Performance of binary markers for censored failure time outcome: nonparametric approach based on proportions

This work focuses on the assessment of the discrimination ability of a binary marker to identify patients that will relapse in time. We consider the cumulative definition of sensitivity and dynamic definition of specificity at a time horizon, that is, the probability of a positive marker in the population that will relapse (cases) and that will not relapse (controls). In the presence of censoring, sensitivity and specificity cannot be estimated by proportions because it is not known whether censored subjects should be considered as cases or controls. The solutions proposed do not enable to obtain asymptotic confidence intervals. We explore the use of inverse probability of censoring weighting/imputation (borrowed from the methodology used to correct for verification bias) to adjust the classification matrix for the presence of censoring. The adjustment based on weights estimated conditional on the marker turned to be equivalent to the adjustment based on imputation. These approaches, which address for the presence of marker-dependent censoring, showed a better performance than the adjustment based on weights estimated on the entire sample, even in the case of marker-independent censoring. We derived single intervals and confidence region for sensitivity and 1-specificity using the delta method. The confidence region is particularly useful for a binary marker because the marker has some ability to discriminate among cases and controls only if the region does not intersect the first quadrant bisector.