Length Biased Sampling in Etiologic Studies

The problem of estimating and comparing the frequency of a characteristic in newly diagnosed patients based upon a length biased sample of living patients is described in this paper. This problem is of considerable importance in immunogenetics for determining whether a characteristic is related to disease etiology, or whether, instead, it is of prognostic importance for individuals who have already developed the disease. Maximum likelihood estimation of the proportion of newly diagnosed patients having a characteristic is outlined. The estimator and its variance depend upon the proportion of living patients having the characteristic and upon the survivals of patients with and without the characteristic in the length biased sample.