Analysis of prevalent cohort survival data

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Cross-sectional sampling is a data collection scheme often used in follow-up studies on duration of a condition when logistic or other constraints preclude the possibility of following-up subjects since initiation of the condition. The condition of interest may be, for instance, a disease, in medical applications, or the unemployment spell in labour force studies. Subjects recruited through a cross-sectional survey have already experienced the onset of the condition of interest, say a disease. Such subjects are known as prevalent cases in epidemiological studies. It is well-known that the duration data collected on prevalent cases are biased. In fact, subjects with longer duration have a greater chance to be included in the sample. A further complication encountered in a cross-sectional survery with follow-up is the issue of informative censoring. This latter feature of cross-sectional surverys, render any direct application of existing methodologies in the classical survival analysis, i.e. analysis based on incident cases, impossible. For, the independence between failure and censoring time plays a crucial role in the martingale machinary used in the classical setting. In addition to the aforementioned features, the data presented to us for analysis have quite a number of other peculiarities which are seemingly shared by many other prevalent cohort studies. Ascertainment of the disease onset is, for example, a great challenge in many prevalent cohort studies. The onset of disease may be completely unknown or, at best, known with uncertainty for many subjects. Modelling and analysis of covariates is another complicated issue in prevalent cohort studies. While a modification of Cox partial likelihood has been used quite often in application, it is possible to show that the estimators obtained using this model, while consistent, are not most efficient.