A nonparametric likelihood test for detecting discordance between two measurements with application to censored viral load determinations.

Patient management frequently involves quantitative evaluation of a patient's attributes. For example, in HIV studies, a high viral load can be a trigger to initiate or modify an antiretroviral therapy. At times, a new method of evaluation may substitute for an established one, provided that the new method does not result in different clinical decisions compared with the old method. Traditional measures of agreement between the two methods are inadequate for deciding if a new method can replace the old. Especially, when the data are censored by a detection limit, estimates of agreement can be biased unless the distribution for the censored data is correctly specified; this is usually not feasible in practice. We propose a nonparametric likelihood test that seamlessly handles censored data. We further show that the proposed test is a generalization of the test on nominal measurement concordance to continuous measurement. An exact permutation procedure is proposed for implementing the test. Our application is an HIV study to determine whether one method of processing plasma samples can safely substitute for the other. The plasma samples are used to determine viral load and a large portion of data are left censored due to a lower detection limit.