In observational studies, incidence cohort sampling is ideally adopted to study individuals, who have not experienced a disease, from disease onset to a failure event. Logistic or other constraints (rare disease, cost of study) may, however, preclude the possibility of recruiting incident cases. A feasible alternative in such circumstances is to sample subjects who have already experienced the onset of a disease, through cross-sectional sampling.
In this presentation, we discuss the nonparametric estimation of the regression function
\(m(x) = E[ Y| X = x]\), under the model
\(Y = m(X) + \epsilon \), when the data
\((Y, X\)) is subject to biased selection and random censoring. We introduce a methodology for known parametric forms of the left-truncation distribution. In the length-biased case, our method show efficiency as compared to the one of Iglesias-Perez & Gonzalez-Manteiga (1999). The proposed method is then applied to analyze two data sets on the mortality of patients with AIDS and the survival of elderly individuals with dementia.
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