Test‐Based Exact Confidence Intervals for the Difference of Two Binomial Proportions

Abstract

Confidence intervals are often provided to estimate a treatment difference. When the sample size is small, as is typical in early phases of clinical trials, confidence intervals based on large sample approximations may not be reliable. In this report, we propose test-based methods of constructing exact confidence intervals for the difference in two binomial proportions. These exact confidence intervals are obtained from the unconditional distribution of two binomial responses, and they guarantee the level of coverage. We compare the performance of these confidence intervals to ones based on the observed difference alone. We show that a large improvement can be achieved by using the standardized Z test with a constrained maximum likelihood estimate of the variance.

13-Valent Pneumococcal Conjugate Vaccine (PCV13) in Preterm Versus Term Infants

“…The between-group difference in the proportion was computed with an exact, unconditional, 2-sided 95% CI and P value. 14 The geometric mean concentration (GMC) ratio of the 2 groups with 2-sided 95% CIs were calculated for each serotype. The same immunogenicity analyses were performed 1 month after the toddler dose.…”

Shedding of live vaccine virus, comparative safety, and influenza-specific antibody responses after administration of live attenuated and inactivated trivalent influenza vaccines to HIV-infected children

“…The HAI GMTs and GMT ratios, defined as the ratio of GMT in LAIV and GMT in TIV, was summarized by treatment group and 95% CIs were calculated by the bootstrap method. Two-sided exact confidence intervals around the difference between the response rates of LAIV and TIV recipients were constructed using the unconditional exact method proposed by Chan and Zhang (33). Univariate linear regression analyses were performed to identify predictors of baseline and week 4 HAI titers.…”

A Posterior Density for the Difference Between Two Binominal Proportions and the Highest Posterior Density Credible Interval

“…In addition, we took up some actual examples in Table 3. The first example is a vaccine study (Chan and Zhang (1999)). The second example was taken from StatXact (Cytel Software (1995)), and the third example was from an influenza vaccine study reported by Fries et al (1993).…”

“…Santner and Snell (1980) proposed the exact confidence interval that uses the relationship between the hypothesis test and confidence interval. However, Chan and Zhang (1999) pointed out that the exact confidence interval proposed by these two authors is too conservative. Yanakawa and Bian (2001) recommended an improvement for the case in which the observation value is extreme.…”