Sequential Neutral Zone Classiers With Application to Longitudinal Data
Neutral zone classifiers include 'no-decision' as a classification outcome. This paper extends neutral zone classifiers to sequential contexts for analyzing longitudinal data. Applications could include medical diagnosis where a decision variable is repeatedly measured on each subject with the expectation of being able to ultimately identify a patient disease status. Sequential classifiers monitor the sequence of measurements and decide when to stop sampling and how to classify the subject. Bayesian sequential classification rules make classifications on the basis of the minimum expected loss. This approach is a challenge due to computational complexity associated with evaluating the expected future costs. We consider Gaussian contexts. In the homogeneous case we demonstrate the equivalence between sequential Bayesian classifier and a simpler boundary-based framework. A solution for the heterogeneous Gaussian case is presented using the boundary-based framework. A recursive algorithm is developed to efficiently determine decision boundaries that minimize the overall expected cost.
Alternative decision boundaries which are competitive with the optimal decision boundaries are studied. Misclassification rates and expected sample size are investigated and the results are compared with non-sequential classifiers.