Estimating the VA total health care cost using a semi-parametric heteroscedastic two-part model

  • X. H. Zhou
  • G. Qin
  • M. L. Maciejewski


To appropriately assess the impact of the establishment of community-based outpatient clinics (CBOCs) on the total health care costs in a VA study, we need to deal with three methodological problems inherent in the data. The first problem is skewness of the data. The second one is zero costs for some patients. The third one is heteroscedasticity. We proposed a semi-parametric heteroscedastic two-part transformation regression model to deal with these problems, and the proposed model would allow us to explicit model heteroscedasticity.


Extra zeros Health care costs Heteroscedastic regression model Retransformation Skewed data Smearing Two-part model 



Professor Xiao-Hua Zhou is presently a Core Investigator and Senior Biostatistician at the Northwest HSR&D Center of Excellence within the VA Puget Sound Health Care System. Matt Maciejewski is presently a Core Investigator at the Northwest HSR&D Center of Excellence within the VA Puget Sound Health Care System. The research reported here was supported by Department of Veterans Affairs, Veterans Health Administration, Health Services Research and Development Service, ECI-03-206 and in part by AHRQ grant R01HS013105. We would like to thank John Fortney for providing us with the data.


  1. Ai, C., Norton, E.C.: Standard errors for the retransformation problem with heteroscedasticity. J. Health Economics 19, 697–718 (2000)CrossRefGoogle Scholar
  2. Carroll, R.J., Ruppert, D.: Comment on “The analysis of transformed data" by D.V. Hinkley and G. Runger. J. Am. Stat. Assoc. 79, 312–313 (1984)Google Scholar
  3. Crisp, A., Burridge, J.: A note on nonregular likelihood function in heteroscedastic regression. Biometrika 81, 585–587 (1994)CrossRefGoogle Scholar
  4. Duan, N.: Smearing estimate: A nonparametric retransformation estimate. J. Am. Stat. Assoc. 78, 605–610 (1983)CrossRefGoogle Scholar
  5. Fortney, J., Rost, K., Warren, J.: Comparing alternative methods of measuring geographic access to health services. Health Serv. Outcomes Res. Methodol. 1, 173–184 (2000)CrossRefGoogle Scholar
  6. Fortney, J., Maciejewski, M.L., Warren, J., Burgess, J.F.: Does improving geographic access to VA primary care services impact patients’ patterns of utilization and costs?. Inquiry 42, 29–42 (2005)PubMedGoogle Scholar
  7. Lee, S.M.S.: On a class of m out of n bootstrap confidence intervals. J. Roy. Stat. Soc. B 61, 901–911 (1999)CrossRefGoogle Scholar
  8. Manning, W.G.: The logged dependent variable, heteroscedasticity, and the retransformation. J. Health Economics 17, 283–295 (1998)CrossRefGoogle Scholar
  9. Manning, W.G., Mullahy, J.: Estimating log models: to transform or not to transform? J. Health Economics 20, 461–494 (2001)PubMedCrossRefGoogle Scholar
  10. Park, R.: Estimation with Heteroskedastic Error Terms. Econometrica 34, 888 (1966)CrossRefGoogle Scholar
  11. Taylor, J.M.G.: The retransformed mean after a fitted power transformation. J. Am. Stat. Assoc. 81, 114–118 (1986)CrossRefGoogle Scholar
  12. Weinberger M., Oddone E.Z., Henderson W.G.: Does increased access to primary care reduce hospital readmissions? Veterans affairs cooperative study group on primary care and hospital readmission. N. Engl. J. Med. 334, 1441–1447 (1996)PubMedCrossRefGoogle Scholar
  13. Welsh, A.H., Zhou, X.H.: Estimating the retransformed mean in a heteroskedastic two-part model. UW working series, working paper 215 (2003)Google Scholar
  14. Zhou, X.H., Stroupe, K.T., Tierney, W.M.: Regression analysis of health care charges with heteroskedasticity. JRSS Series C 50, 303–312 (2001)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.U.S. Department of Veterans AffairsPuget Sound Health Care SystemSeattleUSA
  2. 2.Department of BiostatisticsUniversity of WashingtonSeattleUSA
  3. 3.Department of Mathematics and StatisticsGeorgia State UniversityAtlantaUSA
  4. 4.Department of Health ServicesUniversity of WashingtonSeattleUSA

Personalised recommendations