![]() ![]() ![]() If the researcher believes there are two different data generating mechanisms producing zeros, then the ZINB regression model may provide greater flexibility when modeling the zero-inflation and overdispersion. Conclusionsīased on this study, we recommend to the researchers that they consider the ZIP models for count data with zero-inflation only and NB models for overdispersed data or data with combinations of zero-inflation and overdispersion. In the empirical data analysis, we demonstrated that fitting incorrect models to overdispersed data leaded to incorrect regression coefficients estimates and overstated significance of some of the predictors. NB model provided the best fit in overdispersed data and outperformed the ZINB model in many simulation scenarios with combinations of zero-inflation and overdispersion, regardless of the sample size. NB and ZINB regression models faced substantial convergence issues when incorrectly used to model equidispersed data. ZIP outperformed the rest of the regression models when the overdispersion is due to zero-inflation only. Results showed that Poisson and ZIP models performed poorly in overdispersed data. Analysis of hospital LOS was conducted using empirical data from the Medical Information Mart for Intensive Care database. Methodsĭata were generated under different simulation scenarios with varying sample sizes, proportions of zeros, and levels of overdispersion. In this study, we compared the performance of the Poisson, negative binomial (NB), zero-inflated Poisson (ZIP), and zero-inflated negative binomial (ZINB) regression models using simulated and empirical data. Hospital LOS data can be treated as count data, with discrete and non-negative values, typically right skewed, and often exhibiting excessive zeros. Therefore, understanding hospital LOS variability is always an important healthcare focus. Hospital LOS is often used as a measure of a post-medical procedure outcome, as a guide to the benefit of a treatment of interest, or as an important risk factor for adverse events. This is joint research with Veronika Rockova, Paul Rosenbaum, Ville Satopaa and Jeffrey Silber.Hospital length of stay (LOS) is a key indicator of hospital care management efficiency, cost of care, and hospital planning. As a viable alternative, we propose a full population direct standardization which yields correctly calibrated mortality rates devoid of patient-mix variation. ![]() It is seen that indirect standardization, as currently used by Hospital Compare, fails to adequately control for differences in patient risk factors and systematically underestimates mortality rates at the low volume hospitals. Such standardization can be accomplished with counterfactual mortality predictions for any patient at any hospital. ![]() And for the ultimate purpose of meaningful public reporting, predicted mortality rates must then be standardized to adjust for patient-mix variation across hospitals. This process of calibrating individualized predictions against general empirical advice leads to substantial revisions in the Hospital Compare model for AMI mortality, revisions that hierarchically incorporate information about hospital volume, nursing staff, medical residents, and the hospital’s ability to perform cardiovascular procedures. Here we calibrate these Bayesian recommendation systems by checking, out of sample, whether their predictions aggregate to give correct general advice derived from another sample. Before individualized Bayesian predictions, people derived general advice from empirical studies of many hospitals e.g., prefer hospitals of type 1 to type 2 because the observed mortality rate is lower at type 1 hospitals. Except for the largest hospitals, these predictions are not individually checkable against data, because data from smaller hospitals are too limited. Hospital Compare’s current predictions are based on a random-effects logit model with a random hospital indicator and patient risk factors. In particular, Medicare’s Hospital Compare webpage provides information to patients about specific hospital mortality rates for a heart attack or Acute Myocardial Infarction (AMI). Bayesian models are increasingly fit to large administrative data sets and then used to make individualized predictions. ![]()
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