Survival analysis under cross-sectional sampling: length bias and multiplicative censoring

Consider a parametric, nonparametric or semiparametric model for survival times. Interest is in estimation of Euclidean and Banach parameters for these models. However, not the survival times themselves will be observed, since this might be quite time consuming. Instead, cross-sectional sampling is applied: at some point in time one identifies a random sample from the population under study and one registers the survival time up to this time-point. Typically, the resulting reduced survival times do not have the same distributions as the true survival times. On the one hand, longer survival times have a higher probability to be sampled than smaller ones. On the other hand, the observed survival times have been censored multiplicatively. The length bias and multiplicative censoring properties of cross-sectional sampling will be discussed and reviewed as well as estimation in the resulting parametric, nonparametric, and semiparametric models. (C) 2000 Elsevier Science B.V. Ail rights reserved.