Research Article
Sample size calculation for comparing two negative binomial rates
Abstract
Negative binomial model has been increasingly used to model the count data in recent clinical trials. It is frequently chosen over Poisson model in cases of overdispersed count data that are commonly seen in clinical trials. One of the challenges of applying negative binomial model in clinical trial design is the sample size estimation. In practice, simulation methods have been frequently used for sample size estimation. In this paper, an explicit formula is developed to calculate sample size based on the negative binomial model. Depending on different approaches to estimate the variance under null hypothesis, three variations of the sample size formula are proposed and discussed. Important characteristics of the formula include its accuracy and its ability to explicitly incorporate dispersion parameter and exposure time. The performance of the formula with each variation is assessed using simulations. Copyright © 2013 John Wiley & Sons, Ltd.
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Number of times cited according to CrossRef: 30
- Xiaohong Li, Nigel G. F. Cooper, Timothy E. O’Toole, Eric C. Rouchka, Choice of library size normalization and statistical methods for differential gene expression analysis in balanced two-group comparisons for RNA-seq studies, BMC Genomics, 10.1186/s12864-020-6502-7, 21, 1, (2020).
- Darryn Knobel, Christianah Ibironke Odita, Anne Conan, Donna Barry, Marshalette Smith-Anthony, Juliet Battice, Shianne England, Bradford D. Gessner, Non-specific effects of rabies vaccine on the incidence of common infectious disease episodes: study protocol for a randomized controlled trial, Trials, 10.1186/s13063-020-04467-z, 21, 1, (2020).
- Alemu Takele Assefa, Jo Vandesompele, Olivier Thas, On the utility of RNA sample pooling to optimize cost and statistical power in RNA sequencing experiments, BMC Genomics, 10.1186/s12864-020-6721-y, 21, 1, (2020).
- Gosuke Homma, Takashi Daimon, Sample Size Calculation for “Gold-Standard” Noninferiority Trials With Fixed Margins and Negative Binomial Endpoints, Statistics in Biopharmaceutical Research, 10.1080/19466315.2020.1766551, (1-13), (2020).
- Yongqiang Tang, Liang Zhu, Jiezhun Gu, An Improved Sample Size Calculation Method for Score Tests in Generalized Linear Models, Statistics in Biopharmaceutical Research, 10.1080/19466315.2020.1756398, (1-10), (2020).
- Piotr Ponikowski, Bridget‐Anne Kirwan, Stefan D. Anker, Maria Dorobantu, Jarosław Drozdz, Vincent Fabien, Gerasimos Filippatos, Teba Haboubi, Andre Keren, Irakli Khintibidze, Hans Kragten, Felipe A. Martinez, Theresa McDonagh, Marco Metra, Davor Milicic, José C. Nicolau, Marcus Ohlsson, Alexander Parhomenko, Domingo A. Pascual‐Figal, Frank Ruschitzka, David Sim, Hadi Skouri, Peter Meer, Ewa A. Jankowska, Rationale and design of the AFFIRM‐AHF trial: a randomised, double‐blind, placebo‐controlled trial comparing the effect of intravenous ferric carboxymaltose on hospitalisations and mortality in iron‐deficient patients admitted for acute heart failure, European Journal of Heart Failure, 10.1002/ejhf.1710, 21, 12, (1651-1658), (2019).
- Deeann Allison, Erica DeFrain, Brianna D. Hitt, David C. Tyler, Academic library as learning space and as collection: A learning commons' effects on collections and related resources and services, The Journal of Academic Librarianship, 10.1016/j.acalib.2019.04.004, 45, 3, (305-314), (2019).
- Xiaohong Li, Dongfeng Wu, Nigel G.F. Cooper, Shesh N. Rai, Sample size calculations for the differential expression analysis of RNA-seq data using a negative binomial regression model, Statistical Applications in Genetics and Molecular Biology, 10.1515/sagmb-2018-0021, 18, 1, (2019).
- Nina Stefanac, Sarah Hetrick, Carol Hulbert, Matthew J. Spittal, Katrina Witt, Jo Robinson, Are young female suicides increasing? A comparison of sex-specific rates and characteristics of youth suicides in Australia over 2004–2014, BMC Public Health, 10.1186/s12889-019-7742-9, 19, 1, (2019).
- Dateng Li, Song Zhang, Jing Cao, Sample size calculation for clinical trials with correlated count measurements based on the negative binomial distribution, Statistics in Medicine, 10.1002/sim.8378, 38, 28, (5413-5427), (2019).
- Dateng Li, Jing Cao, Considering Over-Dispersion in the Sample Size Calculation for Clinical Trials With Repeated Count Measurements, Statistics in Biopharmaceutical Research, 10.1080/19466315.2019.1575277, (1-20), (2019).
- Chien‐Wei Lin, Serena G. Liao, Peng Liu, Mei‐Ling Ting Lee, Yong Seok Park, George C. Tseng, RNASeqDesign: a framework for ribonucleic acid sequencing genomewide power calculation and study design issues, Journal of the Royal Statistical Society: Series C (Applied Statistics), 10.1111/rssc.12330, 68, 3, (683-704), (2018).
- Thomas Asendorf, Robin Henderson, Heinz Schmidli, Tim Friede, Sample size re‐estimation for clinical trials with longitudinal negative binomial counts including time trends, Statistics in Medicine, 10.1002/sim.8061, 38, 9, (1503-1528), (2018).
- Gosuke Homma, Takashi Daimon, A simple test for the treatment effect in clinical trials with a sequential parallel comparison design and negative binomial outcomes, Pharmaceutical Statistics, 10.1002/pst.1913, 18, 2, (184-197), (2018).
- Lin Wang, Chunpeng Fan, Sample size calculations for comparing two groups of count data, Journal of Biopharmaceutical Statistics, 10.1080/10543406.2018.1489409, 29, 1, (115-127), (2018).
- Nobuya Hayashi, Yohji Itoh, A Re-examination of Japanese Sample Size Calculation for Multi-regional Clinical Trial Evaluating Survival Endpoint, Japanese Journal of Biometrics, 10.5691/jjb.38.79, 38, 2, (79-92), (2018).
- Masataka Igeta, Kunihiko Takahashi, Shigeyuki Matsui, Power and sample size calculation incorporating misspecifications of the variance function in comparative clinical trials with over‐dispersed count data, Biometrics, 10.1111/biom.12878, 74, 4, (1459-1467), (2018).
- David Machin, Michael J. Campbell, Say Beng Tan, Sze Huey Tan, Cumulative References, Sample Sizes for Clinical, Laboratory and Epidemiology Studies, 10.1002/9781118874905, (363-380), (2018).
- David Machin, Michael J. Campbell, Say Beng Tan, Sze Huey Tan, Rate Outcomes, Sample Sizes for Clinical, Laboratory and Epidemiology Studies, 10.1002/9781118874905, (83-98), (2018).
- Lindsay E Young, Phil Schumm, Leigh Alon, Alida Bouris, Matthew Ferreira, Brandon Hill, Aditya S Khanna, Thomas W Valente, John A Schneider, PrEP Chicago : A randomized controlled peer change agent intervention to promote the adoption of pre-exposure prophylaxis for HIV prevention among young Black men who have sex with men , Clinical Trials, 10.1177/1740774517730012, 15, 1, (44-52), (2017).
- Yongqiang Tang, Sample size for comparing negative binomial rates in noninferiority and equivalence trials with unequal follow-up times, Journal of Biopharmaceutical Statistics, 10.1080/10543406.2017.1333998, 28, 3, (475-491), (2017).
- Evan M. Lowder, Sarah L. Desmarais, Candalyn B. Rade, Tim Coffey, Richard A. Van Dorn, Models of Protection Against Recidivism in Justice-Involved Adults With Mental Illnesses, Criminal Justice and Behavior, 10.1177/0093854817710966, 44, 7, (893-911), (2017).
- Yu-Wei Chang, Yi Tsong, Zhigen Zhao, Sample size determination for a three-arm equivalence trial of Poisson and negative binomial responses, Journal of Biopharmaceutical Statistics, 10.1080/10543406.2016.1269787, 27, 2, (239-256), (2016).
- Haiyuan Zhu, Sample Size Calculation for Comparing Two Poisson or Negative Binomial Rates in Noninferiority or Equivalence Trials, Statistics in Biopharmaceutical Research, 10.1080/19466315.2016.1225594, 9, 1, (107-115), (2016).
- Megan Johanson, Ann M. Arthur, Improving the Language Skills of Pre-kindergarten Students: Preliminary Impacts of the Let’s Know! Experimental Curriculum, Child & Youth Care Forum, 10.1007/s10566-015-9332-z, 45, 3, (367-392), (2015).
- Bonnie Cundill, Neal DE Alexander, Sample size calculations for skewed distributions, BMC Medical Research Methodology, 10.1186/s12874-015-0023-0, 15, 1, (2015).
- Haiyuan Zhu, Xiao Wu, Confidence interval estimation for number of patient‐years needed to treat, Pharmaceutical Statistics, 10.1002/pst.1650, 13, 6, (403-409), (2014).
- Haiyuan Zhu, Hassan Lakkis, Authors' reply to comments on ‘Sample size calculation for comparing two negative binomial rates’, Statistics in Medicine, 10.1002/sim.6186, 33, 16, (2880-2880), (2014).
- H. Zhu, H. Lakkis, Comments on ‘Sample size calculation for comparing two negative binomial rates’, Statistics in Medicine, 10.1002/sim.6119, 33, 11, (1979-1979), (2014).
- Dateng Li, Song Zhang, Jing Cao, Incorporating pragmatic features into power analysis for cluster randomized trials with a count outcome, Statistics in Medicine, 10.1002/sim.8707, 0, 0, (undefined).
