Abstract
We analyze three sets of doubly-censored cohort data on incubation times, estimating incubation distributions using semiparametric methods and assessing the comparability of the estimates. Weibull models appear to be inappropriate for at least one of the cohorts, and the estimates for the different cohorts are substantially different. We use these estimates as inputs for backcalculation, using a nonparametric method based on maximum penalized likelihood. The different incubations all produce fits to the reported AIDS counts that are as good as the fit from a nonstationary incubation distribution that models treatment effects, but the estimated infection curves are very different. We also develop a method for estimating nonstationarity as part of the backcalculation procedure and find that such estimates also depend very heavily on the assumed incubation distribution. We conclude that incubation distributions are so uncertain that meaningful error bounds are difficult to place on backcalculated estimates and that backcalculation may be too unreliable to be used without being supplemented by other sources of information on HIV prevalence and incidence.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bacchetti, P. (1990). Estimating the Incubation Period of AIDS by Comparing Population Infection and Diagnosis Patterns. Journal of the American Statistical Association 85: 1002–1008.
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.
Brookmeyer, R. (1991). Reconstruction and Future Trends of the AIDS Epidemic in the United States. Science 253: 37–42.
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. (1990). The Analysis of Delays in Disease Reporting: Methods and Results for the Acquired Immunodeficiency Syndrome. American Journal of Epidemiology 132: 355–365.
Centers for Disease Control (1990). HIV Prevalence Estimates and AIDS Case Projections for the United States: Report Based on a Workshop. Morbidity and Mortality Weekly Report 39 (RR-16): 1–31.
DeGruttola, V. and Lagakos, S.W. (1989). Analysis of Doubly-Censored Survival Data, with Application to AIDS. Biometrics 45: 1–11.
Efron, B. (1985). Bootstrap Confidence Intervals for a Class of Parametric Problems. Biometrika 72: 45–58.
Gail, M.H., Rosenberg, P.S. and Goedert, JJ. (1990). Therapy May Explain Recent Deficits in AIDS Incidence. Journal of Acquired Immune Deficiency Syndromes 3: 296–306.
Goedert, J.J., Kessler, C.M., Aledort, L.M., et al. (1989). A Prospective Study of Human Immunodeficiency Virus Type 1 Infections and the Development of AIDS in Subjects with Hemophilia. New England Journal of Medicine 321: 1141–1148.
Harris, J.E. (1990). Reporting Delays and the Incidence of AIDS. Journal of the American Statistical Association 85: 915–924.
Hessol, N.A., Lifson, A.R., O’Malley, P.M., Doll, L.S., Jaffe, H.W. and Rutherford, G.W. (1989). Prevalence, Incidence, and Progression of Human Immunodeficiency Virus Infection in Homosexual and Bisexual Men in Hepatitis B Vaccine Trials, 1978–1988. American Journal of Epidemiology 130: 1167–1175.
Rosenberg, P.S., Biggar, R.J., Goedert, J.J. and Gail, M.H. (1991). Backcalculation of the Number with Human Immunodeficiency Virus Infection in the United States. American Journal of Epidemiology 133: 276–285.
Rosenberg, P.S., Gail, M.H. and Pee, D. (1991). Mean Square Error of Estimates of HIV Prevalence and Short Term AIDS Projections Derived by Backcalculation. To appear.
Segal, M. and Bacchetti, P. (1990). Deficits in AIDS Incidence. Journal of Acquired Immune Deficiency Syndromes 3: 832–833.
Taylor, J.M.G. (1989). Models for the HIV Infection and AIDS Epidemic in the United States. Statistics in Medicine 8: 45–58.
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
Bacchetti, P.R., Segal, M.R., Jewell, N.P. (1992). Uncertainty About the Incubation Period of AIDS and Its Impact on Backcalculation. 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_3
Download citation
DOI: https://doi.org/10.1007/978-1-4757-1229-2_3
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4757-1231-5
Online ISBN: 978-1-4757-1229-2
eBook Packages: Springer Book Archive