Backcalculation of flexible linear models of the human immunodeficiency virus infection curve

The authors present a regression approach to the backcalculation of flexible linear models of the HIV infection curve. They note that "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." These concepts are illustrated by projecting AIDS incidence in the United States up to 1993.