Bilateral data are frequently occur in medical research. Asymptotic approaches are traditionally used to construct confidence intervals for proportion difference. However, they are often have unsatisfactory performance with regards to coverage, with the actual coverage below the nominal level or being too conservative. For these reasons, we propose developing exact one-sided limits for proportion difference in a parallel study with bilateral data to guarantee the coverage probability when sample size is small to medium. A statistical quantity has to be used for sample space ordering in the exact limit calculation. Four asymptotic limits are utilized as statistical quantities: the Wald limits under the independence or dependence assumptions for variance estimates, the Wald limits with the difference estimate under the dependence assumption, and the bootstrap percentile limits. We compare the performance of these exact limits with regards to average length and the limits of all possible samples. A real example from a randomized clinical trial in otolaryngology is used to illustrate the application of the proposed exact limits.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Buehler RJ (1957) Confidence intervals for the product of two binomial parameters. J Am Stat Assoc 52(280):482–493
Lloyd CJ, Moldovan MV (2007) Exact one-sided confidence limits for the difference between two correlated proportions. Stat Med 26(18):3369–3384
Mandel EM, Bluestone CD, Rockette HE, Blatter MM, Reisinger KS, Wucher FP, Harper J (1982) Duration of effusion after antibiotic treatment for acute otitis media: comparison of cefaclor and amoxicillin. Pediatr Infect Dis 1(5):310–316
Rosner B (1982) Statistical methods in ophthalmology: an adjustment for the intraclass correlation between eyes. Biometrics 38(1):105–114
Shan G, Ma C (2014a) Efficient tests for one sample correlated binary data with applications. Stat Methods Appl 23(2):175–188
Shan G, Ma C (2014b) Exact methods for testing the equality of proportions for binary clustered data from otolaryngologic studies. Stat Biopharm Res 6(1):115–122
Shan G, Wang W (2013) ExactCIdiff: an R package for computing exact confidence intervals for the difference of two proportions. R J 5(2):62–71
Shan G, Banks S, Miller JB, Ritter A, Bernick C, Lombardo J, Cummings JL (2018) Statistical advances in clinical trials and clinical research. Alzheimer’s Dement Transl Res Clin Interv 4:366–371
Tang N-S, Tang M-L (2002) Exact unconditional inference for risk ratio in a correlated 2 \(\times \) 2 table with structural zero. Biometrics 58(4):972–80
Tang N-S, Tang M-L, Qiu S-F (2008) Testing the equality of proportions for correlated otolaryngologic data. Comput Stat Data Anal 52(7):3719–3729
Tang N-S, Qiu S-F, Tang M-L, Pei Y-B (2011) Asymptotic confidence interval construction for proportion difference in medical studies with bilateral data. Stat Methods Med Res 20(3):233–259
Ying G-S, Maguire MG, Glynn R, Rosner B (2018) Tutorial on biostatistics: statistical analysis for correlated binary eye data. Ophthalmic Epidemiol 25(1):1–12
Zhang H, Shan G (2019) Letter to the Editor: A novel confidence interval for a single proportion in the presence of clustered binary outcome data (SMMR, 2019). Stat Methods Med Res. https://doi.org/10.1177/0962280219840056
We are very grateful to Editor, Associate Editor, and two reviewers for their insightful comments that help improve the manuscript.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Shan, G. Exact confidence limits for proportion difference in clinical trials with bilateral outcome. Stat Methods Appl 29, 515–525 (2020). https://doi.org/10.1007/s10260-019-00491-9
- Bilateral data
- Binary data
- Confidence interval
- Exact limits
- Proportion difference