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.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
It is valid to apply analytical methods for the power analysis of negative binomial regression models.
“Hence, it is valid to apply analytical methods for the power analysis of negative binomial regression models64.”
From scPower accelerates and optimizes the design of multi-sample single cell transcriptomic studies (2021) · cites this paper as [64]
Cites
Negative Binomial Regression: Index
Hilbe, J. (2007) · Cambridge University Press eBooks · doi:10.1017/cbo9780511973420 · Cited by 3,253 · see citing works
Salmeterol and Fluticasone Propionate and Survival in Chronic Obstructive Pulmonary Disease
CALVERLEY, P. M. A., Anderson, J. A., Celli, B. R., Ferguson, G. T., Jenkins, C. R., Jones, P., Yates, J., & Vestbo, J. (2007) · New England Journal of Medicine · doi:10.1056/nejmoa063070 · Cited by 3,233 · see citing works
Tiotropium in Asthma Poorly Controlled with Standard Combination Therapy
Kerstjens, H. A. M., Engel, M., Dahl, R., Paggiaro, P., Beck, E. C., Vandewalker, M. L., Sigmund, R., Seibold, W., Moroni-Zentgraf, P., & Bateman, E. D. (2012) · New England Journal of Medicine · doi:10.1056/nejmoa1208606 · Cited by 663 · see citing works
Farrington, P., & Manning, G. (1990) · Statistics in Medicine · doi:10.1002/sim.4780091208 · Cited by 658 · see citing works
Sample size determination for logistic regression revisited
Demidenko, E. (2006) · Statistics in Medicine · doi:10.1002/sim.2771 · Cited by 435 · see citing works
Sample size for Poisson regression
Signorini, D. F. (1991) · Biometrika · doi:10.1093/biomet/78.2.446 · Cited by 119 · see citing works
Statistical analysis of exacerbation rates in COPD: TRISTAN and ISOLDE revisited
Keene, O. N., Calverley, P. M. A., Jones, P., Vestbo, J., & Anderson, J. A. (2008) · European Respiratory Journal · doi:10.1183/09031936.00161507 · Cited by 110 · see citing works
Keene, O. N., Jones, M. R. K., Lane, P. W., & Anderson, J. A. (2007) · Pharmaceutical Statistics · doi:10.1002/pst.250 · Cited by 109 · see citing works
Aban, I., Cutter, G., & Mavinga, N. (2008) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2008.07.034 · Cited by 69 · see citing works
Tutorial in biostatistics: sample sizes for parallel group clinical trials with binary data
Julious, S. A., & Campbell, M. J. (2012) · Statistics in Medicine · doi:10.1002/sim.5381 · Cited by 64 · see citing works
Lyles, R. H., Lin, H., & Williamson, J. M. (2007) · Statistics in Medicine · doi:10.1002/sim.2617 · Cited by 57 · see citing works
A UMPU TEST FOR COMPARING MEANS OF TWO NEGATIVE BINOMIAL DISTRIBUTIONS
Wang, Y., Young, L. J., & Johnson, D. E. (2001) · Communications in Statistics - Simulation and Computation · doi:10.1081/sac-100107795 · Cited by 8 · see citing works
Power Analyses for Negative Binomial Models with Application to Multiple Sclerosis Clinical Trials
Rettiganti, M., & Nagaraja, H. N. (2012) · Journal of Biopharmaceutical Statistics · doi:10.1080/10543406.2010.528105 · Cited by 7 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
scPower accelerates and optimizes the design of multi-sample single cell transcriptomic studies
Schmid, K. T., Höllbacher, B., Cruceanu, C., Böttcher, A., Lickert, H., Binder, E. B., Theis, F. J., & Heinig, M. (2021) · Nature Communications · doi:10.1038/s41467-021-26779-7 · Cited by 108 · see citing works
Stefanac, N., Hetrick, S., Hulbert, C., Spittal, M. J., Witt, K., & Robinson, J. (2019) · BMC Public Health · doi:10.1186/s12889-019-7742-9 · Cited by 105 · see citing works
- Authors
- Zhu, H., & Lakkis, H.
- Affiliations
- Forest Laboratories (United States) (US)
- Corresponding author
- Zhu, Haiyuan
- ORCID
- Zhu, Haiyuan
- Venue
- Statistics in Medicine
- Publisher
- Wiley
- Published
- 2013-08-23
- Volume
- 33
- Issue
- 3
- Pages
- 376-387
- ISSN
- 0277-6715 (ISSN-L)
- OpenAlex
- W2147657405
- Cited by
- 97
- References
- 13
- Citations by year
- 2026: 8 · 2025: 6 · 2024: 9 · 2023: 6 · 2022: 8 · 2021: 19 · 2020: 12 · 2019: 8 · 2018: 8 · 2017: 4 · 2016: 2 · 2015: 2 · 2014: 5
- FWCI
- 2.65
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Statistics in Medicine (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Keywords
- sample size determination, negative binomial regression, count data, overdispersion, clinical trial design, dispersion parameter, exposure time, explicit formula
- MeSH terms
- Tiotropium Bromide, Asthma, Clinical Trials as Topic, Computer Simulation, Humans, Scopolamine Derivatives, Models, Statistical, Likelihood Functions, Sample Size
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
