Estimating survival from partially observed data

Often, in cross-sectional-follow-up studies, survival data are obtained from prevalent cases only. This sampling mechanism introduces lenght-bias. An added difficulty is that in some cases the times of the onset cannot be ascertained or are recorded with great uncertainty. Such was the situation in the Canadian Study of Health and Aging (CSHA), an ongoing nation-wide study of dementia conducted by Health Canada. This paper proposes methods to estimate the survival function nonparametrically, when the data are length-biased and only partially observed. By using the “forward recurrence times” only, we suggest how one can overcome the difficulty caused by missing onset times, while by using the “backward recurrence times” only, one can avoid the cost and effort of follow-up. We illustrate our methods through an application to data derived from the CSHA. J1 : I