The mixed trunsored model with applications to the SARS case


H. Hirose


"3rd Hawaii International Conference on Statistics, Mathematics and Related Fields", June 9-12, 2004, at Sheraton Waikiki Hotel,Honolulu


The trunsored model, which is a new incomplete data model regarded as a unified model of the censored and truncated models in lifetime analysis, can not only estimate the ratio of the fragile population to the mixed fragile and durable populations or the cured and fatal mixed populations, but also test a hypothesis that the ratio equals to a prescribed value with ease.

Since SARS showed a severe death rate, our concern is to know such a death rate as soon as possible after a similar outbreak begins. The epidemic analysis of SARS differs from the lifetime analysis, but the probabilistic growth curves fitted to the infected cases, fatal cases, and cured cases of SARS can similarly be treated as the lifetime analysis. Using the truncated data models to the infected and fatal cases with some censoring time, we may estimate the total (or final) numbers of the patients and deaths, and the death rate may be estimated by these two numbers. We may also estimate the death rate using the numbers of the patients and recoveries, but this estimate differs from that using the numbers of the patients and deaths, especially when the censoring time is located at early stages.

To circumvent this inconsistency, and to obtain much more reliable estimates, we propose a mixed trunsored model, an extension of the trunsored model, which can use the data of the patients, deaths, and recoveries simultaneously. The estimate of the death rate and its error are easily and stably obtained in a numerical sense. This paper mainly treats the case in Hong Kong.


Key Words
truncated data; censored data; grouped data; lognormal distribution; Weibull distribution; gamma distribution; death rate; bootstrap.



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