# A semiparametric regression cure model for doubly censored data

## Abstract

This paper discusses regression analysis of doubly censored failure time data when there may exist a cured subgroup. By doubly censored data, we mean that the failure time of interest denotes the elapsed time between two related events and the observations on both event times can suffer censoring (Sun in The statistical analysis of interval-censored failure time data. Springer, New York, 2006). One typical example of such data is given by an acquired immune deficiency syndrome cohort study. Although many methods have been developed for their analysis (De Gruttola and Lagakos in Biometrics 45:1–12, 1989; Sun et al. in Biometrics 55:909–914, 1999; 60:637–643, 2004; Pan in Biometrics 57:1245–1250, 2001), it does not seem to exist an established method for the situation with a cured subgroup. This paper discusses this later problem and presents a sieve approximation maximum likelihood approach. In addition, the asymptotic properties of the resulting estimators are established and an extensive simulation study indicates that the method seems to work well for practical situations. An application is also provided.

## Keywords

Cure model Doubly censored data Multiple imputation Proportional hazards model## Notes

### Acknowledgements

The authors wish to thank the Editor-in-Chief, Dr. Mei-Ling Lee, the Associate Editor and two reviewers for their many helpful comments and suggestions that greatly improved the paper. This work was partly supported by the National Nature Science Foundation of China Grant Nos. 11371062, 11671338, 11731011, 11671168 and the Science and Technology Developing Plan of Jilin Province Grant No. 20170101061JC.

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