Estimators of quantile difference between two samples with length-biased and right-censored data

• Li Xun ^[1] ; Li Tao ^[1] ; Yong Zhou ^[2]
  1. [1] Changchun Institute of Technology

     Changchun Institute of Technology

     China

     
  2. [2] Key Laboratory of Advanced Theory and Application in Statistics and Data Science, MOE, Academy of Statistics and Interdisciplinary Sciences, East China Normal University, Shanghai, 200062, China
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 29, Nº. 2, 2020, págs. 409-429
• Idioma: inglés
• DOI: 10.1007/s11749-019-00657-3
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper, the difference between the quantiles of two samples is investigated. One sample comes from a prevalent cohort with a stable incidence rate. Then, the observed survival times are length-biased and right-censored data. Another sample is drawn from an incident cohort study with right-censored data. We estimate the quantile difference based on different estimating equations. That is because the estimating equation estimators have higher efficiency than the difference of two one-sample quantile estimators in the sense of minimizing the mean squared error. Moreover, the consistency and asymptotic normality of these estimators are established. Then, the confidence intervals of quantile difference can be constructed by using the normal approximations. Finally, the performance of the proposed methods is presented in the numerical studies, especially with small sample sizes.

• Referencias bibliográficas
  • Addona V, Wolfson DB (2006) A formal test for the stationarity of the incidence rate using data from a prevalent cohort study with follow-up....
  • Asgharian M, Wolfson D (2005) Asymptotic behavior of the unconditional NPMLE of the length-biased survivor function from right censored prevalent...
  • Asgharian M, M’Lan C, Wolfson D (2002) Length-biased sampling with right censoring. J Am Stat Assoc 97:201–209
  • Bai F, Huang J, Zhou Y (2014) Semiparametric estimation of treatment effects in two sample problems with censored data. Stat Sin 24:121–146
  • Bickel PJ, Klaassen CAJ, Ritov Y, Wellner JA (1993) Efficient and adaptive inference in semi-parametric models. Johns Hopkins University Press,...
  • Han X, Small DS, Foster DP, Patel V (2011) The effect of winning an Oscar award on survival: correcting for healthy performer survivor bias...
  • Li G, Lin C (2009) Analysis of two-sample censored data using a semiparametric mixture model. Acta Math Appl Sin 25:389–398
  • Li G, Tiwari RC, Wells MT (1999) Semiparametric inference for a quantile comparison function with applications to receiver operating characteristic...
  • Lin C, Zhou Y (2014) Inference for the treatment effects in two sample problems with right-censored and length-biased data. Stat Probab Lett...
  • Qin YS (1997) Semi-parametric likelihood ratio confidence intervals for various differences of two populations. Stat Probab Lett 33:135–143
  • Qin J, Shen Y (2010) Statistical methods for analyzing right-censored length-biased data under Cox model. Biometrics 66:382–392
  • Qin YS, Zhao LC (1997) Empirical likelihood ratio intervals for the quantile differences of two populations. Chin Ann Math (Ser A) 18:687–694...
  • Redelmeier DA, Singh SM (2001) Survival in academy award-winning actors and actresses. Ann Intern Med 134:955–962
  • Shen Y, Ning J, Qin J (2009) Analyzing length-biased data with semiparametric transformation and accelerated failure time models. J Am Stat...
  • Simon R (1980) Length-biased sampling in etiologic studies. Am J Epidemiol 111:444–452
  • Sylvestre M, Hustzi E, Hanley J (2006) Do Oscar winners live longer than less successful peers? A reanalysis of the evidence. Ann Intern Med...
  • Tsiatis A (2007) Semiparametric theory and missing data. Springer, Berlin
  • Vardi Y (1982) Nonparametric estimation in the presence of length bias. Ann Stat 10:616–620
  • Vardi Y (1985) Empirical distributions in selection bias models (with discussion). Ann Stat 13:178–203
  • Vardi Y (1989) Multiplicative censoring, renewal processes, deconvolution and decreasing density: nonparametric estimation. Biometrika 76:751–761
  • Wolkewitz M, Allignol A, Schumacher M, Beyersmann J (2010) Two pitfalls in survival analysis of time-dependent exposure: a case study in a...
  • Yang HF, Yau C, Zhao YC (2014) Smoothed empirical likelihood inference for the difference of two quantiles with right censoring. J Stat Plan...
  • Zelen M (2005) Forward and backward recurrence times and length biased sampling: age specific models. Lifetime Data Anal 10:325–334
  • Zhou Y, Liang H (2005) Empirical likelihood-based semi-parametric inference of the treatment effect in the two-sample problem with censoring....