Confidence intervals for proportions with small expected number of positive counts estimated from survey data - ARCHIVED

In the nonsurvey setting,"exact" confidence intervals for proportions calculated using the binomial distribution are frequently used instead of intervals based on approximate normality when the number of positive counts is small. With complex survey data, the binomial intervals are not applicable, so intervals based on the assumed approximate normality of the sample-weighted proportion are used, even if the number of positive counts is small. We propose a simple modification of the binomial intervals to be used in this situation. Limited simulations are presented that show the coverage probability of the proposed intervals is superior to that of the normality-based intervals, logit-transform intervals, and intervals based on a Poisson approximation. Applications are given involving the prevalence of Human Immunodeficiency Virus (HIV) based on data from the third National Health and Nutrition Examination Survey, and the proportion of users of cocaine based on data from the Hispanic Health and Nutrition Examination Survey.