Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A GEE approach for the semiparametric accelerated lifetime model with multivariate interval-censored data

  • Maru Kim (Department of Statistics, Korea University) ;
  • Sangbum Choi (Department of Statistics, Korea University)
  • Received : 2022.12.22
  • Accepted : 2023.03.10
  • Published : 2023.07.31
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Abstract

Multivariate or clustered failure time data often occur in many medical, epidemiological, and socio-economic studies when survival data are collected from several research centers. If the data are periodically observed as in a longitudinal study, survival times are often subject to various types of interval-censoring, creating multivariate interval-censored data. Then, the event times of interest may be correlated among individuals who come from the same cluster. In this article, we propose a unified linear regression method for analyzing multivariate interval-censored data. We consider a semiparametric multivariate accelerated failure time model as a statistical analysis tool and develop a generalized Buckley-James method to make inferences by imputing interval-censored observations with their conditional mean values. Since the study population consists of several heterogeneous clusters, where the subjects in the same cluster may be related, we propose a generalized estimating equations approach to accommodate potential dependence in clusters. Our simulation results confirm that the proposed estimator is robust to misspecification of working covariance matrix and statistical efficiency can increase when the working covariance structure is close to the truth. The proposed method is applied to the dataset from a diabetic retinopathy study.

Keywords

Acknowledgement

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (No. 2022M3J6A1063595, 2022R1A2C1008514).

References

  1. Buckley J and James I (1979). Linear regression with censored data, Biometrika, 66, 429-436. https://doi.org/10.1093/biomet/66.3.429
  2. Chen L, Sun J, and Xiong C (2016). A multiple imputation approach to the analysis of clustered interval-censored failure time data with the additive hazards model, Computational Statistics & Data Analysis, 103, 242-249. https://doi.org/10.1016/j.csda.2016.05.011
  3. Chiou SH, Kang S, Kim J, and Yan J (2014). Marginal semiparametric multivariate accelerated failure time model with generalized estimating equations, Lifetime Data Analysis, 20, 599-618. https://doi.org/10.1007/s10985-014-9292-x
  4. Choi S and Huang X (2021). Efficient inferences for linear transformation models with doubly-censored data, Communications in Statistics-Theory and Methods, 50, 2188-2200. https://doi.org/10.1080/03610926.2019.1662046
  5. Choi T and Choi S (2021). A fast algorithm for the accelerated failure time model with high-dimensional time-to-event data, Journal of Statistical Computation and Simulation, 91, 3385-3403. https://doi.org/10.1080/00949655.2021.1927034
  6. Choi T, Choi S, and Bandyopadhyay D (2023). Rank-Based inferences for the accelerated failure time model with partially interval-censored data. Submitted.
  7. Choi T, Kim AK, and Choi S (2021). Semiparametric least-squares regression with doubly-censored data, Computational Statistics & Data Analysis, 164, 107306.
  8. Efron B (1967). The two sample problem with censored data. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA, 831-853.
  9. Gao F and Chan KCG (2019). Semiparametric regression analysis of length-biased interval-censored data, Biometrics, 75, 121-132. https://doi.org/10.1111/biom.12970
  10. Gao F, Zeng D, and Lin DY (2017). Semiparametric estimation of the accelerated failure time model with partly interval-censored data, Biometrics, 73, 1161-1168. https://doi.org/10.1111/biom.12700
  11. Huang J (1996). Efficient estimation for the proportional hazards model with interval censoring, The Annals of Statistics, 24, 540-568. https://doi.org/10.1214/aos/1032894452
  12. Huang J (1999). Asymptotic properties of nonparametric estimation based on partly interval-censored data, Statistica Sinica, 9, 501-519.
  13. Huang J and Wellner JA (1997). Interval-Censored survival data: A review of recent progress. In Proceedings of the First Seattle Symposium in Biostatistics, Springer, New York.
  14. Ji S, Peng L, Cheng Y, and Lai HC (2012). Quantile regression for doubly-censored data, Biometrics, 68, 101-112. https://doi.org/10.1111/j.1541-0420.2011.01667.x
  15. Jin Z, Lin DY, and Ying Z (2006). On least-squares regression with censored data, Biometrika, 93, 147-161. https://doi.org/10.1093/biomet/93.1.147
  16. Kalbfleisch JD and Prentice RL (2002). The Statistical Analysis of Failure Time Data, Wiley, New York.
  17. Kim JS (2003). Maximum likelihood estimation for the proportional hazards model with partly interval-censored data, Journal of the Royal Statistical Society. Series B (Statistical Methodology), 65, 489-502. https://doi.org/10.1111/1467-9868.00398
  18. Kim YJ, Cho H, Kim J, and Jhun M (2010). Median regression model with interval-censored data, Biometrical Journal, 52, 201-208. https://doi.org/10.1002/bimj.200900111
  19. Kor CT, Cheng KF, and Chen YH (2013). A method for analyzing clustered interval-censored data based on cox's model, Statistics in Medicine, 32, 822-832. https://doi.org/10.1002/sim.5562
  20. Lam KF, Xu Y, and Cheung TL (2010). A multiple imputation approach for clustered interval-censored survival data, Statistics in Medicine, 29, 680-693. https://doi.org/10.1002/sim.3835
  21. Liang KY and Zeger SL (1986). Longitudinal data analysis using generalized linear models, Biometrika, 73, 13-22. https://doi.org/10.1093/biomet/73.1.13
  22. Lin G, He X, and Portnoy S (2012). Quantile regression with doubly-censored data, Computational Statistics & Data Analysis, 56, 797-812. https://doi.org/10.1016/j.csda.2011.03.009
  23. Mao L, Lin DY, and Zeng D (2017). Semiparametric regression analysis of interval-censored competing risks data, Biometrics, 73, 857-865. https://doi.org/10.1111/biom.12664
  24. McCulloch CE and Searle SR (2004). Generalized, Linear, and Mixed Models, John Wiley & Sons.
  25. Peng L and Huang Y (2008). Survival analysis with quantile regression models, Journal of the American Statistical Association, 103, 637-649. https://doi.org/10.1198/016214508000000355
  26. Portnoy S (2003). Censored regression quantiles, Journal of the American Statistical Association, 98, 1001-1012. https://doi.org/10.1198/016214503000000954
  27. Ren JJ (2003). Regression m-estimators with non-iid doubly-censored data, The Annals of Statistics, 31, 1186-1219. https://doi.org/10.1214/aos/1059655911
  28. Ren JJ and Gu M (1997). Regression m-estimators with doubly-censored data, The Annals of Statistics, 25, 2638-2664. https://doi.org/10.1214/aos/1030741089
  29. Ritov Y (1990). Estimation in a linear regression model with censored data, The Annals of Statistics, 18, 303-328. https://doi.org/10.1214/aos/1176347502
  30. Shen X (1998). Proportional odds regression and sieve maximum likelihood estimation, Biometrika, 85, 165-177. https://doi.org/10.1093/biomet/85.1.165
  31. Sun J (2006). The Statistical Analysis of Interval-Censored Failure Time Data, Springer, New Yrok.
  32. Turnbull BW (1974). Nonparametric estimation of a survivorship function with doubly-censored data, Journal of the American Statistical Association, 69, 169-173. https://doi.org/10.1080/01621459.1974.10480146
  33. Turnbull BW (1976). The empirical distribution function with arbitrarily grouped, censored and truncated data, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 38, 290-295. https://doi.org/10.1111/j.2517-6161.1976.tb01597.x
  34. Wellner JA and Zhan Y (1997). A hybrid algorithm for computation of the nonparametric maximum likelihood estimator from censored data, Journal of the American Statistical Association, 92, 945-959. https://doi.org/10.1080/01621459.1997.10474049
  35. Zeng D, Gao F, and Lin DY (2017). Maximum likelihood estimation for semiparametric regression models with multivariate interval-censored data, Biometrika, 104, 505-525. https://doi.org/10.1093/biomet/asx029
  36. Zeng D, Mao L, and Lin D (2016). Maximum likelihood estimation for semiparametric transformation models with interval-censored data, Biometrika, 103, 253-271. https://doi.org/10.1093/biomet/asw013
  37. Zhao X, Zhao Q, Sun J, and Kim JS (2008). Generalized log-rank tests for partly interval-censored failure time data, Biometrical Journal, 50, 375-385. https://doi.org/10.1002/bimj.200710419