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.