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 is
equal to a prescribed value with ease.
Since SARS showed a severe case fatality ratio, our concern is
to know such a case fatality ratio as soon as possible after
a similar outbreak begins. The epidemiological determinants
of spread
of SARS can be dealt with as the probabilistic growth curve models,
and the parameter estimation procedure for the probabilistic
growth curve models may similarly be treated as the lifetime
analysis.
Thus, we try to do the parameter estimation to the SARS cases
for the infected cases, fatal cases, and cured cases here,
as we usually
do it in 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 case fatality ratio may be estimated by these two numbers.
We may also estimate the case fatality ratio 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, 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 case fatality ratio and its confidence interval are
easily obtained in a numerical sense.
This paper mainly treats the case in Hong Kong. The estimated
epidemiological determinants of spread of SARS, fitted to
the infected, fatal,
and cured cases in Hong Kong, could be the logistic distribution
function among the logistic, lognormal, gamma, and Weibull
models. Using the proposed method, it would be appropriate
that the SARS
case fatality ratio is roughly estimated to be 17% in Hong
Kong. Worldwide, it is roughly estimated to be about 12−18%,
if we
consider the safety side without the Chinese case. Unlike
the questionably
small confidence intervals for the case fatality ratio using
the truncated models, the case fatality ratio in the proposed
model
provides a reasonable confidence interval.
