The Annals of Applied Statistics

Pseudo-value approach for conditional quantile residual lifetime analysis for clustered survival and competing risks data with applications to bone marrow transplant data

Kwang Woo Ahn and Brent R. Logan

Full-text: Open access

Enhanced PDF (246 KB)

Abstract

Quantile residual lifetime analysis is conducted to compare remaining lifetimes among groups for survival data. Evaluating residual lifetimes among groups after adjustment for covariates is often of interest. The current literature is limited to comparing two groups for independent data. We propose a pseudo-value approach to compare quantile residual lifetimes given covariates between multiple groups for independent and clustered survival data. The proposed method considers clustered event times and clustered censoring times in addition to independent event times and censoring times. We show that the method can also be used to compare multiple groups on the cause-specific residual life distribution in the competing risk setting, for which there are no current methods which account for clustering. The empirical Type I errors and statistical power of the proposed study are examined in a simulation study, which shows that the proposed method controls Type I errors very well and has higher power than an existing method. The proposed method is illustrated by a bone marrow transplant data set.

Article information

Source
Ann. Appl. Stat., Volume 10, Number 2 (2016), 618-637.

Dates
Received: July 2015
Revised: March 2016
First available in Project Euclid: 22 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1469199887

Digital Object Identifier
doi:10.1214/16-AOAS927

Mathematical Reviews number (MathSciNet)
MR3528354

Zentralblatt MATH identifier
06625663

Keywords
Pseudo-value residual lifetime clustered data

Citation

Ahn, Kwang Woo; Logan, Brent R. Pseudo-value approach for conditional quantile residual lifetime analysis for clustered survival and competing risks data with applications to bone marrow transplant data. Ann. Appl. Stat. 10 (2016), no. 2, 618--637. doi:10.1214/16-AOAS927. https://projecteuclid.org/euclid.aoas/1469199887


Export citation

References

  • Ahn, K. W. and Logan, B. R. (2016). Supplement to “Pseudo-value approach for conditional quantile residual lifetime analysis for clustered survival and competing risks data with applications to bone marrow transplant data.” DOI:10.1214/16-AOAS927SUPP.
    Mathematical Reviews (MathSciNet): MR3528354
    Digital Object Identifier: doi:10.1214/16-AOAS927
    Project Euclid: euclid.aoas/1469199887
  • Ahn, K. W. and Mendolia, F. (2014). Pseudo-value approach for comparing survival medians for dependent data. Stat. Med. 33 1531–1538.
    Mathematical Reviews (MathSciNet): MR3240767
    Digital Object Identifier: doi:10.1002/sim.6072
  • Andersen, P. K., Klein, J. P. and Rosthøj, S. (2003). Generalised linear models for correlated pseudo-observations, with applications to multi-state models. Biometrika 90 15–27.
    Mathematical Reviews (MathSciNet): MR1966547
    Digital Object Identifier: doi:10.1093/biomet/90.1.15
  • Binder, N., Gerds, T. A. and Andersen, P. K. (2014). Pseudo-observations for competing risks with covariate dependent censoring. Lifetime Data Anal. 20 303–315.
    Mathematical Reviews (MathSciNet): MR3181016
    Digital Object Identifier: doi:10.1007/s10985-013-9247-7
  • Breslow, N. E. (1972). Discussion of the paper by D. R. Cox. J. Roy. Statist. Soc. Ser. B 34 216–217.
  • Commenges, D. and Andersen, P. K. (1995). Score test of homogeneity for survival data. Lifetime Data Anal. 1 145–159.
    Mathematical Reviews (MathSciNet): MR1353846
    Digital Object Identifier: doi:10.1007/BF00985764
  • Cox, D. R. (1972). Regression models and life-tables. J. Roy. Statist. Soc. Ser. B 34 187–220.
    Mathematical Reviews (MathSciNet): MR341758
  • Eapen, M., Logan, B. R., Appelbaum, F. R., Antin, J. H., Anasetti, C., Couriel, D. R., Chen, J., Maziarz, R. T., McCarthy, P. L., Nakamura, R., Ratanatharathorn, V., Vij, R. and Champlin, R. E. (2015). Long-term survival after transplantation of unrelated donor peripheral blood or bone marrow hematopoietic cells for hematologic malignancy. Biol. Blood Marrow Transplant. 21 55–59.
  • Ferry, C., Gemayel, G., Rocha, V., Labopin, M., Esperou, H., Robin, M., de Latour, R. P., Ribaud, P., Devergie, A., Leblanc, T., Baruchel, E. G. A. and Socie, G. (2007). Long-term outcomes after allogeneic stem cell transplantation for children with hematological malignancies. Bone Marrow Transplant. 40 219–224.
  • He, P., Eriksson, F., Scheike, T. H. and Zhang, M. J. (2016). A proportional hazards regression model for the subdistribution with covariates–adjusted censoring weight for competing risks data. Scand. J. Stat. 43 103–122.
    Mathematical Reviews (MathSciNet): MR3466996
    Digital Object Identifier: doi:10.1111/sjos.12167
  • Jacobsen, M. and Martinussen, T. (2014). A note on the large sample properties of estimators based on generalized linear models for correlated pseudo-observations. Research Report 14/4. Dept. Biostatistics, Univ. Copenhagen.
  • Jacobsohn, D. A. (2015). Outcomes of pediatric bone marrow transplantation for leukemia and myelodysplasia using matched sibling, mismatched related, or matched unrelated donor. Bone Marrow Transplant. 50 749–750.
  • Jeong, J.-H. and Fine, J. P. (2009). A note on cause-specific residual life. Biometrika 96 237–242.
    Mathematical Reviews (MathSciNet): MR2482149
    Digital Object Identifier: doi:10.1093/biomet/asn063
  • Jeong, J.-H. and Fine, J. P. (2013). Nonparametric inference on cause-specific quantile residual life. Biom. J. 55 68–81.
    Mathematical Reviews (MathSciNet): MR3042385
    Digital Object Identifier: doi:10.1002/bimj.201100190
  • Kim, M.-O., Zhou, M. and Jeong, J.-H. (2012). Censored quantile regression for residual lifetimes. Lifetime Data Anal. 18 177–194.
    Mathematical Reviews (MathSciNet): MR2903719
    Digital Object Identifier: doi:10.1007/s10985-011-9212-2
  • Klein, J. P. and Andersen, P. K. (2005). Regression modeling of competing risks data based on pseudovalues of the cumulative incidence function. Biometrics 61 223–229.
    Mathematical Reviews (MathSciNet): MR2135864
    Digital Object Identifier: doi:10.1111/j.0006-341X.2005.031209.x
  • Lee, E. W., Wei, L. J. and Amato, D. A. (1992). Cox-type regression analysis for large numbers of small groups of correlated failure time observations. In Survival Analysis: State of the Art (Columbus, OH, 1991). NATO Adv. Sci. Inst. Ser. E Appl. Sci. 211 237–247. Kluwer Academic, Dordrecht.
    Mathematical Reviews (MathSciNet): MR1175646
    Digital Object Identifier: doi:10.1007/978-94-015-7983-4_14
  • Liang, K. Y. and Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika 73 13–22.
    Mathematical Reviews (MathSciNet): MR836430
    Digital Object Identifier: doi:10.1093/biomet/73.1.13
  • Lin, D. Y. (2007). On the Breslow estimator. Lifetime Data Anal. 13 471–480.
    Mathematical Reviews (MathSciNet): MR2416534
    Digital Object Identifier: doi:10.1007/s10985-007-9048-y
  • Lin, C., Zhang, L. and Zhou, Y. (2015). Conditional quantile residual lifetime models for right censored data. Lifetime Data Anal. 21 75–96.
    Mathematical Reviews (MathSciNet): MR3299891
    Digital Object Identifier: doi:10.1007/s10985-013-9289-x
  • Logan, B. R., Zhang, M.-J. and Klein, J. P. (2011). Marginal models for clustered time-to-event data with competing risks using pseudovalues. Biometrics 67 1–7.
    Mathematical Reviews (MathSciNet): MR2898811
    Digital Object Identifier: doi:10.1111/j.1541-0420.2010.01416.x
  • Ma, Y. and Wei, Y. (2012). Analysis on censored quantile residual life model via spline smoothing. Statist. Sinica 22 47–68.
    Mathematical Reviews (MathSciNet): MR2933167
  • Majhail, N. S. and Rizzo, J. D. (2013). Surviving the cure: Long term followup of hematopoietic cell transplant recipients. Bone Marrow Transplant. 48 1145–1151.
  • Martin, P. J., Counts, G. W., Appelbaum, F. R., Lee, S. J., Sanders, J. E., Deeg, H. J., Flowers, M. E. D., Syrjala, K. L., Hansen, J. A., Storb, R. F. and Storer, B. E. (2010). Life expectancy in patients surviving more than 5 years after hematopoietic cell transplantation. J. Clin. Oncol. 28 1011–1016.
  • Prentice, R. L., Kalbfleisch, J. D., Peterson, A. V. Jr., Flournoy, N., Farewell, V. T. and Breslow, N. E. (1978). The analysis of failure times in the presence of competing risks. Biometrics 34 541–554.
  • Shaw, P. J., Kan, F., Ahn, K. W., Spellman, S. R., Aljurf, M., Ayas, M., Burke, M., Cairo, M. S., Chen, A. R., Davies, S. M., Frangoul, H., Gajewski, J., Gale, R. P., Godder, K., Hale, G. A., Heemskerk, M. B. A., Horan, J., Kamani, N., Kasow, K. A., Chan, K. W., Lee, S. J., Leung, W. H., Lewis, V. A., Miklos, D., Oudshoorn, M., Petersdorf, E. W., Ringdén, O., Sanders, J., Schultz, K. R., Seber, A., Setterholm, M., Wall, D. A., Yu, L. and Pulsipher, M. A. (2010). Outcomes of pediatric bone marrow transplantation for leukemia and myelodysplasia using matched sibling, mismatched related, or matched unrelated donors. Blood 116 4007–4015.
  • Spiekerman, C. F. and Lin, D. Y. (1998). Marginal regression models for multivariate failure time data. J. Amer. Statist. Assoc. 93 1164–1175.
    Mathematical Reviews (MathSciNet): MR1649210
    Digital Object Identifier: doi:10.1080/01621459.1998.10473777
  • Yin, G. and Cai, J. (2004). Additive hazards model with multivariate failure time data. Biometrika 91 801–818.
    Mathematical Reviews (MathSciNet): MR2126034
    Digital Object Identifier: doi:10.1093/biomet/91.4.801
  • Zeger, S. L., Liang, K.-Y. and Albert, P. S. (1988). Models for longitudinal data: A generalized estimating equation approach. Biometrics 44 1049–1060.
    Mathematical Reviews (MathSciNet): MR980999
    Digital Object Identifier: doi:10.2307/2531734
  • Zeng, D. and Lin, D. Y. (2008). Efficient resampling methods for nonsmooth estimating functions. Biostat. 9 355–363.
  • Zhao, Y. Q., Zeng, D., Laber, E. B., Song, R., Yuan, M. and Kosorok, M. R. (2015). Doubly robust learning for estimating individualized treatment with censored data. Biometrika 102 151–168.
    Mathematical Reviews (MathSciNet): MR3335102
    Digital Object Identifier: doi:10.1093/biomet/asu050
  • Zhou, B., Fine, J., Latouche, A. and Labopin, M. (2012). Competing risks regression for clustered data. Biostat. 13 371–383.

Supplemental materials

The Institute of Mathematical Statistics

The Annals of Applied Statistics

New content alerts

Email RSS ToC RSS Article
  • You have access to this content.
  • You have partial access to this content.
  • You do not have access to this content.
Turn Off MathJax

What is MathJax?

More like this

+ See more