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Backcalculation of Flexible Linear Models of the Human Immunodeficiency Virus Infection Curve

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  • Philip S. Rosenberg
  • Mitchell H. Gail

Abstract

The method of backcalculation can be used both to estimate the number of persons infected with the human immunodeficiency virus (HIV) and to project future acquired immune deficiency syndrome (AIDS) incidence. We present a regression approach to backcalculation of flexible linear models of the HIV infection curve. These models include step functions and splines. Because expected AIDS incidence can be expressed as a linear function of unknown parameters, regression methods may be used to obtain parameter and covariance estimates for a variety of interesting quantities, such as the expected number of people infected in previous time intervals and the projected AIDS incidence in future time intervals. We exploit these ideas to show that estimates based on maximum likelihood are, for practical purposes, equivalent to approximate estimates based on quasi‐likelihood and on Poisson regression. These algorithms are readily implemented on a personal computer. We illustrate by projecting AIDS incidence in the USA.

Suggested Citation

  • Philip S. Rosenberg & Mitchell H. Gail, 1991. "Backcalculation of Flexible Linear Models of the Human Immunodeficiency Virus Infection Curve," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 40(2), pages 269-282, June.
    • Handle: RePEc:bla:jorssc:v:40:y:1991:i:2:p:269-282
    DOI: 10.2307/2347592
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    Cited by:

    1. Lessner, Lawrence, 1998. "Estimating HIV incidence: An ill-posed problem," Socio-Economic Planning Sciences, Elsevier, vol. 32(1), pages 45-55, March.
    2. Angela Noufaily & Paddy Farrington & Paul Garthwaite & Doyo Gragn Enki & Nick Andrews & Andre Charlett, 2016. "Detection of Infectious Disease Outbreaks From Laboratory Data With Reporting Delays," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 488-499, April.
    3. Wai-Yuan Tan & Si Chin Tang & Sho Rong Lee, 1998. "Estimation of HIV seroconversion and effects of age in the San Francisco homosexual population," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(1), pages 85-102.

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