Quantile comparison functions in two-sample problems, with application to comparisons of diagnostic markers

In this article a control percentile lest, a chi-squared test, and a Kolmogorov-type test are proposed for comparing two distributions from incomplete survival data. These tests are obtained by examining a vertical shift comparison function at a single point, a finite number of points, and an entire set of points on an interval. The proposed methods also have applications in receiver operating characteristic (ROC) analysis, which has been widely used in such diverse fields as signal detection theory, psychology, epidemiology, and medicine. The results are derived under very general conditions that hold for the well-known random censorship and random truncation models. The performances of the proposed procedures are studied using Monte Carlo simulation. The methods are applied to analyze Mayo Clinic ovarian carcinoma data.