An application of multinomial logistic regression to estimating performance of a multiple-screening test with incomplete verification

The paper describes a method of estimating the performance of a multiple-screening test where those who test negatively do not have their true disease status determined. The methodology is motivated by a data set on 49927 subjects who were given "K"=6 binary tests for bowel cancer. A complicating factor is that individuals may have polyps in the bowel, a condition that the screening test is not designed to detect but which may be worth diagnosing. The methodology is based on a multinomial logit model for Pr("S"|"R" 6 ), the probability distribution of patient status "S" (healthy, polyps or diseased) conditional on the results "R" 6 from six binary tests. An advantage of the methodology described is that the modelling is data driven. In particular, we require no assumptions about correlation within subjects, the relative sensitivity of the "K" tests or the conditional independence of the tests. The model leads to simple estimates of the trade-off between different errors as the number of tests is varied, presented graphically by using receiver operating characteristic curves. Finally, the model allows us to estimate better protocols for assigning subjects to the disease group, as well as the gains in accuracy from these protocols. Copyright 2008 Royal Statistical Society.