This article proposes two improved prediction intervals, the
score prediction interval and the adjusted prediction interval,
with closed forms for predicting disease count. Both of them
can increase the coverage probability when p is close to the
boundaries compared with the existing prediction intervals.
A simulation study shows the score interval has the shortest expected
length of these intervals. The two new intervals are also
evaluated in terms of the Kullback–Leibler distance through the
predictive distributions. The comparison shows the predictive
distribution corresponding to the score interval can approximate
the binomial distribution better than that corresponding to the
adjusted prediction interval.
In addition, to obtain more accurate results, we can employ
the procedure of Wang (2008) to derive an appropriate value
of z(1+γ )/2 such that the prediction intervals can achieve either
a desired minimum coverage probability or a desired average
coverage probability.