| Random weighting method for Cox’s proportional hazards model |
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| 摘 要： | Variance of parameter estimate in Cox’s proportional hazards model is based on asymptotic variance. When sample size is small, variance can be estimated by bootstrap method. However, if censoring rate in a survival data set is high, bootstrap method may fail to work properly. This is because bootstrap samples may be even more heavily censored due to repeated sampling of the censored observations. This paper proposes a random weighting method for variance estimation and confidence interval estimation for proportional hazards model. This method, unlike the bootstrap method, does not lead to more severe censoring than the original sample does. Its large sample properties are studied and the consistency and asymptotic normality are proved under mild conditions. Simulation studies show that the random weighting method is not as sensitive to heavy censoring as bootstrap method is and can produce good variance estimates or confidence intervals.
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Random weighting method for Cox’s proportional hazards model |
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| Authors: | WenQuan Cui Kai Li YaNing Yang and YueHua Wu |
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| Institution: | (1) Department of Statistics and Finance, University of Science and Technology of China, Hefei, 230026, China;(2) Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada |
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| Abstract: | Variance of parameter estimate in Cox’s proportional hazards model is based on asymptotic variance. When sample size is small,
variance can be estimated by bootstrap method. However, if censoring rate in a survival data set is high, bootstrap method
may fail to work properly. This is because bootstrap samples may be even more heavily censored due to repeated sampling of
the censored observations. This paper proposes a random weighting method for variance estimation and confidence interval estimation
for proportional hazards model. This method, unlike the bootstrap method, does not lead to more severe censoring than the
original sample does. Its large sample properties are studied and the consistency and asymptotic normality are proved under
mild conditions. Simulation studies show that the random weighting method is not as sensitive to heavy censoring as bootstrap
method is and can produce good variance estimates or confidence intervals.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 10471136, 10671189), PhD Program Foundation
of Ministry of Education of China and Foundations from the Chinese Academy of Sciences |
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| Keywords: | bootstrap Cox model censoring rate random weighting consistency asymptotic normality |
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