Weighted censored quantile regression
Section 5. Conclusions
We proposed a method which effectively use the auxiliary information to improve the efficiency of the censored quantile regression estimator. We developed a methodology to transform the population information available from previous clinical trials or from some existing facts into non-parametric empirical likelihood based data driven probabilities. We developed the EL based data driven probability computation for both known and unknown cases of prior information regarding population parameters. We applied these probabilities as the weights into Peng and Huang (2008) censored quantile regression model. Our proposed method is efficient compared to standard censored quantile regression and provides consistent estimators of regression coefficients with asymptotic normality. Our simulations studies showed that the standard error of the parameter estimates based on our proposed methods (CQR-EL1 and CQR-EL2) is lower than the standard method (CQR) when we use all the covariates for computing the EL based data driven probability weights. Our proposed weighted censored quantile regression method provides almost the same coverage probability compared to the nominal level. In the case of heteroscedastic models, even the use of the auxiliary information regarding a subset of population parameters improved the efficiency of the estimates of all the parameters by using CQR-EL1. But in CQR-EL2, the efficiency improvement was limited to the corresponding subset of variables and intercept. In homoscedastic models, the use of auxiliary information regarding a subset of population parameters improved the efficiency only for that particular subset of parameters and the intercept in both CQR-EL1 and CQR-EL2. In the real data analysis, we observed that our proposed method provides more efficient quantile estimates and narrower confidence limits compared to the standard censored quantile regression.
Acknowledgements
The authors thank the Editor, Associate Editor, and referees whose suggestions greatly contributed to improving this paper. The research of Variyath and Fan are partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada.
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