Parametric Estimation of Menarcheal Age Distribution Based on Recall Data

Menarche, the onset of menstruation, is an important maturational event of female childhood. Most of the studies of age at menarche make use of dichotomous (status quo) data. More information can be harnessed from recall data, but such data are often censored in a informative way. We show that the usual maximum likelihood estimator based on interval censored data, which ignores the informative nature of censoring, can be biased and inconsistent. We propose a parametric estimator of the menarcheal age distribution on the basis of a realistic model of the recall phenomenon. We identify the additional information contained in the recall data and demonstrate theoretically as well as through simulations the advantage of the maximum likelihood estimator based on recall data over that based on status quo data.