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. Even though this type of incompleteness may be regarded as interval censoring, the censoring is likely to be informative. For such data, methods of parametric and non-parametric estimation of the survival function of the time-to-event have been provided by the authors. In this paper, we consider the problem of regression through Cox’s proportional hazards model. 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 a recent Anthropometric study of adolescent and young adult females in Kolkata, India.