Ӧ�ø���ͳ�� 2011, 27(6) 614-632 DOI:      ISSN: 1001-4268 CN: 31-1256

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Improving Estimation Efficiency of Cox Model via Using\\
Other Related Survival Data
Cui Wenquan
University of Science and Technology of China
Abstract:

Cox model is the most popular model in
modelling the relationship between a survival outcome and predictive
covariates, and has been gotten great success about regression
modelling survival data. It is well known that the maximum partial
likelihood estimates of regression parameters of Cox model are
consistent, asymptotically normal and semiparametrically efficient.
In this paper, based on marginal proportional hazards model and a
partitioning-based method, we develop an approach to improve
estimation efficiency of regression parameters in Cox model through
introducing some other handy or easily collected survival data.
Practically, for each subject, there frequently exist some other
possibly-multivariate survival data available in addition to the
main endpoint of survival times, which are easily collected or
handy, and belong to the same subject or group as the survival data
of interest. All the data construct multivariate survival data, and
the famous WLW model, one important marginal proportional hazards
model of multivariate survival data proposed in 1989 by Wei, Lin and
Weissfels (1989), is the model of natural choice to regression
modelling the aforementioned multivariate survival data. But, as
pointed out in this paper, by making direct use of the WLW method ,
the estimation efficiency of regression parameters of interest
cannot be improved. Based on the partitioning-based method for WLW
model, an approach to improve the estimation of regression parameter
of Cox model is proposed and discussed. Simulation studies are
conducted to investigate behavior of the proposed approach under
practical sample size. Our results show that it performs well, only
if the constructed multivariate survival data are correlated between
the survival data of interest and the introduced survival data, even
for small to moderate sample size.

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