Profile likelihood confidence interval for the prevalence assessed by an imperfect diagnostic test

We present a new confidence interval for the prevalence of a disease for a situation when sensitivity and specificity of the diagnostic test are estimated from validation samples independent of the study sample. The new interval is based on profile likelihood and incorporates an adjustment improving the coverage probability. Its coverage probability and expected length were assessed by simulation and compared to two other methods for this problem, namely those by Lang and Reiczigel (2014) and Flor et al. (2020). Expected length of the new interval is less than that of the Lang and Reiczigel interval while its coverage is about the same. Comparison to the Flor interval resulted in similar expected length but higher coverage probabilities for the new interval. All in all, the new interval proved to be better than both its competitors.