Dynamic Logistic Regression and Dynamic Model Averaging for Binary Classification

We propose an online binary classification procedure for cases when there is uncertainty about the model to use and parameters within a model change over time. We account for model uncertainty through dynamic model averaging, a dynamic extension of Bayesian model averaging in which posterior model probabilities may also change with time. We apply a state-space model to the parameters of each model and we allow the data-generating model to change over time according to a Markov chain. Calibrating a "forgetting" factor accommodates different levels of change in the data-generating mechanism. We propose an algorithm that adjusts the level of forgetting in an online fashion using the posterior predictive distribution, and so accommodates various levels of change at different times. We apply our method to data from children with appendicitis who receive either a traditional (open) appendectomy or a laparoscopic procedure. Factors associated with which children receive a particular type of procedure changed substantially over the 7 years of data collection, a feature that is not captured using standard regression modeling. Because our procedure can be implemented completely online, future data collection for similar studies would require storing sensitive patient information only temporarily, reducing the risk of a breach of confidentiality.