| Summary: | 碩士 === 國立中正大學 === 數理統計研究所 === 87 === In survival analysis, we often use the Kaplan-Meier method to estimate and plot survival curves. We know that a person's exact survival time become missing after the follow-up period, when the person does still survives before the study ends or the person
is lost during the study period. However, when the data become heavily censored, the Kaplan-Meier estimator will become liberal causing serious loss of accuracy. The drawback with the Kaplan-Meier estimator is that it ignores the information ontained in the number of missing persons. It is a biased estimate of survival function. This paper suggests an improvement of
the Kaplan-Meier estimator under the heavy censoring at right side. The new semi-parametric estimator is to use the parametric
model to find out the death portion of the censored data. Assuming that the underlying the survival distribution belongs to some
parametric family. Then the maximum likelihood estimator is used to estimate the survial function. However, in reality, we can
only give educated guess on the actual parametric survival distribution. We consider typical models including the exponential
distribution, weibull distribution and lognormal distribution in this study. The new semi-parametric estimator is proposed for large sample.
An example estimating the survival function of patients with angina pectoris in the Mayo Clinic is also provided for purpose of illustration.
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