Jackknife Empirical Likelihood for Smoothed Weighted Rank Regression with Censored Data

Rank regression is a highly-efficient and robust approach to estimate regression coefficients and to make inference in the presence of outlying survival times. Heller (2007) developed a smoothed weighted rank regression function, which is used to estimate the regression parameter vector in an accelerated failure time model with right censored data. This function can be expressed as a U -statistic. However, since inference is based on a normal approximation approach, it could perform poorly when sample sizes are small and censoring rates are high. To increase inference accuracy and robustness, we propose a jackknife empirical likelihood method for the U -statistic obtained from the estimating function of Heller. The jackknife empirical likelihood ratio is shown to be a standard Chi-squared statistic. Simulations were conducted to compare the proposed method with the normal approximation method. As expected, the new method gives better coverage probability for small samples with high censoring rates. The Stanford Heart Transplant Data, Veterans Administration Lung Cancer Data and Multiple Myeloma Data sets are used to illustrate the proposed method.