Use of Empirical Transformations in Nonparametric Back-projection of Aids Incidence Data

  • Niels G. Becker
  • Lyndsey F. Watson

Abstract

Among methods used for estimating the HIV-infection incidence curve, smoothed nonparametric back-projection has a number of attractive features. Here an empirical transformation is incorporated into the method for the purpose of reducing bias and its effectiveness for reducing bias is studied.

Keywords

Infection Intensity Calendar Time Time Transformation Smoothing Kernel Infection Incidence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Bacchetti, P. and Jewell, N.P. (1991). Nonparametric estimation of the incubation period of AIDS based on a prevalent cohort with unknown infection times. Biometrics, 47, 947–960.PubMedCrossRefGoogle Scholar
  2. Bacchetti, P. and Moss, A.R. (1989). Incubation period of AIDS in San Francisco. Nature, 338, 251–253.PubMedCrossRefGoogle Scholar
  3. Becker, N.G. and Marschner, I.C. (1991). A method for estimating the age-specific relative risk of HIV infection from AIDS incidence data. Submitted for publication.Google Scholar
  4. Becker, N.G., Watson, L.F. and Carlin, J.B. (1991). A method of non-parametric back-projection and its application to AIDS data. Statistics in Medicine, 10, 1527–1542.PubMedCrossRefGoogle Scholar
  5. Becker, N.G. and Yip, P. (1989). Analysis of variations in an infection rate. Australian Journal of Statistics, 31, 42–52.CrossRefGoogle Scholar
  6. Brookmeyer, R. and Gail, M.H. (1988). A method for obtaining short-term projections and lower bounds on the size of the AIDS epidemic. Journal of the American Statistical Association, 83, 301–308.CrossRefGoogle Scholar
  7. Brookmeyer, R. and Goedert, J. (1989). Censoring in an epidemic with an application to hemophiliac-associated AIDS. Biometrics, 45, 325–335.PubMedCrossRefGoogle Scholar
  8. Brookmeyer, R. and Liao, J. (1990) Statistical modelling of the AIDS epidemic for forecasting health care needs. Biometrics, 46, 1151–1163.PubMedCrossRefGoogle Scholar
  9. Centers for Disease Control (1990). HIV prevalence estimates and AIDS case projections for the US: report based upon a workshop. Morbidity and Mortality Weekly Report, 39, RR-16.Google Scholar
  10. Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion), Journal of the Royal Statistical Society, B, 39, 1–38.Google Scholar
  11. Ramlau-Hansen, H. (1983). Smoothing counting process intensities by means of kernel functions. Annals of Statistics, 11, 453–466.CrossRefGoogle Scholar
  12. Rosenberg, P.S. and Gail, M.H. (1991). Backcalculation of flexible linear models of the HIV infection curve. Applied Statist, 40, 269–282.CrossRefGoogle Scholar
  13. Ruppert, D. and Cline, D.B.H. (1991). Transformation-kernel density estimation - bias reduction by empirical transformations. Submitted for publication.Google Scholar
  14. Silverman, B.W. (1986). Density Estimation for Statistics and data analysis. London: Chapman and Hall.Google Scholar
  15. Silverman, B.W., Jones, M.C., Wilson, J.D. and Nychka, D.W. (1990). A smoothed EM approach to indirect estimation problems, with particular reference to stereology and emission tomography. Journal of the Royal Statistical Society, B, 52, 271–324.Google Scholar
  16. Taylor, J.M. (1989). Models for the HIV infection and AIDS epidemic in the United States. Statistics in Medicine, 8, 45–58.PubMedCrossRefGoogle Scholar
  17. Wand, M.P., Marron, J.S. and Ruppert, D. (1991). Transformations in density estimation (with discussion). Journal of the American Statistical Association, 86, 341–361.Google Scholar
  18. Watson, L.F. (1990). Prediction of AIDS incidence using the method of back-projection. MSc Thesis, La Trobe University.Google Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Niels G. Becker
    • 1
  • Lyndsey F. Watson
    • 1
  1. 1.Department of StatisticsLa Trobe UniversityBundooraAustralia

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