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Title: Regression analysis with censored covariates in the presence of a cured fraction Authors:  Bella Vakulenko-Lagun - University of Haifa (Israel) [presenting]
Abstract: Many health surveys collect data in a cross-sectional way and record only a current value of a Patient Reported Outcome. Any such study encounters a problem in that at the time of data collection, some of the important events, related to the studied outcome, had happened for some of the survey participants, but not for others. In addition, the incompleteness in this time-to-event covariate might be complicated by the presence of a cured fraction (those patients who do belong to the target population but will never experience this event). An example of such data is the data from the Web-based Adult Perthes Survey, which was launched in order to collect data on the physical functioning of patients who had a rare Perthes' disease in childhood. A total hip replacement (THR) in adulthood is a life-changing event for those Perthes patients who need it, but it might not be needed for some of the Perthes patients. We aim to estimate trajectories of the physical functioning of Perthes patients in adulthood as functions of their Perthes history, including THR and age-at-THR. There are few available approaches for cross-sectionally measured outcomes with censored covariates, and none of them accounts for a cured fraction. We propose an approach based on a pseudo-likelihood and assess its finite sample performance in simulations. We derive its asymptotic properties and apply our approach to the data on the long-term outcomes of Perthes' disease.