EM for regularized zero-inflated regression models with applications to postoperative morbidity after cardiac surgery in children

This paper proposes a new statistical approach for predicting postoperative morbidity such as intensive care unit length of stay and number of complications after cardiac surgery in children. In a recent multi-center study sponsored by the National Institutes of Health, 311 children undergoing cardiac surgery were enrolled. Morbidity data are count data in which the observations take only nonnegative integer values. Often, the number of zeros in the sample cannot be accommodated properly by a simple model, thus requiring a more complex model such as the zero-inflated Poisson regression model. We are interested in identifying important risk factors for postoperative morbidity among many candidate predictors. There is only limited methodological work on variable selection for the zero-inflated regression models. In this paper, we consider regularized zero-inflated Poisson models through penalized likelihood function and develop a new expectation-maximization algorithm for numerical optimization. Simulation studies show that the proposed method has better performance than some competing methods. Using the proposed methods, we analyzed the postoperative morbidity, which improved the model fitting and identified important clinical and biomarker risk factors.