A method to obtain the estimate and its confidence interval for
the number of fragile samples in mixed populations of the fragile
and durable samples, i.e., in the trunsored model, is introduced.
The confidence interval in the trunsored model is compared with
that in the truncated model. Although the maximum likelihood estimates
for the parameters in the underlying probability distribution in
both models are the same, the confidence interval for the estimated
number of samples in the trunsored model is differ from that in
the truncated model. When the censoring time goes to infinity,
the confidence interval in the truncated model converges to zero,
whereas the confidence interval in the trunsored model converges
to a positive constant value.
The error for the number of fragile samples in the trunsored model
is affected by the two kinds of fluctuation effect due to the censoring
time: one is the fluctuation of the parameter estimates, and the
other is the ratio of the number of fragile samples to the total
number of samples. However, in the truncated model, the fluctuation
depends only on the parameter estimates, and the error by this
effect will vanish when the censoring time goes to infinity.
A typical example of the method is applied to the case fatality
ratio for the infectious diseases such as SARS.
