PRM51 Nonparametric Regression Analysis Controls Cost Analysis in Data with Outliers

Abstract

Cost analysis is often complicated to analyze because of skewed data caused by outliers in the upper tail of the distribution. Some of these outlier expenses are a result of extreme expenses before an observation period starts or during an episode of illness. Theil regression is a non-parametric linear regression method that provides accurate estimates of slope and intercept when outliers are present by calculating values based on the median. In a study intended to measure the length of time it took for patient costs to return to normal pre-episode costs after pneumonia, the Theil method was used and compared to Ordinary Least Squares (OLS) results on the same data. The baseline cost was computed as the mean cost for the six months prior to diagnosis, the study allowed for a three month episode period and the OLS and Theil regression methods were computed on the monthly costs for the six months after the episode. High cost outliers during the three month episode led to elevated costs for the first post episode period. This caused an underestimate of cost using the OLS method. Theil regression correctly estimated the increased time to return to normal in 11 of the 21 variables tracked. These differences ranged from 15 to 370 days. OLS found extended time over Theil for 5 of 21 comparisons. These differences ranged from 2 to 26 days. Agreement between OLS and Theil was found for 5 of 21 comparisons. Outliers in regression analysis frequently occur when the variable of interest is cost. Theil regression offers considerable advantages over OLS regression when the outlier is in one of the tails of the distribution. The advantages include more accurate results as well being able to use all the data without exclusion of any data elements.