A simple two-sample rank test for multivariate survival outcomes with left truncation and right censoring

A distribution-free two-sample rank test is proposed for testing for differences between survival distributions in the analysis of biomedical studies in which two groups of subjects are followed over time for a particular outcome, which may recur. This method is motivated by an observational HIV (human immunodeficiency virus) study in which a group of HIV-seropositive women and a comparable group of HIV-seronegative women were examined every 6 months for the presence of cervical intraepithelial neoplasia (CIN), the cervical cancer precursor. Women entered the study serially and were subject to random loss to follow-up. Only women free of CIN at study entry were followed resulting in left-truncated survival times. If a woman is found to be CIN infected at a later examination, she is treated and then followed until CIN recurs. The two groups of women were compared at both occurrences of CIN on the basis of rank statistics. For the first occurrence of CIN, survival times since the beginning of the study (based on calendar time) are compared. For a recurrence of CIN, survival times since the first development of CIN are compared. The proposed test statistic for an overall difference between the two groups follows a chi-square distribution with two degrees of freedom. Simulation results demonstrate the usefulness of the proposed test proposed test statistic, which reduces to the Gehan statistic if each person is followed only to the first failure and there is no serial enrollment.