Skip to main content
Erschienen in: Lifetime Data Analysis 1/2017

16.04.2016

Nonparametric and semiparametric regression estimation for length-biased survival data

verfasst von: Yu Shen, Jing Ning, Jing Qin

Erschienen in: Lifetime Data Analysis | Ausgabe 1/2017

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

For the past several decades, nonparametric and semiparametric modeling for conventional right-censored survival data has been investigated intensively under a noninformative censoring mechanism. However, these methods may not be applicable for analyzing right-censored survival data that arise from prevalent cohorts when the failure times are subject to length-biased sampling. This review article is intended to provide a summary of some newly developed methods as well as established methods for analyzing length-biased data.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat 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. Lifetime Data Anal 12(3):267–284MathSciNetCrossRefMATH 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. Lifetime Data Anal 12(3):267–284MathSciNetCrossRefMATH
Zurück zum Zitat Andersen P, Borgan O, Gill R, Keiding N (1993) Statistical models based on counting processes. Springer, New YorkCrossRefMATH Andersen P, Borgan O, Gill R, Keiding N (1993) Statistical models based on counting processes. Springer, New YorkCrossRefMATH
Zurück zum Zitat Asgharian M, M’Lan CE, Wolfson DB (2002) Length-biased sampling with right censoring: an unconditional approach. J Am Stat Assoc 97(457):201–209MathSciNetCrossRefMATH Asgharian M, M’Lan CE, Wolfson DB (2002) Length-biased sampling with right censoring: an unconditional approach. J Am Stat Assoc 97(457):201–209MathSciNetCrossRefMATH
Zurück zum Zitat Asgharian M, Wolfson DB et al (2005) Asymptotic behavior of the unconditional npmle of the length-biased survivor function from right censored prevalent cohort data. Ann Stat 33(5):2109–2131MathSciNetCrossRefMATH Asgharian M, Wolfson DB et al (2005) Asymptotic behavior of the unconditional npmle of the length-biased survivor function from right censored prevalent cohort data. Ann Stat 33(5):2109–2131MathSciNetCrossRefMATH
Zurück zum Zitat Asgharian M, Wolfson DB, Zhang X (2006) Checking stationarity of the incidence rate using prevalent cohort survival data. Stat Med 25(10):1751–1767MathSciNetCrossRef Asgharian M, Wolfson DB, Zhang X (2006) Checking stationarity of the incidence rate using prevalent cohort survival data. Stat Med 25(10):1751–1767MathSciNetCrossRef
Zurück zum Zitat Asgharian M, Wolfson C, Wolfson DB (2014) Analysis of biased survival data: the canadian study of health and aging and beyond. In: Statistics in action: a Canadian outlook. CRC Press, pp 193–208 Asgharian M, Wolfson C, Wolfson DB (2014) Analysis of biased survival data: the canadian study of health and aging and beyond. In: Statistics in action: a Canadian outlook. CRC Press, pp 193–208
Zurück zum Zitat Bergeron PJ, Asgharian M, Wolfson DB (2008) Covariate bias induced by length-biased sampling of failure times. J Am Stat Associ 103(482):734–742MathSciNetCrossRefMATH Bergeron PJ, Asgharian M, Wolfson DB (2008) Covariate bias induced by length-biased sampling of failure times. J Am Stat Associ 103(482):734–742MathSciNetCrossRefMATH
Zurück zum Zitat Chan KCG, Chen YQ, Di CZ (2012) Proportional mean residual life model for right-censored length-biased data. Biometrika 99(4):995–1000MathSciNetCrossRefMATH Chan KCG, Chen YQ, Di CZ (2012) Proportional mean residual life model for right-censored length-biased data. Biometrika 99(4):995–1000MathSciNetCrossRefMATH
Zurück zum Zitat Cheng YJ, Huang CY (2014) Combined estimating equation approaches for semiparametric transformation models with length-biased survival data. Biometrics 70(3):608–618MathSciNetCrossRefMATH Cheng YJ, Huang CY (2014) Combined estimating equation approaches for semiparametric transformation models with length-biased survival data. Biometrics 70(3):608–618MathSciNetCrossRefMATH
Zurück zum Zitat Cook RJ, Bergeron PJ (2011) Information in the sample covariate distribution in prevalent cohorts. Stat Med 30(12):1397–1409MathSciNetCrossRef Cook RJ, Bergeron PJ (2011) Information in the sample covariate distribution in prevalent cohorts. Stat Med 30(12):1397–1409MathSciNetCrossRef
Zurück zum Zitat Cox DR (1972) Regression models and life-tables. J R Stat Soc Ser B (Methodol) 34(2):187–220 Cox DR (1972) Regression models and life-tables. J R Stat Soc Ser B (Methodol) 34(2):187–220
Zurück zum Zitat Davidov O, Fokianos K, Iliopoulos G (2010) Order-restricted semiparametric inference for the power bias model. Biometrics 66(2):549–557MathSciNetCrossRefMATH Davidov O, Fokianos K, Iliopoulos G (2010) Order-restricted semiparametric inference for the power bias model. Biometrics 66(2):549–557MathSciNetCrossRefMATH
Zurück zum Zitat de Una-Álvarez J, Otero-Giráldez MS, Álvarez-Llorente G (2003) Estimation under length-bias and right-censoring: an application to unemployment duration analysis for married women. J Appl Stat 30(3):283–291MathSciNetCrossRefMATH de Una-Álvarez J, Otero-Giráldez MS, Álvarez-Llorente G (2003) Estimation under length-bias and right-censoring: an application to unemployment duration analysis for married women. J Appl Stat 30(3):283–291MathSciNetCrossRefMATH
Zurück zum Zitat Gill RD, Vardi Y, Wellner JA (1988) Large sample theory of empirical distributions in biased sampling models. Ann Stat 16:1069–1112MathSciNetCrossRefMATH Gill RD, Vardi Y, Wellner JA (1988) Large sample theory of empirical distributions in biased sampling models. Ann Stat 16:1069–1112MathSciNetCrossRefMATH
Zurück zum Zitat Gross ST, Lai TL (1996) Nonparametric estimation and regression analysis with left-truncated and right-censored data. J Am Stat Assoc 91(435):1166–1180MathSciNetCrossRefMATH Gross ST, Lai TL (1996) Nonparametric estimation and regression analysis with left-truncated and right-censored data. J Am Stat Assoc 91(435):1166–1180MathSciNetCrossRefMATH
Zurück zum Zitat Huang CY, Qin J (2012) Composite partial likelihood estimation under length-biased sampling, with application to a prevalent cohort study of dementia. J Am Stat Assoc 107(499):946–957MathSciNetCrossRefMATH Huang CY, Qin J (2012) Composite partial likelihood estimation under length-biased sampling, with application to a prevalent cohort study of dementia. J Am Stat Assoc 107(499):946–957MathSciNetCrossRefMATH
Zurück zum Zitat Huang CY, Qin J (2013) Semiparametric estimation for the additive hazards model with left-truncated and right-censored data. Biometrika 100(4):877–888MathSciNetCrossRefMATH Huang CY, Qin J (2013) Semiparametric estimation for the additive hazards model with left-truncated and right-censored data. Biometrika 100(4):877–888MathSciNetCrossRefMATH
Zurück zum Zitat Huang CY, Qin J, Follmann DA (2012) A maximum pseudo-profile likelihood estimator for the cox model under length-biased sampling. Biometrika 99:199–210MathSciNetCrossRefMATH Huang CY, Qin J, Follmann DA (2012) A maximum pseudo-profile likelihood estimator for the cox model under length-biased sampling. Biometrika 99:199–210MathSciNetCrossRefMATH
Zurück zum Zitat Kalbfleisch JD, Lawless JF (1989) Inference based on retrospective ascertainment: an analysis of the data on transfusion-related aids. J Am Stat Assoc 84:360–372MathSciNetCrossRefMATH Kalbfleisch JD, Lawless JF (1989) Inference based on retrospective ascertainment: an analysis of the data on transfusion-related aids. J Am Stat Assoc 84:360–372MathSciNetCrossRefMATH
Zurück zum Zitat Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data, 2nd edn. Wiley-Interscience, HobokenCrossRefMATH Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data, 2nd edn. Wiley-Interscience, HobokenCrossRefMATH
Zurück zum Zitat Keiding N (1992) Independent delayed entry. In: Klein JP, Goel P (eds) Survival analysis: state of the art. Kluwer Academic Publishers, Boston, pp 309–326CrossRef Keiding N (1992) Independent delayed entry. In: Klein JP, Goel P (eds) Survival analysis: state of the art. Kluwer Academic Publishers, Boston, pp 309–326CrossRef
Zurück zum Zitat Keiding N, Kvist K, Hartvig H, Tvede M, Juul S (2002) Estimating time to pregnancy from current durations in a cross-sectional sample. Biostatistics 3:565–578CrossRefMATH Keiding N, Kvist K, Hartvig H, Tvede M, Juul S (2002) Estimating time to pregnancy from current durations in a cross-sectional sample. Biostatistics 3:565–578CrossRefMATH
Zurück zum Zitat Keiding N, Fine JP, Hansen OH, Slama R (2011) Accelerated failure time regression for backward recurrence times and current durations. Stat Probab Lett 81(7):724–729MathSciNetCrossRefMATH Keiding N, Fine JP, Hansen OH, Slama R (2011) Accelerated failure time regression for backward recurrence times and current durations. Stat Probab Lett 81(7):724–729MathSciNetCrossRefMATH
Zurück zum Zitat Kim JP, Lu W, Sit T, Ying Z (2013) A unified approach to semiparametric transformation models under general biased sampling schemes. J Am Stat Assoc 108(501):217–227MathSciNetCrossRefMATH Kim JP, Lu W, Sit T, Ying Z (2013) A unified approach to semiparametric transformation models under general biased sampling schemes. J Am Stat Assoc 108(501):217–227MathSciNetCrossRefMATH
Zurück zum Zitat Lagakos SW, Barraj LM, De Gruttola V (1988) Nonparametric analysis of truncated survival data, with application to aids. Biometrika 75:515–523MathSciNetCrossRefMATH Lagakos SW, Barraj LM, De Gruttola V (1988) Nonparametric analysis of truncated survival data, with application to aids. Biometrika 75:515–523MathSciNetCrossRefMATH
Zurück zum Zitat Lin C, Zhou Y (2014) Analyzing right-censored and length-biased data with varying-coefficient transformation model. J Multivar Anal 130:45–63MathSciNetCrossRefMATH Lin C, Zhou Y (2014) Analyzing right-censored and length-biased data with varying-coefficient transformation model. J Multivar Anal 130:45–63MathSciNetCrossRefMATH
Zurück zum Zitat Liu H, Qin J, Shen Y (2012) Imputation for semiparametric transformation models with biased-sampling data. Lifetime Data Anal 18(4):470–503MathSciNetCrossRefMATH Liu H, Qin J, Shen Y (2012) Imputation for semiparametric transformation models with biased-sampling data. Lifetime Data Anal 18(4):470–503MathSciNetCrossRefMATH
Zurück zum Zitat Martin EC, Betensky RA (2005) Testing quasi-independence of failure and truncation times via conditional kendall’s tau. J Am Stat Assoc 100(470):484–492MathSciNetCrossRefMATH Martin EC, Betensky RA (2005) Testing quasi-independence of failure and truncation times via conditional kendall’s tau. J Am Stat Assoc 100(470):484–492MathSciNetCrossRefMATH
Zurück zum Zitat Ning J, Qin J, Shen Y (2010) Non-parametric tests for right-censored data with biased sampling. J R Stat Soc 72(5):609–630MathSciNetCrossRef Ning J, Qin J, Shen Y (2010) Non-parametric tests for right-censored data with biased sampling. J R Stat Soc 72(5):609–630MathSciNetCrossRef
Zurück zum Zitat Ning J, Qin J, Shen Y (2011) Buckley-james-type estimator with right-censored and length-biased data. Biometrics 67(4):1369–1378MathSciNetCrossRefMATH Ning J, Qin J, Shen Y (2011) Buckley-james-type estimator with right-censored and length-biased data. Biometrics 67(4):1369–1378MathSciNetCrossRefMATH
Zurück zum Zitat Ning J, Qin J, Shen Y (2014a) Score estimating equations from embedded likelihood functions under accelerated failure time model. J Am Stat Assoc 109(508):1625–1635MathSciNetCrossRef Ning J, Qin J, Shen Y (2014a) Score estimating equations from embedded likelihood functions under accelerated failure time model. J Am Stat Assoc 109(508):1625–1635MathSciNetCrossRef
Zurück zum Zitat Ning J, Qin J, Shen Y (2014b) Semiparametric accelerated failure time model for length-biased data with application to dementia study. Stat Sin 24(1):313MATH Ning J, Qin J, Shen Y (2014b) Semiparametric accelerated failure time model for length-biased data with application to dementia study. Stat Sin 24(1):313MATH
Zurück zum Zitat Nowell C, Stanley LR (1991) Length-biased sampling in mall intercept surveys. J Mark Res 28(4):475–479CrossRef Nowell C, Stanley LR (1991) Length-biased sampling in mall intercept surveys. J Mark Res 28(4):475–479CrossRef
Zurück zum Zitat Qin J, Shen Y (2010) Statistical methods for analyzing right-censored length-biased data under Cox model. Biometrics 66(2):382–392MathSciNetCrossRefMATH Qin J, Shen Y (2010) Statistical methods for analyzing right-censored length-biased data under Cox model. Biometrics 66(2):382–392MathSciNetCrossRefMATH
Zurück zum Zitat Qin J, Ning J, Liu H, Shen Y (2011) Maximum likelihood estimations and em algorithms with length-biased data. J Am Stat Assoc 106(496):1434–1449MathSciNetCrossRefMATH Qin J, Ning J, Liu H, Shen Y (2011) Maximum likelihood estimations and em algorithms with length-biased data. J Am Stat Assoc 106(496):1434–1449MathSciNetCrossRefMATH
Zurück zum Zitat Shen Y, Ning J, Qin J (2009) Analyzing length-biased data with semiparametric transformation and accelerated failure time models. J Am Stat Assoc 104(487):1192–1202MathSciNetCrossRefMATH Shen Y, Ning J, Qin J (2009) Analyzing length-biased data with semiparametric transformation and accelerated failure time models. J Am Stat Assoc 104(487):1192–1202MathSciNetCrossRefMATH
Zurück zum Zitat Shen Y, Ning J, Qin J (2012) Likelihood approaches for the invariant density ratio model with biased-sampling data. Biometrika 99(2):363–378MathSciNetCrossRefMATH Shen Y, Ning J, Qin J (2012) Likelihood approaches for the invariant density ratio model with biased-sampling data. Biometrika 99(2):363–378MathSciNetCrossRefMATH
Zurück zum Zitat Simon R (1980) Length biased sampling in etiologic studies. Am J Epidemiol 111(4):444–452 Simon R (1980) Length biased sampling in etiologic studies. Am J Epidemiol 111(4):444–452
Zurück zum Zitat Terwilliger JD, Shannon WD, Lathrop GM, Nolan JP, Goldin LR, Chase GA, Weeks DE (1997) True and false positive peaks in genomewide scans: applications of length-biased sampling to linkage mapping. Am J Hum Genet 61(2):430–438CrossRef Terwilliger JD, Shannon WD, Lathrop GM, Nolan JP, Goldin LR, Chase GA, Weeks DE (1997) True and false positive peaks in genomewide scans: applications of length-biased sampling to linkage mapping. Am J Hum Genet 61(2):430–438CrossRef
Zurück zum Zitat Turnbull BW (1976) The empirical distribution function with arbitrarily grouped, censored and truncated data. J R Stat Soc Ser B (Methodol) 38(3):290–295MathSciNetMATH Turnbull BW (1976) The empirical distribution function with arbitrarily grouped, censored and truncated data. J R Stat Soc Ser B (Methodol) 38(3):290–295MathSciNetMATH
Zurück zum Zitat Vardi Y (1989) Multiplicative censoring, renewal processes, deconvolution and decreasing density: Nonparametric estimation. Biometrika 76:751–761MathSciNetCrossRefMATH Vardi Y (1989) Multiplicative censoring, renewal processes, deconvolution and decreasing density: Nonparametric estimation. Biometrika 76:751–761MathSciNetCrossRefMATH
Zurück zum Zitat Wang MC, Jewell NP, Tsai WY (1986) Asymptotic properties of the product limit estimate under random truncation. Ann Stat 14:1597–1605MathSciNetCrossRefMATH Wang MC, Jewell NP, Tsai WY (1986) Asymptotic properties of the product limit estimate under random truncation. Ann Stat 14:1597–1605MathSciNetCrossRefMATH
Zurück zum Zitat Wang X, Wang Q (2015) Estimation for semiparametric transformation models with length-biased sampling. J Stat Plan Inference 156:80–89MathSciNetCrossRefMATH Wang X, Wang Q (2015) Estimation for semiparametric transformation models with length-biased sampling. J Stat Plan Inference 156:80–89MathSciNetCrossRefMATH
Zurück zum Zitat Wolfson C, Wolfson DB, Asgharian M, M’Lan CE, Østbye T, Rockwood K, Df Hogan (2001) A reevaluation of the duration of survival after the onset of dementia. N Engl J Med 344(15):1111–1116CrossRef Wolfson C, Wolfson DB, Asgharian M, M’Lan CE, Østbye T, Rockwood K, Df Hogan (2001) A reevaluation of the duration of survival after the onset of dementia. N Engl J Med 344(15):1111–1116CrossRef
Zurück zum Zitat Zelen M (2004) Forward and backward recurrence times and length biased sampling: age specific models. Lifetime Data Anal 10(4):325–334MathSciNetCrossRefMATH Zelen M (2004) Forward and backward recurrence times and length biased sampling: age specific models. Lifetime Data Anal 10(4):325–334MathSciNetCrossRefMATH
Zurück zum Zitat Zhang F, Chen X, Zhou Y (2014) Proportional hazards model with varying coefficients for length-biased data. Lifetime Data Anal 20(1):132–157MathSciNetCrossRefMATH Zhang F, Chen X, Zhou Y (2014) Proportional hazards model with varying coefficients for length-biased data. Lifetime Data Anal 20(1):132–157MathSciNetCrossRefMATH
Metadaten
Titel
Nonparametric and semiparametric regression estimation for length-biased survival data
verfasst von
Yu Shen
Jing Ning
Jing Qin
Publikationsdatum
16.04.2016
Verlag
Springer US
Erschienen in
Lifetime Data Analysis / Ausgabe 1/2017
Print ISSN: 1380-7870
Elektronische ISSN: 1572-9249
DOI
https://doi.org/10.1007/s10985-016-9367-y

Weitere Artikel der Ausgabe 1/2017

Lifetime Data Analysis 1/2017 Zur Ausgabe

Editorial

Editorial