Statistical Science

Backcalculation of HIV Infection Rates

Peter Bacchetti, Mark R. Segal, and Nicholas P. Jewell

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Abstract

Backcalculations is an important method for reconstructing past rates of human immunodeficiency virus (HIV) infection and for estimating current prevalence of HIV infection and future incidence of acquired immunodeficiency syndrome (AIDS). This paper reviews the backcalculation technique, focusing on the key assumptions of the method, including the necessary information regarding incubation, reporting delay, and models for the infection curve. A summary is given of the extend to which the appropriate external information is available and whether checks of the relevant assumptions are possible through use of data on AIDS incidence from surveillance systems. A likelihood approach to backcalculation is described and implemented on AIDS incidence data in the United States. New features of the approach influence incorporation of seasonal variation in diagnosis rates, smooth nonparametric estimation of both the HIV infection curve and nonstationary aspects of the incubation period and reporting delay distributions, and an analysis of residuals from backcalculation fits. Unexplained lack of fit is examined and discussed. A fundamental concern is the appropriate acknowledgment of uncertainty associated with backcalculation estimates caused by misspecified assumptions and inaccurate external estimates of key components of the technique. Such uncertainty limits the usefulness of backcalculation and highlights the need for complementary approaches.

Article information

Source
Statist. Sci. Volume 8, Number 2 (1993), 82-101.

Dates
First available: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.ss/1177010994

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/ss/1177010994

Citation

Bacchetti, Peter; Segal, Mark R.; Jewell, Nicholas P. Backcalculation of HIV Infection Rates. Statistical Science 8 (1993), no. 2, 82--101. doi:10.1214/ss/1177010994. http://projecteuclid.org/euclid.ss/1177010994.


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See also

  • See Comment: Ron Brookmeyer. [Backcalculation of HIV Infection Rates]: Comment. Statist. Sci., Volume 8, Number 2 (1993), 102--104.
  • See Comment: John B. Carlin, Andrew Gelman. [Backcalculation of HIV Infection Rates]: Comment: Assessing Uncertainty in Backprojection. Statist. Sci., Volume 8, Number 2 (1993), 104--106.
  • See Comment: Mitchell H. Gail, Philip S. Rosenberg. [Backcalculation of HIV Infection Rates]: Comment. Statist. Sci., Volume 8, Number 2 (1993), 107--109.
  • See Comment: Victor De Gruttola, Marcello Pagano. [Backcalculation of HIV Infection Rates]: Comment. Statist. Sci., Volume 8, Number 2 (1993), 109--109.
  • See Comment: John M. Karon, Glen A. Satten. [Backcalculation of HIV Infection Rates]: Comment. Statist. Sci., Volume 8, Number 2 (1993), 109--112.
  • See Comment: Patricia J. Solomon, Susan R. Wilson. [Backcalculation of HIV Infection Rates]: Comment. Statist. Sci., Volume 8, Number 2 (1993), 112--114.
  • See Comment: Peter Bacchetti, Mark R. Segal, Nicholas P. Jewell. [Backcalculation of HIV Infection Rates]: Rejoinder. Statist. Sci., Volume 8, Number 2 (1993), 114--119.