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Confidence intervals for binomial proportions with applications to product safety signaling in drug exposure registries [Abstract].
Coverage behavior for confidence intervals for binomial proportions have been investigated by various authors including Vollset (1993), Newcomb (1998), Agresti et al (1998, 2001), and Brown, Cai and DasGupta (2001). A general consensus is that the commonly used Wald confidence interval is flawed, particularly if the proportion is near 0 or 1, but agreement on a replacement is lacking. Previous investigations in this area have focused on the aggregate behavior of the confidence interval coverage across all possible values of the binomial proportion. Most recommended methods either have under coverage issues if the proportion is near 0 or 1, or else are excessively conservative. We shall compare a variety of confidence intervals based on asymptotic, exact, and quasi-exact methods when the rate of success is near 0, which is the usual context of adverse event signaling in drug exposure registries. Upon examination of the coverage probabilities for a range of sample sizes n and p near 0, we find that recommended methods such as Wilson's method have notable deficiencies, and present alternatives.