Approximate confidence intervals for the likelihood ratios of a binary diagnostic test in the presence of partial disease verification.

The classic parameters used to assess the accuracy of a binary diagnostic test (BDT) are sensitivity and specificity. Other parameters used to describe the performance of a BDT are likelihood ratios (LRs). The LRs depend on the sensitivity and the specificity of the diagnostic test, and they reflect how much greater the probability of a positive or negative diagnostic test result for individuals with the disease than that for the individuals without the disease. In this study, several confidence intervals are studied for the LRs of a BDT in the presence of missing data. Two confidence intervals were studied through the method of maximum likelihood and seven confidence intervals were studied by applying the multiple imputation by chained equations method. A program in R software has been written that allows us to solve the estimation problem posed. The results obtained have been applied to the two real examples.