Effect of random abnormal cell proportion on specimen classifier performance

A series of papers had analyzed a simplified model of an automated cytology prescreening configuration consisting of a two-class cell classifier followed by a two-class specimen classifier. This has shown, among other things, that the proportion (p) of abnormal cells on an abnormal specimen dictates the number (N) of cells that must be classified before the specimen can be classified with specified accuracy (Anal Quant Cytol, 2:117-122, 1980). It has also shown that if a system designed assuming one fixed value, po, encounters a specimen with a different fixed value, p, then the specimen classifier false negative rate will deviate significantly from the design value, increasing for p < po and vice versa (Cytometry, 2: 155-158, 1981). Using a Gaussian approximation, Timmers and Gelsema (Cytometry, 6:22-25, 1985) extended this to the case where p is a Beta-distributed random variable. They showed that N increases dramatically with the width (coefficient of variation) of the distribution of p. They also concluded that the randomness of p imposes a fundamental lower limit on the specimen false negative rate below which it is impossible to go, even with an error-free cell classifier. In this paper we also extend the basic model to cover the case of random p, but by using an asymptotic expansion (rather than the Gaussian approximation), to develop an expression for N. We show that the limit cited by Timmers and Gelsema is not real, but is actually an artifact of the breakdown of the Gaussian approximation.(ABSTRACT TRUNCATED AT 250 WORDS)