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

Philip S. Rosenberg and Mitchell H. Gail

Journal of the Royal Statistical Society Series C, 1991, vol. 40, issue 2, 269-282

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.

Date: 1991
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