36
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Cost-efficient fixed-width confidence intervals for the difference of two Bernoulli proportions

, &
Received 05 Jul 2022, Accepted 18 Jul 2023, Published online: 17 Nov 2023

References

  • Agresti, A., & Coull, B. A. (1998). Approximate is better than “exact” for interval estimation of binomial proportions. The American Statistician, 52(2), 119–126. https://doi.org/10.1080/00031305.1998.10480550
  • Alter, D. (2017). When do we decide that generic and brand-name drugs are clinically equivalent? Circulation: Cardiovascular Quality and Outcomes, 10(10), e004158. https://doi.org/10.1161/CIRCOUTCOMES.117.004158
  • Andrade, C. (2015, June). Bioequivalence of generic drugs: A simple explanation for a U.S. Food and Drug Administration requirement. Journal of Clinical Psychiatry, 76(6), e742–4. https://doi.org/10.4088/JCP.15f10094
  • Armitage, P. (1958). Numerical studies in the sequential estimation of a binomial parameter. Biometrika, 45(1–2), 1–15. https://doi.org/10.1093/biomet/45.1-2.1
  • Association for Accessible Medicines. (2021). The U.S. Generic & Biosimilar Medicines Savings Report, available in https://accessiblemeds.org/sites/default/files/2021-10/AAM-2021-US-Generic-Biosimilar-Medicines-Savings-Report-web.pdf.
  • Brown, L. D., Cai, T., & Dasgupta, A. (2001). Interval estimation for a binomial proportion. Statistical Science, 16(2), 101–133. https://doi.org/10.1214/ss/1009213286
  • Brown, L. D., Cai, T., & Dasgupta, A. (2002). Interval estimation for a binomial proportion and asymptotic expansions. Annals of Statistics, 30(1), 160–201. https://doi.org/10.1214/aos/1015362189
  • Cheridito, P., & Baes, M. (2018). KKT conditions and applications, accessible at https://people.math.ethz.ch/patrickc/co/CO18L06.pdf.
  • Davit, B., Nwakama, P. E., Buehler, G., Conner, D., Haidar, S., Patel, D. T., Yang, Y., Yu, L., & Woodcock, J. (2009). Comparing generic and innovator drugs: A review of 12 years of bioequivalence data from the United States Food and Drug Administration. Annals of Pharmacotherapy, 43(10), 1583–1597. https://doi.org/10.1345/aph.1M141
  • Desai, R. J., Sarpatwari, A., Dejene, S., Khan, N. F., Lii, J., Rogers, J. R., Dutcher, S. K., Raofi, S., Bohn, J., Connolly, J. G., Fischer, M. A., Kesselheim, A. S., Gagne, J. J., & Basu, S. (2019). Comparative effectiveness of generic and brand-name medication use: A database study of U.S. health insurance claims. PLOS Medicine, 16(3), e1002763. https://doi.org/10.1371/journal.pmed.1002763
  • Erazo, I., & Goldsman, D. (2021). Efficient confidence intervals for the difference of two Bernoulli distributions’ success parameters. Journal of Simulation, 17(1), 76–93. https://doi.org/10.1080/17477778.2021.1955629
  • Frey, J. (2010). Fixed-width sequential confidence intervals for a proportion. The American Statistician, 64(3), 242–249. https://doi.org/10.1198/tast.2010.09140
  • Gallelli, L., Palleria, C., De Vuono, A., Mumoli, L., Vasapollo, P., Piro, B., & Russo, E. (2013, December). Safety and efficacy of generic drugs with respect to brand formulation. Journal of Pharmacology and Pharmacotherapeuthics, 4(Suppl 1), S110–4. https://doi.org/10.4103/0976-500X.120972
  • Hines, W. W., Montgomery, D. C., Goldsman, D., & Borror, C. M. (2003). Probability and Statistics in Engineering (4th ed.). John Wiley and Sons.
  • Khan, R. A. (1998). Fixed width confidence sequences for the normal mean and the binomial Probability. Sequential Analysis, 17(3–4), 205–217. https://doi.org/10.1080/07474949808836409
  • Leclerc, J., Blais, C., Rochette, L., Hamel, D., Guénette, L., & Poirier, P. (2017). Impact of the commercialization of three generic Angiotensin II receptor blockers on adverse events in Quebec, Canada: A population-based time series analysis. Circulation: Cardiovascular Quality and Outcomes, 10(10), e003891. https://doi.org/10.1161/CIRCOUTCOMES.117.003891
  • Lehmann, E. L., & Casella, G. (1998). Theory of Point Estimation (2nd ed.). Springer-Verlag.
  • Liu, Y., Pedrielli, G., Li, H., Lee, L. H., Chen, C.-H., & Shortle, J. F. (2019). Optimal computing budget allocation for stochastic N–k problem in the power grid system. IEEE Transactions on Reliability, 68(3), 778–789. https://doi.org/10.1109/TR.2019.2913741
  • Robbins, H., & Siegmund, D. (1974). Sequential estimation of p in Bernoulli trials. In E. J. G. Pitman & E. J. Williams (Eds.), Studies in Probability and Statistics (pp. 103–107). Jerusalem Academic Press.
  • Sheen, H., & Mei, Y. (2021). An elementary approach for minimax estimation of Bernoulli proportion in the restricted parameter space. Statistics Theory.
  • Tian, Y., Reichardt, B., Dunkler, D., Winkelmayer, W. C., Strohmaier, A., Bucsics, S., Heinze, G., & Heinze, G. (2020). Comparative effectiveness of branded vs. generic versions of antihypertensive, lipid-lowering and hypoglycemic substances: A population-wide cohort study. Scientific Reports, 10(1), 5964. https://doi.org/10.1038/s41598-020-62318-y
  • Turner, A. J., Balestrini-Robinson, S., & Mavris, D. (2013). Heuristics for the regression of stochastic simulations. Journal of Simulation, 7(4), 229–239. https://doi.org/10.1057/jos.2013.1
  • UpToDate. (2022), Prices for some common brand-name medicines and their generic versions (without insurance), available on https://www.uptodate.com/contents/image?imageKey=PC%2F90835.
  • U.S. Food and Drug Administration. (2022a). Generic drug overview, available in https://www.fda.gov/drugs/buying-using-medicine-safely/generic-drugs.
  • U.S. Food and Drug Administration. (2022b). FDA ensures equivalence of generic drugs, available in https://www.fda.gov/drugs/resources-you-drugs/fda-ensures-equivalence-generic-drugs.
  • U.S. Food and Drug Administration. (2022c). Generic drug facts, available in https://www.fda.gov/media/107601/download.
  • Yaacoub, T., Moustakides, G. V., & Mei, Y. (2018). Optimal stopping for interval estimation in Bernoulli trials, IEEE Transactions on information Theory, https://doi.org/10.1109/TIT.2018.2885405
  • Zacks, S., & Mukhopadhyay, N. (2007). Distributions of sequential and two-stage stopping times for fixed-width confidence intervals in Bernoulli trials: Application in reliability. Sequential Analysis, 26(4), 425–441. https://doi.org/10.1080/07474940701620907

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.