187
Views
4
CrossRef citations to date
0
Altmetric
Review Article

Non-parametric quantile estimate for length-biased and right-censored data with competing risks

&
Pages 2407-2424 | Received 05 Apr 2015, Accepted 01 Jun 2016, Published online: 08 Feb 2018

References

  • Andersen, P. K., O. Borgan, R. D. Gill, and N. Keiding. 1993. Statistical Models Basedon Counting Processes. New York: Springer-Verlag.
  • Asgharian, M., M. L. Cyr Emile, and D. B. Wolfson. 2002. Length-biased sampling with right censoring. J. Am. Stat. Assoc. 97:201–209.
  • Cox, D. R. 1969. Some sampling problems in technology. In: Johnson, N.L., Smith, H., eds. New Developments in Survey Sampling. New York: Wiley.
  • Dauxois, J. Y., and A. Guilloux. 2008. Nonparametric inference under competing risks and selection-biased sampling. J. Multivariate Anal. 99:589–605.
  • De Uña-álvarez, J. 2004. Nonparametric estimation under length-biased sampling and type i censoring: A moment based approach. Ann. Inst. Stat. Math. 56:667–681.
  • De Uña-ÁLvarez, J., M. S. Otero-Giráldez, and G. Alvarez-Llorente. 2003. Estimation under length-bias and right-censoring: An application to unemployment duration analysis for married women. J. Appl. Stat. 30:283–291.
  • De Uña-Álvarez, J., and A. Rodríguez-Casal. 2007. Nonparametric estimation from length-biased data under competing risks. Comput. Stat. Data Anal. 51:2653–2669.
  • Dewanji, A., and J. D. Kalbfleisch. 1987. Estimation of sojourn time distributions for cyclic semi-Markov processes in equilibrium. Biometrika 74:281–288.
  • Gordis, L. 2000. Epidemiology, 2nd ed. Philadelphia: Sanders Company.
  • Huang, C. Y., and J. Qin. 2011. Nonparametric estimation for length-biased and right-censored data. Biometrika 98:177–186.
  • Huang, Y., and M. C. Wang. 1995. Estimating the occurrence rate for prevalent survival data in competing risks models. J. Am. Stat. Assoc. 90:1406–1415.
  • Kalbfleisch, J. D., and R. L. Prentice. 2002. The Statistical Analysis of Failure Time Data. 2nd ed. New York: John Wiley & Sons.
  • Keiding, N. 1991. Age-specific incidence and prevalence: a statistical perspective. J. Royal Stat. Soc. Ser. A 154:371–412.
  • Kvam, P. 2008. Length bias in the measurements of carbon nanotubes. Technometrics 50:462–467.
  • Lagakos, S. W., L. M. Barraj, and V. De Gruttola. 1988. Nonparametric analysis of truncated survival data, with application to aids. Biometrika 75:515–523.
  • Lancaster, T. 1992. The Econometric Analysis of Transition Data. Cambridge: Cambridge University Press.
  • Luo, X., and W. Y. Tsai. 2009. Nonparametric estimation for right-censored length-biased data: A pseudo-partial likelihood approach. Biometrika 96:873–886.
  • McClean, S., and C. Devine. 1995. A nonparametrie maximum likelihood estimator for incomplete renewal data. Biometrika 82:791–803.
  • Parzen, M. I., L. J. Wei, and Z. Ying. 1994. A resampling method based on pivotal estimating functions. Biometrika 81:341–350.
  • Peng, L., and J. P. Fine. 2007. Nonparametric quantile inference with competing–risks data. Biometrika 94:735–744.
  • Sansgiry, P., and O. Akman. 2000. Transformations of the lognormal distribution as a selection model. Am. Stat. 54:307–309.
  • Scheike, T. H., and N. Keiding. 2006. Design and analysis of time-to-pregnancy. Stat. Methods Med. Res. 15:127–140.
  • Shen, P., and Y. Yang. 2010. Semiparametric estimation of the cumulative incidence function under competing risks and left-truncated sampling. J. Stat. Plann. Inference 140 (7):1863–1873.
  • Simon, R. 1980. Length biased sampling in etiologic studies. Am. J. Epidemiol. 111:444–452.
  • Terwilliger, J. D., W. D. Shannon, G. M. Lathrop, J. P. Nolan, L. R. Goldin, G. A. Chase, and D. E. Weeks. 1997. True and false positive peaks in genomewide scans: Applications of length-biased sampling to linkage mapping. Am. J. Hum. Genet. 61:430–438.
  • Tsai, W. Y., N. P. Jewell, and M. C. Wang. 1987. A note on the product-limit estimator under right censoring and left truncation. Biometrika 74:883–886.
  • Turnbull, B. W. 1976. The empirical distribution function with arbitrarily grouped, censored and truncated data. J. Royal Stat. Soc. Ser. B 38:290–295.
  • van der Vaart, A. 1998. Asymptotic Statistics. Cambridge: Cambridge University Press.
  • Vardi, Y. 1982. Nonparametric estimation in the presence of length bias. Ann. Stat. 10:616–620.
  • Vardi, Y. 1989. Multiplicative censoring, renewal processes, deconvolution and decreasing density: Nonparametric estimation. Biometrika 76:751–761.
  • Wang, J. L., and T. P. Hettmansperger. 1990. Two-sample inference for median survival times based on one-sample procedures for censored survival data. J. Am. Stat. Assoc. 85:529–536.
  • Wang, M. C. 1991. Nonparametric estimation from cross-sectional survival data. J. Am. Stat. Assoc. 86:130–143.
  • Wang, M. C., N. P. Jewell, and W. Y. Tsai. 1986. Asymptotic properties of the product limit estimate under random truncation. Ann. Stat. 14:1597–1605.
  • Winter, B. B., and A. Földes. 1988. A product-limit estimator for use with length-biased data. Can. J. Stat. 16:337–355.
  • Zelen, M. 2004. Forward and backward recurrence times and length biased sampling: age specific models. Lifetime Data Anal. 10:325–334.
  • Zelen, M., and M. Feinleib. 1969. On the theory of screening for chronic diseases. Biometrika 56:601–614.
  • Zhang, M. J., and J. Fine. 2008. Summarizing differences in cumulative incidence functions. Stat. Med. 27:4939–4949.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.