Regression under Cox’s model for recall-based time-to-event data in observational studies

In some retrospective observational studies, the subject is asked to recall the age at a particular landmark event. The resulting data may be partially incomplete because of the inability of the subject to recall. This type of incompleteness may be regarded as interval censoring, where the censoring is likely to be informative. The problem of fitting Cox’s relative risk regression model to such data is considered. While a partial likelihood is not available, a method of semi-parametric inference of the regression parameters as well as the baseline distribution is proposed. Monte Carlo simulations show reasonable performance of the regression parameters, compared to Cox estimators of the same parameters computed from the complete version of the data. The proposed method is illustrated through the analysis of data on age at menarche from an anthropometric study of adolescent and young adult females in Kolkata, India.