We consider here the problem of classifying a macro-level object based on measurements of embedded (micro-level) observations within each object, for example, classifying a patient based on measurements on a collection of a random number of their cells. Classification problems with this hierarchical, nested structure have not received the same statistical understanding as the general classification problem. Some heuristic approaches have been developed and a few authors have proposed formal statistical models. We focus on the problem where heterogeneity exists between the macro-level objects within a class. We propose a model-based statistical methodology that models the log-odds of the macro-level object belonging to a class using a latent-class variable model to account for this heterogeneity. The latent classes are estimated by clustering the macro-level object density estimates. We apply this method to the detection of patients with cervical neoplasia based on quantitative cytology measurements on cells in a Papanicolaou smear. Quantitative cytology is much cheaper and potentially can take less time than the current standard of care. The results show that the automated quantitative cytology using the proposed method is roughly equivalent to clinical cytopathology and shows significant improvement over a statistical model that does not account for the heterogeneity of the data.
