ROBUST STATISTICAL MODELING OF MEDICAL EXPENDITURES: NONLINEAR EFFECTS, INTERACTIONS, AND DISTRIBUTIONAL HETEROGENEITY

Abstract

The cost of medical services is frequently skewed, dispersed unevenly, and highly variable and the models that are commonly used to describe the cost structure are often based on the mean. The study looked at 1,338 individual insurance records, and compared the impact of age, sex, body mass index (BMI), number of children, smoking status and geographic region on medical charges. Descriptive analysis was followed by multiple linear regression, nonlinear specification, interaction modelling, diagnostic testing, heteroskedasticity-consistent inference, and quantile regression. The baseline model accounted for about 75% of the variation in charges; smoking, age, and BMI were most strongly associated with charges. A nonlinear age term and the smoking × BMI interaction term enhanced model fit, leading to a greater proportion of variance explained, of about 87%. There were no cases of non-normal residual behaviour and the level of multicollinearity was low but heteroskedasticity was high, according to the diagnostic testing. Standard errors were thus supplemented by robust HC3, to enhance the statistical inference. The additional results of the quantile regression showed that none of the effects of predictors was uniform over the expenditure distribution. The coefficient on BMI was especially large at 75th and 90th deciles and expenditure differences were especially large at higher expenditure levels, for smoking. These results illustrate that medical expenditure should be understood by using an integrated statistical framework that accounts for the nonlinear effects, interaction terms, robust inference and distribution sensitive modelling, rather than just average relationships.