Multiple regression analysis for dynamics of patient volumes

We study a real data set of 7,894,947 patients who received service from the University of Michigan Health System (UMHS) from January 1, 2003 to December 31, 2008 using regression analysis to understand the dynamics of patient volume. Our objective is to find out patterns from time series of patient volume during economic crisis. We propose a contribution adjusted formula to understand the dynamics of a heterogeneous customer population. We find that the trend of patient volume for a health system is positively correlated to the trend of the underlying adjusted resident population and to the GDP rates and negatively correlated to annual unemployment rate. We also find that the percent change of patient volume in a health system depends on the threshold level curves of resident population and unemployment rate with nonlinear behavior. Our multiple regression model with quadratic response surface explains 98.9% of the variation. Moreover, the multiple regression model having lag 1 with interaction term explains 96.5% of the variation. Furthermore, we propose several models having dummy variables using localities for patient groups. Overall, our results suggest that people use more health services when they have enough income, job and health insurance.