; 111:37-55.
37. Shao K. Bayesian model averaging for toxicity study design and benchmark dose estimation. Unpublished Doctorial Dissertation, Carnegie Mellon University, 2011.
38. Chen MH, Ibrahim JG, Xia HA, Liu T, Henessey V. Bayesian sequential meta-analysis design in evaluating cardiovascular risk in a new antidiabetic drug development program. Statistics in Medicine 2014; 33:1600-1618.
39. Chen MH, Ibrahim JG, Zeng D, Hu K, Jia C. Bayesian design of superiority clinical trials for recurrent events data with applications to bleeding and transfusion events in myelodyplastic syndrome. Biometrics 2014; 70:1003-1013.
40. Ibrahim JG, Chen MH, Ryan LM. Bayesian variable selection for time series count data. Statistica Sinica 2000; 10:971-987.
41. Chen MH, Shao QM. Monte Carlo methods on Bayesian analysis of constrained parameter problems. Biometrika 1998; 85:73-87.
42. Liang F.. A double metropolis-hastings sampler for spatial models with intractable normalizing constants. Journal of Statistical Computation and Simulation 2010; 80:1007-1022.
43. A Monte Carlo . Metropolis-hastings algorithm for sampling from distributions with intractable normalizing constants. Neural computation 2013; 25:2199-2234.
44. Liang F, Jin IH, Song Q, Liu JS. An adaptive exchange algorithm for sampling from distributions with intractable normalizing constants. Journal of the American Statistical Association 2015. DOI: 10.1080/01621459.2015.1009072
45. Duan Y, Smith EP, Ye K. Using power priors to improve the binomial test of water quality. Journal of Agricultural, Biological, and Environmental Statistics 2006; 11:151-168.
46. Charlotte R, Irene K, Kristel JMJ, Krel GMM, Herbert JAH. Incorporation of historical data in the analysis of randomized therapeutic trials. Contemporary Clinical Trials 2011; 32:848-855.
47. Gamalo MA, Tiwari RC, LaVange LM. Bayesian approach to the design and analysis of non-inferiority trials for anti-infective products. Pharmaceutical Statistics 2014; 13:25-40.
48. Zellner A. Bayesian Analysis in Econometrics and Statistics. Edward Elgar: Cheltenham, 1997.
49. Chen CF. On asymptotic normality of limiting density functions with Bayesian implications. Journal of the Royal Statistical Society, Series B 1985; 97:540-546.
50. Ibrahim JG, Laud PW(1994). A predictive approach to the analysis of designed experiments. Journal of the American Statistical Association 1994; 89:309-319.
51. Laud PW, Ibrahim JG. Predictive model selection. Journal of the Royal Statistical Society, Series B 1995; 57:247-262.
52. Bedrick EJ, Christensen R, Johnson W. A new perspective on priors for generalized linear models. Journal of the American Statistical Association 1996; 91:1450-1460.
53. Chen MH, Ibrahim JG. Conjugate priors for generalized linear models. Statistica Sinica 2003; 13:461-476.
54. Ibrahim JG. On properties of predictive priors in linear models. The American Statistician 1997; 51:333-337.
55. Laud PW, Ibrahim JG. Predictive specification of prior model probabilities in variable selection. Biometrika 1996; 83:267-274.
56. Jang H, Lee S, Kim SW. Bayesian analysis for zero-inflated regression models with the power prior: application to road safety countermeasures. Accident Analysis and Prevention 2010; 42:540-547.
57. Matteucci M, Veldkamp BP. The approach of power priors for ability estimation in IRT models. Quality & Quantity 2015; 49:917-926.
58. Neelon B, O'Malley AJ. Bayesian analysis using power priors with application to pediatric quality of care. Journal of Biometrics and Biostatistics 2010; 1:103, available at http://dx.doi.org/10.4172/2155-6180.1000103.
59. Zhang H. Bayesian Power Prior Analysis and Its Application to Operational Risk and Rasch Model. The University of Texas at San Antonio: Unpublished Doctoral Dissertation, 2010.
60. Spiegelhalter DJ, Best NG, Carlin BP, Linde AVD. Bayesian measures of model complexity and fit. Journal of Royal Statistical Society, Series B 2002; 64:583-639.
61. Geisser S. Predictive Inference: An Introduction. Chapman Hall: New York, 1993.
62. Gelfand AE, Dey DK, Chang H. Model determinating using predictive distributions with implementation via sampling-based methods (with discussion). Bayesian Statistics 1992; 4:147-167.
63. Ibrahim JG, Chen MH, Sinha D.. Bayesian semi-parametric models for survival data with a cure fraction. Biometrics 2001; 57:383-388.
64. Shao K. A Comparison of three methods for integrating historical information for Bayesian model averaged benchmark dose estimation. Environmental Toxicology and Pharmacology 2012; 34:288-296.
65. Ibrahim JG, Chen MH, Chu H. Bayesian methods in clinical trials: a Bayesian analysis of ECOG trials E1684 and E1690. BMC Medical Methodology 2012; 12:1-12.
66. Kirkwood JM, Strawderman MH, Ernstoff MS, Smith TJ, Borden EC, Blum RH. Interferon alfa-2b adjuvant therapy of high-risk resected cutaneous melanoma: the Eastern Cooperative Oncology Group Trial EST 1684. Journal of Clinical Oncology 1996; 14:7-17.
67. Kirkwood JM, Ibrahim JG, Sondak VK, Richards J, Flaherty LE, Ernstoff MS, Smith TJ, Rao U, Steele M, Blum RH. The role of high- and low-dose interferon alfa-2b in high-risk melanoma: first analysis of intergroup trial E1690/S9111/C9190. Journal of Clinical Oncology 2000; 18:2444-2458.
68. Stone GW, Ellis SG, Cannon L, Mann JT, Greenberg JD, O'Shaughnessy CD, DeMaio S, Hall P, Popma JJ, Koglin J, Russell, ME for the TAXUS V Investigators . Comparison of a polymer-based paclitaxel-eluting stent with a bare metal stent in patients with complex coronary artery disease: a randomized controlled trial. Journal of the American Medical Association 2005; 294:1215-1223.
69. Stone GW, Ellis SG, Cox DA, Hermiller J, O'Shaughnessy CD, Mann JT, Turco M, Caputo R, Bergin P, Greenberg JD, Popma JJ, Russell MEfortheTAXUS-IVInvestigators. A polymer-based, paclitaxel-eluting stent in patients with coronary artery disease. The New England Journal of Medicine 2004; 350:221-231.