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Health Services Research & Development

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2012 HSR&D/QUERI National Conference Abstract

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2012 National Meeting

1013 — A Nonparametric Heteroscedastic Transformation Model for VA Cost Data

Zhou XA, and Ding XB, VA Seattle Medical Center;

Objectives:
Rich data resources in VA have begun to be utilized to evaluate costs and improve the efficiency and quality of care Veterans receive. To date, analyses of VA cost data have been limited in their scope and validity due to many special distributional features of healthcare costs. One of the features is that cost observations are highly skewed to the right because a small percentage of patients invariably incur extremely high costs relative to most patients and heteroscedasticity (the variance of cost data depends on patient’s characteristics). Without taking these characteristics into account, statistical analysis of cost data can lead to unreliable inferences. In this study, we develop and validate a non-parametric heteroscedastic regression model for VA healthcare costs that allows one to account for skewness and heteroscedasticity in the analysis of costs.

Methods:
In this study, we develop new non-parametric heterocedastic regression models for highly skewed costs with heteroscedasticity. Our proposed approach is to assume there exists an unknown transformation that makes the mean of healthcare costs linear, leaving us to model any heteroscedasticity and to account for possible non-normality of the error term. When the transformation is non-linear, the expected value of costs on the original scale depends on both mean and variance of the transformed costs. By correctly modeling heteroscedasticity, we can provide more efficient estimation of the expected cost of a patient. Using techniques in asymptotic theory for a semi-parametric mode, we show the proposed estimator is consistent and asymptotically normally distributed. Using simulation studies, we compare relative performance of the newly proposed method with existing methods. Finally, we apply the proposed method to VA cost data for 31 common chronic conditions. The patient-level cost data are from the VA Decision Support System (DSS), the VA Patient Treatment File (PTF), the VA Outpatient Clinic File (OCF), and the VA Vital Status Files.

Results:
Our theoretical work shows that the proposed estimators are consistent and asymptotically normal. Our extensive simulation study shows that the proposed estimators for the expected cost of a patient also have good finite-sample performance and outperform existing estimators. Our real example shows that the proposed method is able to provide more accurate estimates for the expected cost of a patient with one of 31 common chronic diseases in VHA.

Implications:
This study provides researchers and policy makers with new tools for examining VA's medical care costs with much more precision. Our newly proposed regression models have the following advantages over existing methods: (1) Our newly proposed transformation regression models for skewed costs allow both the transformation function and error distribution functions to be unknown and can handle unknown heteroscedasticity. (2) Our new non-parametric estimators are asymptotically normal with very good convergent rate. In addition, unlike existing tests for heteroscedasticity, our newly proposed non-parametric test allows us to test for the intrinsic heteroscedasticity of cost data without specifying a parametric form for the mean cost model and heteroscedasticity.

Impacts:
The improved statistical models will allow VA investigators to fully maximize information contained in VA's cost databases. The cost databases are maturing, with comprehensive data beginning in 2002. There is a wealth of information contained in these cost databases, however, current methods that do not address special features of the cost data within VA have limited reliability and accuracy in interpreting variation in costs. Our newly proposed regression models will provide value to VA researchers by allowing for multiple complex covariates to be appropriately included in cost models regardless of their distributional properties.


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