Polynomial modeling of emergency department arrivals: An analysis of local and national utilization patterns

Emergency department (ED) overcrowding is a national problem that is associated with ambulance diversion, decreased patient and provider satisfaction and poor patient outcomes. This study presents a novel approach to modeling the relationship between time of day, day of week, and ED arrivals using a hierarchical polynomial regression model. A series of hierarchical regression models were created to determine polynomial effects and capture the covariability (defined as R²) of the relationships from the 2009 to 2017 National Hospital Ambulatory Medical Care Survey (NHAMCS) Emergency Department Public Use Data File and institutional data from a regional medical center from 2018 to 2019. The following hierarchical regression models were constructed: cubic main effects, cubic interaction effects, quartic main effects, quartic interaction effects, quintic main effects, and quintic interaction effects. Based on maximal improvement in R² and significance of each of the four effects in both the national and institutional data sets, the quartic main effects model was determined to be optimal for describing ED arrival patterns. In alignment with prior studies, significantly higher ED arrival volumes were observed on Mondays in comparison to all other weekdays.