Evaluating water quality using power priors to incorporate historical information
Abstract
To assess water quality standards, measurements of water quality under the Clean Water Act are collected on a regular basis over a period of time. The data are analyzed to evaluate the percentage of samples exceeding the standard. One problem is that current data are limited by the time range and consequently the sample size is inadequate to provide necessary precision in parameter estimation. To address this issue, we present a Bayesian approach using a power prior to incorporate historical data and/or the data collected at adjacent stations. We develop a modified power prior approach and discuss its properties under the normal mean model. Several sets of water quality data are studied to illustrate the implementation of the power prior approach and its differences from alternative methods. Copyright © 2005 John Wiley & Sons, Ltd.
Citing Literature
Number of times cited according to CrossRef: 39
- Nusrat Harun, Chunyan Liu, Mi‐Ok Kim, Critical appraisal of Bayesian dynamic borrowing from an imperfectly commensurate historical control, Pharmaceutical Statistics, 10.1002/pst.2018, 19, 5, (613-625), (2020).
- Yimei Li, Ying Yuan, PA‐CRM: A continuous reassessment method for pediatric phase I oncology trials with concurrent adult trials, Biometrics, 10.1111/biom.13217, 0, 0, (2020).
- Annette Kopp‐Schneider, Silvia Calderazzo, Manuel Wiesenfarth, Power gains by using external information in clinical trials are typically not possible when requiring strict type I error control, Biometrical Journal, 10.1002/bimj.201800395, 62, 2, (361-374), (2019).
- Hui Quan, Bingzhi Zhang, Yu Lan, Xiaodong Luo, Xun Chen, Bayesian hypothesis testing with frequentist characteristics in clinical trials, Contemporary Clinical Trials, 10.1016/j.cct.2019.105858, 87, (105858), (2019).
- Naoki Isogawa, Kentaro Takeda, Kazushi Maruo, Takashi Daimon, A Comparison Between a Meta-analytic Approach and Power Prior Approach to Using Historical Control Information in Clinical Trials With Binary Endpoints, Therapeutic Innovation & Regulatory Science, 10.1177/2168479019862531, (216847901986253), (2019).
- Chenguang Wang, Heng Li, Wei-Chen Chen, Nelson Lu, Ram Tiwari, Yunling Xu, Lilly Q. Yue, Propensity score-integrated power prior approach for incorporating real-world evidence in single-arm clinical studies, Journal of Biopharmaceutical Statistics, 10.1080/10543406.2019.1657133, (1-18), (2019).
- Jing Zhang, Chia-Wen Ko, Lei Nie, Yong Chen, Ram Tiwari, Bayesian hierarchical methods for meta-analysis combining randomized-controlled and single-arm studies, Statistical Methods in Medical Research, 10.1177/0962280218754928, 28, 5, (1293-1310), (2018).
- Matthew A Psioda, Joseph G Ibrahim, Bayesian clinical trial design using historical data that inform the treatment effect, Biostatistics, 10.1093/biostatistics/kxy009, 20, 3, (400-415), (2018).
- Akalu Banbeta, Joost Rosmalen, David Dejardin, Emmanuel Lesaffre, Modified power prior with multiple historical trials for binary endpoints, Statistics in Medicine, 10.1002/sim.8019, 38, 7, (1147-1169), (2018).
- Junjing Lin, Margaret Gamalo‐Siebers, Ram Tiwari, Propensity‐score‐based priors for Bayesian augmented control design, Pharmaceutical Statistics, 10.1002/pst.1918, 18, 2, (223-238), (2018).
- Isaac Gravestock, Leonhard Held, Power priors based on multiple historical studies for binary outcomes, Biometrical Journal, 10.1002/bimj.201700246, 61, 5, (1201-1218), (2018).
- Matthew A. Psioda, Mat Soukup, Joseph G. Ibrahim, A practical Bayesian adaptive design incorporating data from historical controls, Statistics in Medicine, 10.1002/sim.7897, 37, 27, (4054-4070), (2018).
- Philip S Boonstra, Ryan P Barbaro, Incorporating historical models with adaptive Bayesian updates, Biostatistics, 10.1093/biostatistics/kxy053, (2018).
- Stavros Nikolakopoulos, Ingeborg Tweel, Kit C. B. Roes, Dynamic borrowing through empirical power priors that control type I error, Biometrics, 10.1111/biom.12835, 74, 3, (874-880), (2017).
- David Dejardin, Paul Delmar, Charles Warne, Katie Patel, Joost van Rosmalen, Emmanuel Lesaffre, Use of a historical control group in a noninferiority trial assessing a new antibacterial treatment: A case study and discussion of practical implementation aspects, Pharmaceutical Statistics, 10.1002/pst.1843, 17, 2, (169-181), (2017).
- Isaac Gravestock, Leonhard Held, Adaptive power priors with empirical Bayes for clinical trials, Pharmaceutical Statistics, 10.1002/pst.1814, 16, 5, (349-360), (2017).
- Margaret Gamalo‐Siebers, Jasmina Savic, Cynthia Basu, Xin Zhao, Mathangi Gopalakrishnan, Aijun Gao, Guochen Song, Simin Baygani, Laura Thompson, H. Amy Xia, Karen Price, Ram Tiwari, Bradley P. Carlin, Statistical modeling for Bayesian extrapolation of adult clinical trial information in pediatric drug evaluation, Pharmaceutical Statistics, 10.1002/pst.1807, 16, 4, (232-249), (2017).
- Connie Chen, Matthew O. Gribble, Jay Bartroff, Steven M. Bay, Larry Goldstein, The Sequential Probability Ratio Test: An efficient alternative to exact binomial testing for Clean Water Act 303(d) evaluation, Journal of Environmental Management, 10.1016/j.jenvman.2017.01.039, 192, (89-93), (2017).
- Teng Zhang, Ilya Lipkovich, Olga Marchenko, Bridging data across studies using frequentist and Bayesian estimation, Journal of Biopharmaceutical Statistics, 10.1080/10543406.2017.1289948, 27, 3, (426-441), (2017).
- Ivan Lorencin, MiloS Pantos, Evaluating Generating Unit Unavailability Using Bayesian Power Priors, IEEE Transactions on Power Systems, 10.1109/TPWRS.2016.2603469, 32, 3, (2315-2323), (2017).
- Joost van Rosmalen, David Dejardin, Yvette van Norden, Bob Löwenberg, Emmanuel Lesaffre, Including historical data in the analysis of clinical trials: Is it worth the effort?, Statistical Methods in Medical Research, 10.1177/0962280217694506, (096228021769450), (2017).
- Robin A Huff, Jeff D Maca, Mala Puri, Earl W Seltzer, Enhancing pediatric clinical trial feasibility through the use of Bayesian statistics, Pediatric Research, 10.1038/pr.2017.163, (2017).
- Leonhard Held, Rafael Sauter, Adaptive prior weighting in generalized regression, Biometrics, 10.1111/biom.12541, 73, 1, (242-251), (2016).
- Ben Li, Yunxiao Li, Zhaohui S. Qin, Improving Hierarchical Models Using Historical Data with Applications in High-Throughput Genomics Data Analysis, Statistics in Biosciences, 10.1007/s12561-016-9156-x, 9, 1, (73-90), (2016).
- Paul Faya, John W. Seaman, James D. Stamey, Bayesian assurance and sample size determination in the process validation life-cycle, Journal of Biopharmaceutical Statistics, 10.1080/10543406.2016.1148717, 27, 1, (159-174), (2016).
- Beat Neuenschwander, Satrajit Roychoudhury, Heinz Schmidli, On the Use of Co-Data in Clinical Trials, Statistics in Biopharmaceutical Research, 10.1080/19466315.2016.1174149, 8, 3, (345-354), (2016).
- Ian Wadsworth, Lisa V Hampson, Thomas Jaki, Extrapolation of efficacy and other data to support the development of new medicines for children: A systematic review of methods, Statistical Methods in Medical Research, 10.1177/0962280216631359, (096228021663135), (2016).
- Junjing Lin, Margaret Gamalo‐Siebers, Ram Tiwari, Non‐inferiority and networks: inferring efficacy from a web of data, Pharmaceutical Statistics, 10.1002/pst.1729, 15, 1, (54-67), (2015).
- Joseph G. Ibrahim, Ming‐Hui Chen, Yeongjin Gwon, Fang Chen, The power prior: theory and applications, Statistics in Medicine, 10.1002/sim.6728, 34, 28, (3724-3749), (2015).
- Andrew P. Grieve, How to test hypotheses if you must, Pharmaceutical Statistics, 10.1002/pst.1667, 14, 2, (139-150), (2015).
- Kentaro Takeda, Mari Oba, Tomoyuki Kakizume, Kentaro Sakamaki, Masataka Taguri, Satoshi Morita, Bayesian Approach to Utilize Historical Control Data in Clinical Trials, Japanese Journal of Biometrics, 10.5691/jjb.36.25, 36, 1, (25-50), (2015).
- Charlotte Rietbergen, Rolf H. H. Groenwold, Herbert J. A. Hoijtink, Karl G. M. Moons, Irene Klugkist, Expert Elicitation of Study Weights for Bayesian Analysis and Meta-Analysis, Journal of Mixed Methods Research, 10.1177/1558689814553850, 10, 2, (168-181), (2014).
- Yu Jiang, Steve Simon, Matthew S. Mayo, Byron J. Gajewski, Modeling and validating Bayesian accrual models on clinical data and simulations using adaptive priors, Statistics in Medicine, 10.1002/sim.6359, 34, 4, (613-629), (2014).
- Kert Viele, Scott Berry, Beat Neuenschwander, Billy Amzal, Fang Chen, Nathan Enas, Brian Hobbs, Joseph G. Ibrahim, Nelson Kinnersley, Stacy Lindborg, Sandrine Micallef, Satrajit Roychoudhury, Laura Thompson, Use of historical control data for assessing treatment effects in clinical trials, Pharmaceutical Statistics, 10.1002/pst.1589, 13, 1, (41-54), (2013).
- Charlotte Rietbergen, Irene Klugkist, Kristel J.M. Janssen, Karel G.M. Moons, Herbert J.A. Hoijtink, Incorporation of historical data in the analysis of randomized therapeutic trials, Contemporary Clinical Trials, 10.1016/j.cct.2011.06.002, 32, 6, (848-855), (2011).
- Brian P. Hobbs, Bradley P. Carlin, Sumithra J. Mandrekar, Daniel J. Sargent, Hierarchical Commensurate and Power Prior Models for Adaptive Incorporation of Historical Information in Clinical Trials, Biometrics, 10.1111/j.1541-0420.2011.01564.x, 67, 3, (1047-1056), (2011).
- Ming‐Hui Chen, Joseph G. Ibrahim, Peter Lam, Alan Yu, Yuanye Zhang, Bayesian Design of Noninferiority Trials for Medical Devices Using Historical Data, Biometrics, 10.1111/j.1541-0420.2011.01561.x, 67, 3, (1163-1170), (2011).
- Beat Neuenschwander, Michael Branson, David J. Spiegelhalter, A note on the power prior, Statistics in Medicine, 10.1002/sim.3722, 28, 28, (3562-3566), (2009).
- Yuyan Duan, Eric P. Smith, Keying Ye, Using power priors to improve the binomial test of water quality, Journal of Agricultural, Biological, and Environmental Statistics, 10.1198/108571106X110919, 11, 2, (151-168), (2006).




