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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
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.
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.
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.
Brookmeyer, R. (1991). Reconstruction and future trends of the AIDS epidemic in the United States. Science 253, 37–42.
Brookmeyer, R. and Damiano, A. (1989). Statistical methods for short-term projections of AIDS incidence. Statistics in Medicine 8, 23–34.
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.
Brookmeyer, R. and Goedert, J.J. (1989). Censoring in an epidemic with an application to hemophilia-associated AIDS. Biometrics 45, 325–335.
Brookmeyer, R. and Liao, J. (1990a) Statistical modelling of the AIDS epidemic for forecasting health care needs. Biometrics 46, 1151–1163.
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.
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.
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.
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.
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.
Harris, J.E. (1990). Reporting delays and the incidence of AIDS. Journal of the American Statistical Association 85, 915–924.
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.
Jewell, N.P. (1990). Some statistical issues in the epidemiology of AIDS. Statistics in Medicine 9, 1387–1416.
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.
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.
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.
Lawless, J.F. (1987). Negative binomial and mixed Poisson regression. Canadian Journal of Statistics 15, 209–225.
Lawless, J.F. (1991). Adjustments for reporting delays and the prediction of occurred but not yet reported events. Unpublished manuscript.
McCullagh, P. and Nelder, J.A. (1989). Generalized Linear Models. London: Chapman and Hall.
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.
Rosenberg, P. and Gail, M.H. (1991). Back-calculation of flexible linear models of the HIV infection curve. Applied Statistics 40, 269–282.
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.
Taylor, J.M.G. (1989). Models for the HIV infection and AIDS epidemic in the United States. Statistics in Medicine 8, 45–58.
White, H. (1982). Maximum likelihood estimation of misspecified models. Econometrics 50, 1–25.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media New York
About this chapter
Cite this chapter
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
Download citation
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