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A Comprehensive Back-Calculation Framework for the Estimation and Prediction of AIDS Cases

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AIDS Epidemiology

Abstract

We discuss a model for the occurrence of AIDS cases that incorporates uncertainty due to the HIV infection process, incubation times, and delays in the reporting of AIDS cases. The analysis is based on AIDS cases diagnosed and reported by a given time, and provides standard errors for estimates and predictions that recognize the different sources of uncertainty. The approach is illustrated on U.S. AIDS cases reported to the end of 1989.

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Bibliography

  • Bacchetti, P., Segal, M. and Jewell, N.P. (1991). Uncertainty about the incubation period of AIDS and its impact on back calculation. In AIDS Epidemiology: Methodological Issues, N.P. Jewell, K. Dietz, and V. Farewell (eds); Boston: Birkhäuser - Boston.

    Google Scholar 

  • Becker, N.G., Watson, L.F. and Carlin, J.B. (1991). A method of nonparametric back-projection and its application to AIDS data. Statistics in Medicine 10, 1527–1542.

    Article  PubMed  CAS  Google Scholar 

  • Becker, N. and Watson, L. (1992). Use of empirical transformations in nonparametric back-projection of AIDS incidence data. In AIDS Epidemiology: Methodological Issues, N.P. Jewell, K. Dietz, and V. Farewell (eds); Boston: Birkhäuser Boston.

    Google Scholar 

  • Brookmeyer, R. (1991). Reconstruction and future trends of the AIDS epidemic in the United States. Science 253, 37–42.

    Article  PubMed  CAS  Google Scholar 

  • Brookmeyer, R. and Damiano, A. (1989). Statistical methods for short-term projections of AIDS incidence. Statistics in Medicine 8, 23–34.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Brookmeyer, R. and Goedert, J.J. (1989). Censoring in an epidemic with an application to hemophilia-associated AIDS. Biometrics 45, 325–335.

    Article  PubMed  CAS  Google Scholar 

  • Brookmeyer, R. and Liao, J. (1990a) Statistical modelling of the AIDS epidemic for forecasting health care needs. Biometrics 46, 1151–1163.

    Article  PubMed  CAS  Google Scholar 

  • Brookmeyer, R. and Liao, J. (1990b). The analysis of delays in disease reporting: methods and results for the acquired immunodeficiency syndrome. American Journal of Epidemiology 132, 355–365.

    PubMed  CAS  Google Scholar 

  • Brookmeyer, R. and Liao, J. (1992). Statistical methods for reconstructing infection curves. In AIDS Epidemiology: Methodological Issues, N.P. Jewell, K. Dietz, and V. Farewell (eds); Boston: Birkhäuser - Boston.

    Google Scholar 

  • Centers for Disease Control (1990). HIV Prevalence Estimates and AIDS Case Projections for the United States: Report Based upon a Workshop. Morbidity and Mortality Weekly Report, No. RR-16, November 30, 1990.

    Google Scholar 

  • Day, N.E., Gore, S.N., McGee, M.A. and South, M. (1989). Predictions of AIDS epidemic in the UK: The use of the back-projection method. Philosophical Transactions of the Royal Society of London, Series B 325, 123–134.

    Article  CAS  Google Scholar 

  • Gail, M.H. and Rosenberg, P. (1992). Perspectives on using backcalculation to estimate HIV prevalence and project AIDS incidence. In AIDS Epidemiology: Methodological Issues, N.P. Jewell, K. Dietz, and V. Farewell (eds); Boston: Birkhäuser - Boston.

    Google Scholar 

  • Harris, J.E. (1990). Reporting delays and the incidence of AIDS. Journal of the American Statistical Association 85, 915–924.

    Google Scholar 

  • Inagaki, N. (1973). Asymptotic relations between the likelihood estimating function and the maximum likelihood estimator. Annals of the Institute of Statistical Mathematics 265, 1–26.

    Article  Google Scholar 

  • Jewell, N.P. (1990). Some statistical issues in the epidemiology of AIDS. Statistics in Medicine 9, 1387–1416.

    Article  PubMed  CAS  Google Scholar 

  • Kalbfleisch, J.D. and Lawless, J.F. (1989). Inference based on retrospective ascertainment: an analysis of the data on transfusion-associated AIDS. Journal of the American Statistical Association 84, 360–372.

    Article  Google Scholar 

  • Kalbfleisch, J.D. and Lawless, J.F. (1991). Regression models for right truncated data, with applications to AIDS incubation times and reporting lags. Statistica Sinica 1, 19–32.

    Google Scholar 

  • Karon, J.M., Dondero, T.J. and Curran, J.W. (1988). The projected incidence of AIDS and estimated prevalence of HIV infection in the United States. Journal of Acquired Immune Deficiency Syndromes 1, 542–550.

    PubMed  CAS  Google Scholar 

  • Lawless, J.F. (1987). Negative binomial and mixed Poisson regression. Canadian Journal of Statistics 15, 209–225.

    Article  Google Scholar 

  • Lawless, J.F. (1991). Adjustments for reporting delays and the prediction of occurred but not yet reported events. Unpublished manuscript.

    Google Scholar 

  • McCullagh, P. and Nelder, J.A. (1989). Generalized Linear Models. London: Chapman and Hall.

    Google Scholar 

  • Pagano, M., DeGruttola, V., MaWhinney, S. and Tu, X.M. (1992). The HIV epidemic in New York City; projecting AIDS incidence and prevalence. In AIDS Epidemiology: Methodological Issues, N.P. Jewell, K. Dietz, and V. Farewell (eds); Boston: Birkhäuser - Boston.

    Google Scholar 

  • Rosenberg, P. and Gail, M.H. (1991). Back-calculation of flexible linear models of the HIV infection curve. Applied Statistics 40, 269–282.

    Article  PubMed  CAS  Google Scholar 

  • Solomon, P.J. and Wilson, S.R. (1990). Accommodating change due to treatment in the method of back projection for estimating HIV infection incidence. Biometrics 46, 1165–1170.

    Google Scholar 

  • Taylor, J.M.G. (1989). Models for the HIV infection and AIDS epidemic in the United States. Statistics in Medicine 8, 45–58.

    Article  PubMed  CAS  Google Scholar 

  • White, H. (1982). Maximum likelihood estimation of misspecified models. Econometrics 50, 1–25.

    Article  Google Scholar 

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© 1992 Springer Science+Business Media New York

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Lawless, J., Sun, J. (1992). A Comprehensive Back-Calculation Framework for the Estimation and Prediction of AIDS Cases. In: Jewell, N.P., Dietz, K., Farewell, V.T. (eds) AIDS Epidemiology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-1229-2_4

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  • DOI: https://doi.org/10.1007/978-1-4757-1229-2_4

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4757-1231-5

  • Online ISBN: 978-1-4757-1229-2

  • eBook Packages: Springer Book Archive

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