Lognormal-based mixture models for robust fitting of hospital length of stay distributions

Understanding the structure of length of stay distributions can support operational and clinical decision making in hospitals. Our objective is to develop robust methods for fitting these length of stay distributions, which are often skewed and multimodal and contain a significant number of outliers. We define several lognormal-based mixture distributions with two components, one to fit the majority of observations and one to fit the abnormal observations. Specifically, we propose three lognormal-based mixture distributions, one that utilizes the exponential distribution as the second component, one that utilizes the gamma distribution, and one that utilizes the lognormal distribution. We estimate the parameters for each mixture model using the expectation–maximization (EM) algorithm, and validate our models using simulation. Finally, we compare the fit of our mixture models against different distributional fits using real data collected from multiple studies conducted by researchers at the University of Maryland School of Medicine and their colleagues.