Regression analysis for long-term survival rate via empirical likelihood

In recent years, regression models have been shown to be useful for predicting the long-term survival probabilities of patients in clinical trials. For inference on the vector of regression parameters, there are semiparametric procedures based on normal approximations. However, the accuracy of such procedures in terms of coverage probability can be quite low when the censoring rate is heavy. In this paper, we apply an empirical likelihood ratio (ELR) method to the regression model and derive the limiting distribution of the ELR. On the basis of the result, we develop a confidence region for the vector of regression parameters. Furthermore, we use a simulation study to compare the proposed method with the normal approximation-based method proposed by Jung [Jung, S., 1996, Regression analysis for long-term survival rate. Biometrika, 83, 227–232.]. Finally, the proposed procedure is illustrated with data from a clinical trial.

[1]  D. Cox.  Regression Models and Life-Tables , 1972 .

[2]  Xiaotong Shen,et al.  Empirical Likelihood , 2002 .

[3]  A. Owen.  Empirical Likelihood Ratio Confidence Regions , 1990 .

[4]  Ian W. McKeague,et al.  Simultaneous confidence bands for ratios of survival functions via empirical likelihood , 2002 .

[5]  Yu-Sheng Hsu,et al.  Semiparametric Analysis for Additive Risk Model via Empirical Likelihood , 2005 .

[6]  Joseph P. Romano,et al.  Nonparametric confidence limits by resampling methods and least favorable families , 1990 .

[7]  Hengjian Cui,et al.  AN EXTENDED EMPIRICAL LIKELIHOOD FOR GENERALIZED LINEAR MODELS , 2003 .

[8]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[9]  Ian W. McKeague,et al.  CONFIDENCE TUBES FOR MULTIPLE QUANTILE PLOTS VIA EMPIRICAL LIKELIHOOD , 1999 .

[10]  Myles Hollander,et al.  Likelihood Ratio-Based Confidence Bands for Survival Functions , 1997 .

[11]  Art B. Owen,et al.  Empirical Likelihood for Linear Models , 1991 .

[12]  Bing-Yi Jing,et al.  Empirical Likelihood for a Class of Functionals of Survival Distribution with Censored Data , 2001 .

[13]  Bing-Yi Jing,et al.  Empirical Likelihood for Censored Linear Regression , 2001 .

[14]  Parameter estimation in regression for long-term survival rate from censored data , 2001 .

[15]  Song Xi Chen,et al.  On the accuracy of empirical likelihood confidence regions for linear regression model , 1993 .

[16]  Gang Li,et al.  On nonparametric likelihood ratio estimation of survival probabilities for censored data , 1995 .

[17]  A. Owen.  Empirical likelihood ratio confidence intervals for a single functional , 1988 .

[18]  Jian Shi,et al.  Empirical Likelihood for Partially Linear Models , 2000 .

[19]  J. N. K. Rao,et al.  Empirical Likelihood‐based Inference in Linear Models with Missing Data , 2002 .

[20]  Peter Hall,et al.  Pseudo-Likelihood Theory for Empirical Likelihood , 1990 .

[21]  Bing-Yi Jing,et al.  EMPIRICAL LIKELIHOOD FOR COX REGRESSION MODEL UNDER RANDOM CENSORSHIP , 2001 .

[22]  Bing-Yi Jing,et al.  Censored Partial Linear Models and Empirical Likelihood , 2001 .

[23]  DavidR . Thomas,et al.  Confidence Interval Estimation of Survival Probabilities for Censored Data , 1975 .

[24]  Thomas J. DiCiccio,et al.  Empirical Likelihood is Bartlett-Correctable , 1991 .

[25]  Sin-Ho Jung,et al.  Regression analysis for long-term survival rate , 1996 .

[26]  Song Xi Chen,et al.  Empirical Likelihood Confidence Intervals for Linear Regression Coefficients , 1994 .

[27]  Jane-ling Wang,et al.  Inference for the Mean Difference in the Two-Sample Random Censorship Model , 2001 .

[28]  Gang Li,et al.  EMPIRICAL LIKELIHOOD REGRESSION ANALYSIS FOR RIGHT CENSORED DATA , 2003 .

[29]  Thomas J. DiCiccio,et al.  On adjustments based on the signed root of the empirical likelihood ratio statistic , 1989 .

[30]  J. N. K. Rao,et al.  Empirical likelihood for linear regression models under imputation for missing responses , 2001 .

[31]  Bing-Yi Jing,et al.  Empirical likelihood for partial linear models with fixed designs , 1999 .

[32]  Gang Li,et al.  Empirical Likelihood Semiparametric Regression Analysis under Random Censorship , 2002 .

[33]  Gang Li,et al.  Likelihood ratio confidence bands in non-parametric regression with censored data , 2002 .