# Semiparametric model for semi-competing risks data with application to breast cancer study

## Abstract

For many forms of cancer, patients will receive the initial regimen of treatments, then experience cancer progression and eventually die of the disease. Understanding the disease process in patients with cancer is essential in clinical, epidemiological and translational research. One challenge in analyzing such data is that death dependently censors cancer progression (e.g., recurrence), whereas progression does not censor death. We deal with the informative censoring by first selecting a suitable copula model through an exploratory diagnostic approach and then developing an inference procedure to simultaneously estimate the marginal survival function of cancer relapse and an association parameter in the copula model. We show that the proposed estimators possess consistency and weak convergence. We use simulation studies to evaluate the finite sample performance of the proposed method, and illustrate it through an application to data from a study of early stage breast cancer.

## Keywords

Copula model Informative censoring Model diagnostic Semi-competing risks Simultaneous inference## Notes

### Acknowledgments

The authors thank the editor, the associate editor and two reviewers for their constructive comments that have greatly improved the initial version of this paper. This work was supported in part by Cancer Center Support Grants from the National Institutes of Health (CA142543 to Hong Zhu at UT Southwestern Medical Center and CA016672 to Jing Ning at UT MD Anderson Cancer Center) and by a predoctoral fellowship grant from the Cancer Prevention Research Institute of Texas (RP140103 to Renke Zhou).

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