Kernel regression for cause-specific hazard models with nonparametric covariate functions

We study the local kernel pseudo-partial likelihood approach for the cause-specific hazard model with nonparametric covariate functions. The derivative of the covariate function is estimated first, and the estimator of the nonparametric covariate function is then derived by integrating the derivative estimator. The consistency and pointwise asymptotic normality of the local kernel estimator for the interested failure types are obtained. Moreover, numerical studies show that the proposed kernel estimator performs well under a finite sample size. And we compare the local kernel estimator with the regression B-splines estimator. We also apply the proposed method to analyse the kidney and renal pelvis cancer data with composite endpoints.