Reports on HIV/AIDS: 1990

NOVEMBER 30, 1990, MMWR, Vol. 39, RR-16 [inclusive page numbers]
incidence, especially in projecting AIDS cases by extrapolation. Because variations in
the numbers of cases diagnosed from period to period can obscure changing trends,
adjusted data on incidence were plotted (Figures 1-3) with smoothed curves obtained
from the lowess procedure (A2). This procedure requires no assumption about the
overall trend in the data. A fitted value is computed for each month by weightedleast-squares linear regression by using the adjusted number of cases diagnosed
during an interval around the month (here, the 25% of months closest to the chosen
month). Adjusted data on incidence, not the smoothed data, were used in backcalculation and extrapolation analyses.
2. Statistical methods used to estimate cumulative HIV infections from
back-calculation
Back-calculation can be used to estimate cumulative HIV incidence (i.e., the total
number of past HIV infections needed to account for the observed number of AIDS
cases). The resulting estimate of cumulative HIV incidence can then be used to
estimate HIV prevalence.
Five analysts used back-calculation to estimate cumulative HIV infections (Appendix B, Table B1). All analyses summarized in Table B1, with the exception of
Brookmeyer's, used a standard incubation period distribution (median, approximately 10 years) that did not change with time (A3). Brookmeyer, Harris, and
Rosenberg used adjusted AIDS incidence through either mid-1987 or mid-1989 and a
maximum likelihood procedure to estimate the total number infected and the
parameters in a probability distribution, with an assumed form for HIV incidence
(A4,A5). Hyman fit adjusted AIDS incidence through mid-1989 extended by his
extrapolation projections through 1993. He used numerical quadrature methods to
estimate the parameters in the distribution of the dates of HIV infection among
persons who are now infected (A6). Each of these analyses was based on CDC
estimates of reporting delays for AIDS cases.
Hay fit his estimates of adjusted AIDS incidence among adults and adolescents
through 1989 by using a least squares method, subject to the constraint that HIV
incidence in each year must be nonnegative (A7,A8). He excluded pediatric cases
because the incubation time may be shorter for children (A9). Hay's estimates of
adjusted incidence are less than the corresponding CDC estimates. Using the CDC
estimates increased the estimates of cumulative HIV infections 14%-25% (A8) and
therefore might be expected to increase his AIDS case projections by approximately
20%.
To account for the effect of recent changes in the distribution of incubation periods
on back-calculation analyses, Brookmeyer used a method that he developed with Liao
(AO0). They extended the back-calculation procedure to permit the distribution of
incubation periods to change for a specified proportion of those infected, with the
change starting at a specified calendar time. They also extended the procedure to
include a model for a two-stage incubation period; stage one was HIV seroconversion
to CD4+ cell depletion, and stage two was CD4+ cell depletion to diagnosed disease
meeting the AIDS case definition. Brookmeyer applied this method to AIDS cases
diagnosed through June 1989, assuming a change for the incubation distribution
starting in July 1987. On the basis of data from clinical trials, he assumed that therapy
reduces the risk of progression within each stage by 65%. During the second stage, in
a clinical trial setting, the risk of progression to AIDS among treated patients with

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