Fine-Gray proportional subdistribution hazards model for competing risks data under length-biased sampling

In this paper, we study the Fine-Gray proportional subdistribution hazards model for the competing risks data under length-biased sampling. To exploit the special structure of length-biased sampling, we propose an unbiased estimating equation estimator, which can handle both covariateindependent censoring and the covariate-dependent censoring. The large sample properties of the proposed estimator are derived, model-checking techniques for the model adequacy are developed, and the pointwise confidence intervals and the simultaneous confidence bands for the predicted cumulative incidence functions are also constructed. Simulation studies are conducted to assess the finite sample performance of the proposed estimator. An application to the employment data illustrates the method and theory.