Classification of a correlated binary observation

A bivariate binary observation is traditionally classified into one of the two possible groups under the assumption that the cell counts follow a suitable multinomial distribution. But. in the traditional approach, the jointprobability for each of these cell counts is unknown. Consequently it is not clear, how the traditional approach takes into account the correlation that may exist between two 2-dimensional binary observations. In this thesis, following Prentice [27] (Biometrics, 1988). we model the cell probabilities by a suitable bivariate binary distribution and examine the effect of this type of modelling in classifying a new correlated bivariate binary observation. The performance of the usual optimum classification procedure based on the proposed modelling of the cell probabilities are then compared with the model-free existing procedure. This is done through a simulation, by comparing the probabilities of misclassification for the two approaches, for various sample sizes and selected values of the marginal probabilities as well as correlation parameter between the two binary observations. We illustrate the use of the joint probability modelling in classification by analyzing a combined data set from two epidemiological surveys of 6-11 years old children conducted in Connecticut, the New Heaven Child Survey (NHCS) and the Eastern Connecticut Child Survey (ECCS)