Home | Business News | Browse by Publication | J | Journal of the Mississippi Academy of Sciences

A discussion of binomial interval estimators on the boundary.

Article Excerpt
ABSTRACT

Often in biomedical research, a binary outcome variable has minimal expected value, for example, mortality for aspirin users. For moderate sample sizes, it is not uncommon to observe zero successes in these instances. Confidence interval estimation, in this case, may be more informative than hypothesis testing. There is an appeal to using one-sided confidence intervals for this special case; however, this practice is arguably inappropriate unless the decision is made a priori. The commonly used Wald intervals, as presented in most elementary textbooks, are known to perform poorly, particularly when the proportions are near zero or one. Further, for zero observed successes, the Wald interval estimate is [0,0]. A method of confidence interval construction based on the score statistic has been shown to outperform the Wald intervals. This paper will review binomial parameter confidence interval estimates for uncommon events.

Introduction

In pharmaceutical research there are numerous binary events for which the expected proportion is low. For example, the presence of a life threatening adverse effect during post-marketing testing when none have been observed during pre-marketing clinical trials. In the realm of scientific study, a binary outcome with x = observed successes is an often ignored issue, and sometimes incorrectly interpreted as indicating [pi] = 0. Elementary texts typically use a normal approximation, inverted from a Wald statistic, to estimate [pi] under the condition min{n[pi], n(1 - [pi])} [greater than or equal to] 5. There is no guarantee this condition is met since [pi] is unknown. Brown, et al. (2001) discussed problems even when the criterion is met. Further, if p = x/n is used to estimate [pi], np = for the zero success case regardless of sample size. There have been several papers written on the subject of interval estimation for the binomial in this special case, each offering possible solutions (Wilson, 1927; Louis, 1981; Hanley and Lippman-Hand, 1983; Newcombe, 1998; Agresti and Coull, 1998).

This issue is exacerbated by small sample sizes. As sample sizes increase, and thus more information is obtained from the population, observing zero successes is less likely to happen by chance. Note that P(X = 0) = (1 - [pi])[.sup.n], a decreasing function of sample size for fixed [pi], with [pi] = being...

View this article FREE - Now for a Limited Time, try Goliath Business News
Free for 3 Days!