Reports on HIV/AIDS: 1990

NOVEMBER 30, 1990, MMWR, Vol. 39, RR-16 [inclusive page numbers]
Appendix A
HIV-Prevalence Estimates and AIDS Case Projections:
Statistical Methods
Back-calculation and extrapolation, the statistical methods used to estimate HIV
prevalence and to predict future AIDS cases, are based on surveillance data on AIDS.
Preliminary analyses of the surveillance data must be carried out before using these
methods for making estimates and projections. This appendix summarizes these
analyses and explains the methods then used to derive estimates of HIV prevalence
and AIDS case projections.
Section 1 below describes the methods by which AIDS surveillance data were
adjusted for reporting delays, the methods used to account for the effect of the 1987
change in the AIDS surveillance definition, and the methods used to examine time
trends in adjusted data on AIDS incidence. Sections 2 and 3 summarize the statistical
methods used to estimate cumulative HIV incidence from back-calculation and to
predict future AIDS cases, respectively. Section 4 describes the methods by which
HIV-prevalence estimates were derived from estimates of cumulative HIV incidence.
Section 5 contains estimates of length of period of survival after an AIDS diagnosis.
These estimates were used to predict future deaths among persons diagnosed as
having AIDS, numbers of persons alive with AIDS, and deaths associated with HIV
infection.
1. Analysis of AIDS surveillance data
Adjusting for reporting delays. AIDS cases reported through September 1989
were adjusted for reporting delays estimated from a maximum likelihood statistical
procedure (Al ). This procedure is based on the assumption that reporting delays are
independent of time.
Nationally the proportion of cases reported <3 months after diagnosis changes
over time, but the proportions reported with delays of >1 quarter are nearly constant
over calendar time. Because of this pattern, only AIDS cases diagnosed through June
1989 were used. Back-calculation analyses were based on quarterly incidence, with
delays estimated for each risk group separately. The CDC extrapolation analyses were
based on monthly incidence, with delays estimated for all risk groups combined.
(Separating the risk groups changed the figures only slightly.) Analyses of AIDS cases
in individual cities, in risk-behavior groups, and in demographic groups were based
on reported cases adjusted for reporting delays in the corresponding groups.
Accounting for the revision in the AIDS case definition. Data on AIDS incidence
were analyzed both for all cases and separately for cases with diagnoses consistent
with the pre-1987 case definition. Consistent cases are those with a diagnosis
(definitive or presumptive) of a disease that fit the pre-1987 definition. Cases not
consistent with the pre-1987 definition are mainly those diagnosed on the basis of
wasting syndrome, HIV-associated encephalopathy, or disseminated tuberculosis.
Examining time trends in AIDS incidence. To choose the time period to model
and the type of model to fit, it is important to identify changes in trends of AIDS

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