# A semiparametric regression cure model for doubly censored data

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## 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.

## References

- Choi S, Huang X, Chen Y-H (2014) A class of semiparametric transformation models for survival data with a cured proportion. Lifetime Data Anal 20:369–386MathSciNetCrossRefMATHGoogle Scholar
- De Gruttola V, Lagakos SW (1989) Analysis of doubly-censored survival data, with application to AIDS. Biometrics 45:1–12MathSciNetCrossRefMATHGoogle Scholar
- Fang HB, Li G, Sun J (2005) Maximum likelihood estimation in a semiparametric logistic/proportional hazards mixture model. Scand J Stat 32:59–75MathSciNetCrossRefMATHGoogle Scholar
- Farewell VT (1986) Mixture models in survival analysis: Are they worth the risk? Can J Stat 14:257–262MathSciNetCrossRefGoogle Scholar
- Finkelstein DM (1986) A proportional hazards model for interval-censored failure time data. Biometrics 42:845–854MathSciNetCrossRefMATHGoogle Scholar
- Gómez G, Lagakos SW (1994) Estimation of the infection time and latency distribution of AIDS with doubly censored data. Biometrics 50:204–212CrossRefMATHGoogle Scholar
- Hu T, Xiang L (2016) Partially linear transformation cure models for interval-censored data. Comput Stat Data Anal 93:257–269MathSciNetCrossRefGoogle Scholar
- Huang J (1996) Efficient estimation for the proportional hazards model with interval censoring. Ann Stat 24:540–568MathSciNetCrossRefMATHGoogle Scholar
- Huang J, Rossini AJ (1997) Sieve estimation for the proportional odds failure-time regression model with interval censoring. J Am Stat Assoc 92:960–967MathSciNetCrossRefMATHGoogle Scholar
- Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data, 2nd edn. Wiley, New YorkCrossRefMATHGoogle Scholar
- Kim Y, De Gruttola V, Lagakos SW (1993) Analyzing doubly censored data with covariates, with application to AIDS. Biometrics 49:13–22CrossRefMATHGoogle Scholar
- Lam KF, Xue H (2005) A semiparametric regression cure model with current status data. Biometrika 92:573–586MathSciNetCrossRefMATHGoogle Scholar
- Lu W, Ying Z (2004) On semiparametric transformation cure models. Biometrika 91:331–343MathSciNetCrossRefMATHGoogle Scholar
- Ma S (2009) Cure model with current status data. Stat Sin 19:233–249MathSciNetMATHGoogle Scholar
- Ma S (2010) Mixed case interval censored data with a cured subgroup. Stat Sin 20:1165–1181MathSciNetMATHGoogle Scholar
- Pan W (2001) A multiple approach to regression analysis for doubly censored data with application to AIDS studies. Biometrics 57:1245–1250MathSciNetCrossRefMATHGoogle Scholar
- Sun J (1997) Self-consistency estimation of distributions based on truncated and doubly censored data with applications to AIDS cohort studies. Lifetime Data Anal 3:305–313CrossRefMATHGoogle Scholar
- Sun J (2006) The statistical analysis of interval-censored failure time data. Springer, New YorkMATHGoogle Scholar
- Sun J, Liao Q, Pagano M (1999) Regression analysis of doubly censored failure time data with applications to AIDS studies. Biometrics 55:909–914CrossRefMATHGoogle Scholar
- Sun L, Kim Y, Sun J (2004) Regression analysis of doubly censored failure time data using the additive hazards model. Biometrics 60:637–643MathSciNetCrossRefMATHGoogle Scholar
- Turnbull BW (1976) The empirical distribution function with arbitrarily grouped, censored and truncated data. J R Stat Soc Ser B 38:290–295MathSciNetMATHGoogle Scholar