Back-Calculation
1
Peter Bacchetti,
Peter Bacchetti
University of California, San Francisco, CA, USA
Search for more papers by this authorPeter Bacchetti,
Peter Bacchetti
University of California, San Francisco, CA, USA
Search for more papers by this authorFirst published: 15 July 2005
Abstract
Back-calculation estimates past infection rates of an epidemic disease by working backward from observed incidence. This requires: external knowledge about the distribution of incubation times between infection and disease, possibly including how it is changing over time; incidence data that have been adjusted for reporting delay, underreporting, and possibly seasonal effects; and a parametric model or smoothness assumption that imposes some structure on past infection rates. In the case of human immunodeficiency virus, sensitivity analyses have found that uncertainty in back-calculation is mainly due to uncertainty in these inputs. Projected incidence is obtained by applying the assumed incubation distribution to the estimated (and extrapolated) infection rates, but direct extrapolation of observed incidence may do as well or better in some circumstances.
References
- 1 Bacchetti, P. (1994). The impact of lengthening AIDS reporting delays and uncertainty about underreporting on incidence trends and projections, Journal of Acquired Immune Deficiency Syndromes 7, 860–865.
- 2 Bacchetti, P. (1994). Seasonal and other short-term influences on United States AIDS incidence, Statistics in Medicine 13, 1921–1931.
- 3 Bacchetti, P. (1995). Historical assessment of some specific methods for projecting the AIDS epidemic, American Journal of Epidemiology 141, 776–781.
- 4 Bacchetti P. (1996). Reporting delay of deaths with AIDS in the United States, Journal of Acquired Immune Deficiency Syndromes and Human Retrovirology 13, 363–367.
- 5 Bacchetti, P. & 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.
- 6 Bacchetti, P., Segal, M. R. & Jewell, N. P. (1993). Backcalculation of HIV infection rates, Statistical Science 8, 82–119.
- 7 Bacchetti, P., Koblin, B. A., van Griensven, G. J. P. & Hessol, N. A. (1996). Determinants of HIV disease progression among homosexual men, American Journal of Epidemiology 143, 526.
- 8 Bacchetti, P., Segal, M. R., Hessol, N. A. & Jewell, N. P. (1993). Differing AIDS incubation periods and their impacts on reconstructing HIV epidemics and projecting AIDS incidence, Proceedings of the National Academy of Sciences 90, 2194–2196.
- 9 Becker, N. G. & Chao, X. (1994). Dependent HIV incidences in back-projection of AIDS incidence data, Statistics in Medicine 13, 1945–1958.
- 10 Becker, N. G. & Marschner, I. C. (1993). A method for estimating the age-specific relative risk of HIV infection for AIDS incidence data, Biometrika 80, 165–178.
- 11 Becker, N. G., Watson, L. F. & Carlin, J. B. (1991). A method of nonparametric back-projection and its application to AIDS data, Statistics in Medicine 10, 1527–1542.
- 12 Biggar, J. (1990). AIDS incubation in 1891 HIV seroconverters from different exposure groups, AIDS 4, 1059–1066.
- 13 Brookmeyer, R. (1991). Reconstruction and future trends of the AIDS epidemic in the United States, Science 253, 37–42.
- 14 Brookmeyer, R. & Damiano, A. (1989). Statistical methods for short-term projections of AIDS incidence, Statistics in Medicine 8, 23–34.
- 15 Brookmeyer, R. & Gail, M. H. (1986). Minimum size of the acquired immunodeficiency syndrome (AIDS) epidemic in the United States, Lancet 2, 1320–1322.
- 16 Brookmeyer, R. & Gail, M. H. (1988). A method for obtaining short term predictions and lower bounds on the size of the AIDS epidemic, Journal of the American Statistical Association 83, 301–308.
- 17 Brookmeyer, R. & Liao, J. (1990). Statistical modelling of the AIDS epidemic for forecasting health care needs, Biometrics 46, 1151–1163.
- 18 Brookmeyer, R., Quinn, T., Shepherd, M., Mehendale, S., Rodrigues, J. & Bollinger, R. (1995). The AIDS epidemic in India: a new method for estimating current human immunodeficiency virus (HIV) incidence rates, American Journal of Epidemiology 142, 709–713.
- 19 Buehler, J. W., Berkelman, R. L. & Stehr-Green, J. K. (1992). The completeness of AIDS surveillance, Journal of Acquired Immune Deficiency Syndromes 5, 257–264.
- 20
Carlin, J. B. &
Gelman, A.
(1993).
Comment: assessing uncertainty in backprojection,
Statistical Science
8,
104–106.
10.1214/ss/1177010996 Google Scholar
- 21 Centers for Disease Control (1985). Revision of the case definition of acquired immune deficiency syndrome for national reporting-United States, Morbidity and Mortality Weekly Reports 34, 373–375.
- 22 Centers for Disease Control (1987). Revision of the CDC surveillance case definition for acquired immunodeficiency syndrome, Morbidity and Mortality Weekly Reports 36, 3 S–15 S.
- 23 Centers for Disease Control (1991). Pilot study of a household survey to determine HIV seroprevalence, Morbidity and Mortality Weekly Reports 40, 1–5.
- 24 Centers for Disease Control and Prevention (1992). 1993 revised classification system for HIV infection and expanded surveillance case definition for AIDS among adolescents and adults, Morbidity and Mortality Weekly Reports 41, (No. RR-17), 1–18.
- 25 Cooley, P. C., Hamill, D. N., Meyers, L. E. & Liner, E. C. (1993). The assumption of no long reporting delays may result in underestimates of US AIDS incidence, AIDS 7, 1379–1381.
- 26 Day, N. E., Gore, S. M., McGee, M. A. & South, M. (1989). Predictions of the 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.
- 27 DeGruttola, V. & Lagakos, S. W. (1989). Analysis of doubly-censored survival data, with application to AIDS, Biometrics 45, 1–11.
- 28 Gail, M. H., Rosenberg, P. S. & Goedert, J. J. (1990). Therapy may explain recent deficits in AIDS incidence, Journal of Acquired Immune Deficiency Syndromes 3, 296–306.
- 29 Gauvreau, K., DeGruttola, V. & Pagano, M. (1994). The effect of covariates on the induction time of AIDS using improved imputation of exact seroconversion times, Statistics in Medicine 13, 2021–2030.
- 30 Green, P. J. (1990). On use of the EM algorithm for penalized likelihood estimation, Journal of the Royal Statistical Society, Series B 52, 443–452.
- 31 Greenberg, A. E., Hindin, R., Nicholas, A. G., Bryan, E. L. & Thomas, P. A. (1993). The completeness of AIDS case reporting in New York City, Journal of the American Medical Association 269, 2995–3001.
- 32
Greenland, S.
(1996).
Historical HIV incidence modelling in regional subgroups: use of flexible discrete models with penalized splines based on prior curves,
Statistics in Medicine
15,
513–525.
10.1002/(SICI)1097-0258(19960315)15:5<513::AID-SIM175>3.0.CO;2-8 CAS PubMed Web of Science® Google Scholar
- 33 Gwinn, M., Pappaioanou, M., George, J. R., Hannon, W. H., Wasser, S. C., Redus, M. A., Hoff, R., Grady, G. F., Willoughby, A., Novello, A. C., Petersen, L. R., Dondero, T. J., Jr & Curran, J. W. (1991). Prevalence of HIV infection in childbearing women in the United States. Surveillance using newborn blood samples, Journal of the American Medical Association 265, 1704–1708.
- 34 Healy, M. J. R. & Tillet, H. E. (1988). Short-term extrapolation of the AIDS epidemic, Journal of the Royal Statistical Society, Series A 151, 50–65.
- 35 Hessol, N. A., Koblin, B. A., van Griensven, G. J. P., Bacchetti, P., Liu, J. Y., Stevens, C. E., Coutinho, R. A., Buchbinder, S. P. & Katz, M. H. (1994). Progression of human immunodeficiency virus type 1 (HIV-1) infection among homosexual men in hepatitis B vaccine trial cohorts in Amsterdam, New York City, and San Francisco 1978–1991, American Journal of Epidemiology 139, 1077–1087.
- 36 Hoover, D. R., Taylor, J. M. G., Kingsley, L., Chmiel, J. S., Munoz, A., He, Y. & Saah, A. (1994). The effectiveness of interventions on incubation of AIDS as measured by secular increases within a population, Statistics in Medicine 13, 2127–2139.
- 37
Jewell, N. P. &
Kalbfleisch, J. D.
(1992).
Marker models in survival analysis and applications to issues associated with AIDS, in
AIDS Epidemiology: Methodological Issues,
N. P. Jewell,
K. Dietz &
V. T. Farewell, eds.
Birkhauser,
Boston.
10.1007/978-1-4757-1229-2 Google Scholar
- 38 Kalbfleisch, J. D. & Lawless, J. F. (1988). Estimating the incubation period for AIDS patients, Nature 333, 504–505.
- 39 Kalbfleisch, J. D. & Lawless, J. F. (1989). Inference based on retrospective ascertainment: an analysis of the data on transfusion-related AIDS, Journal of the American Statistical Association 84, 360–372.
- 40
Karon, J. M.,
Devine, O. J. &
Morgan, W. M.
(1989).
Predicting AIDS incidence by extrapolating from recent trends, in
Mathematical and Statistical Approaches to AIDS Epidemiology,
C. Castillo-Chavez, ed.
Springer-Verlag,
New York, pp.
58–88.
10.1007/978-3-642-93454-4_3 Google Scholar
- 41 Kuo, J. -M., Taylor, J. M. G. & Detels, R. (1991). Estimating the AIDS incubation period from a prevalent cohort, American Journal of Epidemiology 133, 1050–1057.
- 42 Lagakos, S. W., Barraj, L. M. & DeGruttola, V. (1988). Nonparametric analysis of truncated survival data with applications to AIDS, Biometrika 75, 515–523.
- 43 Lawless, J. F. & Sun, J. (1992). A comprehensive back-calculation framework for the estimation and prediction of AIDS cases, in AIDS Epidemiology: Methodological Issues, N. P. Jewell, K. Dietz & V. T. Farewell, eds. Birkhauser, Boston.
- 44 Liao, J. & Brookmeyer, R. (1995). An empirical Bayes approach to smoothing in backcalculation of HIV infection rates, Biometrics 51, 579–588.
- 45 Marschner, I. C. (1994). Using time of first positive HIV test and other auxiliary data in back-projection of AIDS incidence, Statistics in Medicine 13, 1959–1974.
- 46 Morgan, W. M. & Curran, J. W. (1986). Acquired immunodeficiency syndrome: current and future trends, Public Health Reports 101, 459–465.
- 47 Munoz, A., Wang, M. -C., Bass, S., Taylor, J. M. G., Kingsley, L. A., Chmiel, J. S. & Polk, B. F. (1989). Acquired immunodeficiency syndrome (AIDS)-free time after human immunodeficiency virus type 1 (HIV-1) seroconversion in homosexual men, American Journal of Epidemiology 130, 530–539.
- 48
O'Sullivan, F.
(1986).
A statistical perspective on ill-posed inverse problems,
Statistical Science
1,
502–527.
10.1214/ss/1177013525 Google Scholar
- 49
Pagano, M.,
DeGruttola, V.,
MaWhinney, S. &
Tu, X. M.
(1992).
The HIV epidemic in New York City: statistical methods for projecting AIDS incidence and prevalence, in
AIDS Epidemiology: Methodological Issues,
N. P. Jewell,
K. Dietz &
V. T. Farewell, eds.
Birkhauser,
Boston.
10.1007/978-1-4757-1229-2_6 Google Scholar
- 50 Pagano, M., Tu, X. M., DeGruttola, V. & MaWhinney, S. (1994). Regression analysis of censored and truncated data: estimating reporting-delay distributions and AIDS incidence from surveillance data, Biometrics 50, 1203–1214.
- 51 Pappaioanou, M., Dondero, T. J., Peterson, L. R., Onorato, I. M., Sanchez, C. D. & Curran, J. W. (1990). The family of HIV seroprevalence surveys: objectives, methods, and uses of sentinel surveillance for HIV in the United States, Public Health Reports 105, 113–119.
- 52 Raab, G. M., Fielding, K. L. & Allardice, G. (1994). Incorporating HIV test data into forecasts of the AIDS epidemic in Scotland, Statistics in Medicine 13, 2009–2020.
- 53 Rosenberg, P. S. (1994). Backcalculation models of age-specific HIV incidence rates, Statistics in Medicine 13, 1975–1990.
- 54 Rosenberg, P. S. (1995). Scope of the AIDS epidemic in the United States, Science 270, 1372–1375.
- 55 Rosenberg, P. S. & Gail, M. H. (1990). Uncertainty in estimates of HIV prevalence derived by backcalculation, Annals of Epidemiology 1, 105–115.
- 56 Rosenberg, P. S. & Gail, M. H. (1991). Backcalculation of flexible linear models of the human immunodeficiency virus infection curve, Applied Statistics 40, 269–282.
- 57 Satten, G. A. & Longini, I. M. (1994). Estimation of incidence of HIV infection using cross-sectional marker surveys, Biometrics 50, 675–688.
- 58 Taylor, J. M. G. (1989). Models for the HIV infection and AIDS epidemic in the United States, Statistics in Medicine 8, 45–58.
- 59 Taylor, J. M. G., Kuo, J. -M. & Detels, R. (1991). Is the incubation period of AIDS lengthening?, Journal of Acquired Immune Deficiency Syndromes 4, 69–75.
- 60 van Griensven, G. J. P., Veugelers, P. J., Page-Shafer, K. A., Kaldor, J. M. & Schechter, M. T. (1996). Determinants of HIV disease progression among homosexual men, American Journal of Epidemiology 143, 525.
- 61 Verdecchia, A. & Mariotto, A. B. (1995). A back-calculation method to estimate the age and period HIV infection intensity, considering the susceptible population, Statistics in Medicine 14, 1513–1530.
- 62 Veugelers, P. J., Page, K. A., Tindall, B., Schechter, M. T., Moss, A. R., Winkelstein, W. W., Jr., Cooper, D. A., Craib, K. J. P., Charlebois, E., Coutinho, R. A. & van Griensven, G. J. P. (1994). Determinants of HIV disease progression among homosexual men registered in the Tricontinental Seroconverter Study, American Journal of Epidemiology 140, 747–758.
- 63 Wilson, S. R., Fazekas de St. Groth, C. & Solomon, P. J. (1992). Sensitivity analyses for the backcalculation method of AIDS projections, Journal of Acquired Immune Deficiency Syndromes 5, 523–527.
- 64 Zeger, S. L., See, L. -C. & Diggle, P. J. (1989). Statistical methods for monitoring the AIDS epidemic, Statistics in Medicine 8, 3–21.
- 65 Zwahlen, M., Vlahov, D. & Hoover, D. R. (1996). Determinants of HIV disease progression among homosexual men, American Journal of Epidemiology 143, 523–525.
Bibliography
- Brookmeyer, R. & Gail, M. H. (1994). AIDS Epidemiology: A Quantitative Approach. Oxford University Press, New York.
In addition to the above references, see the following for readable discussions of many topics related to back-calculation as applied to the AIDS epidemic:
