Exact confidence limits for proportion difference in clinical trials with bilateral outcome
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Exact confidence limits for proportion difference in clinical trials with bilateral outcome Guogen Shan1 Accepted: 8 September 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract 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. Keywords Bilateral data · Binary data · Confidence interval · Exact limits · Proportion difference
1 Introduction Bilateral data are common in many medical research areas, such as ophthalmologic studies, orthopaedic studies, otolaryngologic studies, and twin studies. For example, the age-related eye disease study (AREDS) is a national clinical trial to study effectiveness of antioxidants and zinc supplement to reduce the risk of advanced age-related macular degeneration and its associated vision loss (Ying et al. 2018). The primary
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Guogen Shan [email protected] Epidemiology and Biostatistics Program, School of Public Health, University of Nevada Las Vegas, Las Vegas, NV 89154, USA
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outcome is the development of central geographic atrophy (GA) in either eye by year 5. It was reported that the rate of the development of center GA in the placebo is 7.3% while that in the antioxidants group is estimated as 5.8% that is less than the rate in the placebo group. As both eyes are examined in the AREDS, the intra-eye correlation needs to be considered for proper statistical inference. Rosner (1982) was among the first to develop statistical models for bilateral data. For a study with binary outcome, he developed a positive constant to measure the correlation between two outcomes from the same participant through a conditional probability (Rosner 1982; Shan and Ma 2014a). Tang et al. (2008) compared several asymptotic approaches to test the equality of two proportions for bilateral outcome, including the Wald test, the likelihood ratio test, and the score test. In addition, they considered the approximate unconditional approach for p value calculation by enumerating all possible s
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