Modeling Transformed Health Care Cost with Unknown Heteroskedasticity

Log models are widely used to deal with skewed outcome such as health expenditure. They improve the precision of the estimates and diminish the influence of outliers. Retransformation is generally required after estimation and the evidence of heteroskedasticity complicates the process. Smearing estimation suggested in the literature only works for homoskedastic errors or heteroskedastic errors due to categorical variables. Generalized linear models have been proposed as an alternative approach for log models when there exists unknown forms of heteroskedasticity. Recent literature shows that log models are superior to generalized linear models under certain conditions. We present a method for applying transformation that accounts for any form of heteroskedasticity. Our proposed model assumes that errors achieve normality. Hetersokedasticity is modeled seperately. Simulation studies are conducted. We also used the Medstat MarketScan Database to estimate healthcare costs for asthma patients. Finally, a comparison of the method with smearing estimators and generalized linear model (GLM) estimators is established. Log-transformed health care costs of asthma patients were normal. There was an evidence of heteroskedasticity. Confirming the simulation study, heteroskedasiticity adjusted retransformed costs had the lowest mean squared error relative to estimators from smearing retransformation or generalized linear model. This study shows that if log-transformed costs are normally distributed, heteroskedasticity adjusted retransformation produces more efficient results. Copyright c © 2007