Closed form prediction intervals applied for disease counts

The prediction interval is an important tool in medical applications for predicting the number of times a disease will occur in a population. The performance of the existing prediction intervals, however, is unsatisfactory when the true proportion is near a boundary. Since the true proportion can be very small in real applications, in this article, we propose improved prediction intervals with better coverage probability than the existing methods. Their predictive distributions are compared in terms of the Kullback-Leibler distance and the intervals are compared using a hearing screening medical example.