| Multilevel classification is a problem in statistics which has gained increasing importance in many real-world problems, but it has not yet received the same statistical understanding as the general problem of classification. An example we consider here is to develop a method to detect cervical neoplasia (pre-cancer) using quantitative cytology, which involves measurements on the cells obtained in a Papanicolou smear. The multilevel structure comes from the embedded cells within a patient, where we have quantitative measurements on the cells, yet we want to classify the patients, not the cells. An additional challenge comes from the fact that we have a high-dimensional feature vector of measurements on each cell. The problem has historically been approached in two ways: (a) ignore this multilevel structure of the data and perform classification at the microscopic (cellular) level, and then use ad-hoc methods to classify at the macroscopic (patient) level, or (b) summarize the microscopic level data using a few statistics and then use these to compare the subjects at the macroscopic level. We consider a more rigorous statistical approach, the Cumulative Log-Odds (CLO) Method, which models the posterior log-odds of disease for a patient given the cell-level measured feature vectors for that patient. Combining the CLO method with a latent variable model (Latent-Class CLO Method) helps to account for between-patient heterogeneity. We apply many different approaches and evaluate their performance using out of sample prediction. We find that our best methods classify with substantial greater accuracy than the subjective Papanicolou Smear interpretation by a clinical pathologist. |
