The method for making non-parametric inferences about the probability
distribution of the incubation period for AIDS from transfusion-relate
d AIDS data is extended to include data on individuals who have tested
positive for HIV but do not have AIDS at the time of analysis. The me
thod is illustrated with data on individuals infected by transfusion i
n Australia. The shape of the incubation distribution, as represented
by the truncated distribution function, can be estimated, but the addi
tional data contribute very little to the estimation of this shape. Wi
th a general non-parametric form for the incubation distribution the a
dditional data do not overcome the identifiability problem that exists
for non-parametric estimation of this distribution from AIDS data alo
ne. If quarterly rates for HIV testing are specified, the additional d
ata make it possible to estimate the cumulative distribution function
for the incubation period. This is also possible when a simple paramet
ric form, with one or two unknown parameters, is used for the testing
rates. However, the additional data do not allow effective estimation
of the HIV testing rates. The estimated shape of the incubation distri
bution indicates a higher proportion of short incubation periods than
an earlier estimate based on U.S. data. Estimates for the incubation d
istribution itself do not vary much over a plausible range of HIV test
ing rates.