Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
권호 표지
DOI QR코드

DOI QR Code

Nonpararmetric estimation for interval censored competing risk data

  • Kim, Yang-Jin (Department of Statistics, Sookmyung Women's University) ;
  • Kwon, Do young (Department of Statistics, Sookmyung Women's University)
  • Received : 2017.07.03
  • Accepted : 2017.07.26
  • Published : 2017.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

A competing risk analysis has been applied when subjects experience more than one type of end points. Geskus (2011) showed three types of estimators of CIF are equivalent under left truncated and right censored data. We extend his approach to an interval censored competing risk data by using a modified risk set and evaluate their performance under several sample sizes. These estimators show very similar results. We also suggest a test statistic combining Sun's test for interval censored data and Gray's test for right censored data. The test sizes and powers are compared under several cases. As a real data application, the suggested method is applied a data where the feasibility of the vaccine to HIV was assessed in the injecting drug uses.

Keywords

References

  1. Andersen, P. K., Klein, J. P. and Rosthj, S. (2003). Generalized linear models for correlated pseudo- observations, with applications to multi-state models. Biometrika, 90,15-27. https://doi.org/10.1093/biomet/90.1.15
  2. Beyersmann, J., Latouche, A., Buchholz, A. and Schumacher M. (2009). Simulating competing risks data in survival analysis. Statistics in Medicine, 28, 956-971. https://doi.org/10.1002/sim.3516
  3. De Gruttola, V. and Lagakos, S. W. (1989). Analysis of doubly-censored survival data, with application to AIDS. Biometrics, 45, 1-11. https://doi.org/10.2307/2532030
  4. Do, G., Kim, S. and Kim, Y-J. (2015). Statistical analysis of economic activity state of workers with industrial injuries using a competing risk model. Journal of the Korean Data & Information Science Society, 26, 1271-1281. https://doi.org/10.7465/jkdi.2015.26.6.1271
  5. Do, G. and Kim, Y-J. (2017). Analysis of interval censored competing risk data with missing causes of failure using pseudo values approach. Journal of Statistical Computation and Simulation, 87, 631-639. https://doi.org/10.1080/00949655.2016.1222530
  6. Fine, J. P. and Gray, R. J. (1999). Proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association, 94, 496-509. https://doi.org/10.1080/01621459.1999.10474144
  7. Geskus, R. B. (2011). Cause-specific cumulative incidence estimation and the fine and gray model under both left truncation and right censoring. Biometrics, 67, 39-49. https://doi.org/10.1111/j.1541-0420.2010.01420.x
  8. Goetghebeur, E and Ryan, L. P. (1995). Analysis of competing risks survival data when some failure types are missing. Biometrika, 82, 821-834. https://doi.org/10.1093/biomet/82.4.821
  9. Gray, R. J. (1988). A class of k-sample tests for comparing the cumulative incidence of a competing risk. Annals of Statistics, 16, 1141-1154. https://doi.org/10.1214/aos/1176350951
  10. Hudgens, M. G., Li, C., and Fine, J. P. (2014). Parametric likelihood inference for interval censored competing risks data. Biometrics, 70, 1-9. https://doi.org/10.1111/biom.12109
  11. Hudgens, M. G., Satten, G. A. and Longini, I. M. (2001). Nonparametric maximum likelihood estimation for competing risks survival data subject to interval censoring and truncation. Biometrics, 57, 74-80. https://doi.org/10.1111/j.0006-341X.2001.00074.x
  12. Jeong, J. and Fine, J. P. (2006). Direct parametric inference for the cumulative incidence function. Journal of Royal Statistical Society, 55, 187-200. https://doi.org/10.1111/j.1467-9876.2006.00532.x
  13. Jewell, N. P. and Van der Laan, M., and Henneman, T. (2003). Nonparametric estimation from current status data with competing risks. Biometrika, 90, 183-197. https://doi.org/10.1093/biomet/90.1.183
  14. Jewell, N. P. and Kalbfleisch, J. D. (2004). Maximum likelihood estimation of ordered multinominal parameters. Biostatistics, 5, 291-306. https://doi.org/10.1093/biostatistics/5.2.291
  15. Kalbfleisch, J. D. and Prentice, R. (2002). The statistical analysis of failure time data, Wiley, New York.
  16. Lu, K, and Tsiatis, A. A. (2001). Multiple imputation methods for estimating regression coeffcients in the competing risks model with missing cause of failure. Biometrics, 57, 1191-1197. https://doi.org/10.1111/j.0006-341X.2001.01191.x
  17. Moreno-Betancur, M. and Latouche, A. (2013). Regression modeling of the cumulative incidence function with missing cause of failure using pseudo-values. Statistics in Medicine, 32, 3206-3223. https://doi.org/10.1002/sim.5755
  18. Nam, S. J. and Kang, S. B. (2014). Estimation for the extreme value distribution under progressive type-I interval censoring. Journal of the Korean Data & Information Science Society, 25, 643-653. https://doi.org/10.7465/jkdi.2014.25.3.643
  19. Ruan, P. K and Gray, R. J. (2008). Analysis of cumulative incidence functions via non-parametric multiple imputation. Statistics in Medicine, 27, 5709-5724. https://doi.org/10.1002/sim.3402
  20. Sun, J. (1996). A non-parametric test for interval-censored failure time data with application to AIDS studies. Statistics in Medicine, 15, 1387-1395. https://doi.org/10.1002/(SICI)1097-0258(19960715)15:13<1387::AID-SIM268>3.0.CO;2-R
  21. Sun, J. (2006). The statistical analysis of interval-censored failure time data, Springer-Verlag, New-York.
  22. Sun, J. and Shen, J. (2009). Effcient estimation for the proportional hazard model with competing risks and current status data. Canadian Journal of Statistics, 37, 592-606. https://doi.org/10.1002/cjs.10033
  23. Zhao, Q and Sun, J. (2004). Generalized log-rank test for mixed interval-censored failure time data. Statistics in Medicine, 23, 1621-1629. https://doi.org/10.1002/sim.1746