Skip to main content
Erschienen in: Lifetime Data Analysis 1/2014

01.01.2014

Cross-ratio estimation for bivariate failure times with left truncation

verfasst von: Tianle Hu, Xihong Lin, Bin Nan

Erschienen in: Lifetime Data Analysis | Ausgabe 1/2014

Einloggen

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

search-config
loading …

Abstract

The cross-ratio is an important local measure that characterizes the dependence between bivariate failure times. To estimate the cross-ratio in follow-up studies where delayed entry is present, estimation procedures need to account for left truncation. Ignoring left truncation yields biased estimates of the cross-ratio. We extend the method of Hu et al., Biometrika 98:341–354 (2011) by modifying the risk sets and relevant indicators to handle left-truncated bivariate failure times, which yields the cross-ratio estimate with desirable asymptotic properties that can be shown by the same techniques used in Hu et al., Biometrika 98:341–354 (2011). Numerical studies are conducted.

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!

Anhänge
Nur mit Berechtigung zugänglich
Literatur
Zurück zum Zitat Bandeen-Roche K, Ning J (2008) Non-parametric estimation of bivariate failure time associations in the presence of a competing risk. Biometrika 95:221–232CrossRefMATHMathSciNet Bandeen-Roche K, Ning J (2008) Non-parametric estimation of bivariate failure time associations in the presence of a competing risk. Biometrika 95:221–232CrossRefMATHMathSciNet
Zurück zum Zitat Clayton DG (1978) A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65:141–151CrossRefMATHMathSciNet Clayton DG (1978) A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65:141–151CrossRefMATHMathSciNet
Zurück zum Zitat Cox DR (1972) Regression models and life tables (with discussion). J R Stat Soc B 34:187–220MATH Cox DR (1972) Regression models and life tables (with discussion). J R Stat Soc B 34:187–220MATH
Zurück zum Zitat Duffy DL, Martin NG, Matthews JD (1990) Appendectomy in Australian twins. Am J Hum Genet 47:590–592 Duffy DL, Martin NG, Matthews JD (1990) Appendectomy in Australian twins. Am J Hum Genet 47:590–592
Zurück zum Zitat Fan J, Hsu L, Prentice RL (2000a) Dependence estimation over a finite bivariate failure time region. Lifetime Data Anal 6:343–355CrossRefMATHMathSciNet Fan J, Hsu L, Prentice RL (2000a) Dependence estimation over a finite bivariate failure time region. Lifetime Data Anal 6:343–355CrossRefMATHMathSciNet
Zurück zum Zitat Fan J, Prentice RL, Hsu L (2000b) A class of weighted dependence measures for bivariate failure time data. J R Stat Soc B 62:181–190CrossRefMATHMathSciNet Fan J, Prentice RL, Hsu L (2000b) A class of weighted dependence measures for bivariate failure time data. J R Stat Soc B 62:181–190CrossRefMATHMathSciNet
Zurück zum Zitat Fan J, Prentice RL (2002) Covariate-adjusted dependence estimation on a finite bivariate failure time region. Stat Sin 12:689–705MATHMathSciNet Fan J, Prentice RL (2002) Covariate-adjusted dependence estimation on a finite bivariate failure time region. Stat Sin 12:689–705MATHMathSciNet
Zurück zum Zitat Glidden DV (2000) A two-stage estimator of the dependence parameter for the Clayton–Oakes model. Lifetime Data Anal 6:141–156CrossRefMATHMathSciNet Glidden DV (2000) A two-stage estimator of the dependence parameter for the Clayton–Oakes model. Lifetime Data Anal 6:141–156CrossRefMATHMathSciNet
Zurück zum Zitat Glidden DV, Self SG (1999) Semiparametric likelihood estimation in the Clayton–Oakes failure time model. Scand J Stat 26:363–372CrossRefMATHMathSciNet Glidden DV, Self SG (1999) Semiparametric likelihood estimation in the Clayton–Oakes failure time model. Scand J Stat 26:363–372CrossRefMATHMathSciNet
Zurück zum Zitat Gorfine M, Hsu L, Prentice RL (2003) Estimation of dependence between paired correlated failure times in the presence of covariate measurement error. J R Stat Soc Ser B 65(3):643–661CrossRefMATHMathSciNet Gorfine M, Hsu L, Prentice RL (2003) Estimation of dependence between paired correlated failure times in the presence of covariate measurement error. J R Stat Soc Ser B 65(3):643–661CrossRefMATHMathSciNet
Zurück zum Zitat Gürler Ü (1996) Bivariate estimation with right truncated data. J Am Stat Assoc 91:1152–1165MATH Gürler Ü (1996) Bivariate estimation with right truncated data. J Am Stat Assoc 91:1152–1165MATH
Zurück zum Zitat Hsu L, Prentice RL, Zhao LP, Fan JJ (1999) On dependence estimation using correlated failure time data from case–control family studies. Biometrika 86:743–753CrossRefMATHMathSciNet Hsu L, Prentice RL, Zhao LP, Fan JJ (1999) On dependence estimation using correlated failure time data from case–control family studies. Biometrika 86:743–753CrossRefMATHMathSciNet
Zurück zum Zitat Hu T, Nan B, Lin X, Robins J (2011) Time-dependent cross-ratio estimation for bivariate failure times. Biometrika 98(2):341–354CrossRefMATHMathSciNet Hu T, Nan B, Lin X, Robins J (2011) Time-dependent cross-ratio estimation for bivariate failure times. Biometrika 98(2):341–354CrossRefMATHMathSciNet
Zurück zum Zitat Ino Y, Betensky RA, Zlatescu MC, Sasaki H, Macdonald DR, Stemmer-Rachamimov AO, Ramsay DA, Cairncross JG, Louis DN (2001) Molecular subtypes of anaplastic oligodendroglioma: implications for patient management at diagnosis. Clin Cancer Res 7:839–845 Ino Y, Betensky RA, Zlatescu MC, Sasaki H, Macdonald DR, Stemmer-Rachamimov AO, Ramsay DA, Cairncross JG, Louis DN (2001) Molecular subtypes of anaplastic oligodendroglioma: implications for patient management at diagnosis. Clin Cancer Res 7:839–845
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 84:360–372CrossRefMATHMathSciNet Kalbfleisch JD, Lawless JF (1989) Inference based on retrospective ascertainment: an analysis of the data on transfusion-related AIDS. J Am Stat Assoc 84:360–372CrossRefMATHMathSciNet
Zurück zum Zitat Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data, 2nd edn. Wiley, New YorkCrossRefMATH Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data, 2nd edn. Wiley, New YorkCrossRefMATH
Zurück zum Zitat Lagakos SW, Barraj LM, De Gruttola V (1988) Nonparametric analysis of truncated survival data with applications to AIDS. Biometrika 75:515–523CrossRefMATHMathSciNet Lagakos SW, Barraj LM, De Gruttola V (1988) Nonparametric analysis of truncated survival data with applications to AIDS. Biometrika 75:515–523CrossRefMATHMathSciNet
Zurück zum Zitat Li Y, Lin X (2006) Semiparametric normal transformation models for spatially correlated survival data. J Am Stat Assoc 101:591–603CrossRefMATH Li Y, Lin X (2006) Semiparametric normal transformation models for spatially correlated survival data. J Am Stat Assoc 101:591–603CrossRefMATH
Zurück zum Zitat Li Y, Prentice RL, Lin X (2008) Semiparametric maximum likelihood estimation in normal transformation models for bivariate survival data. Biometrika 95:947–960CrossRefMATHMathSciNet Li Y, Prentice RL, Lin X (2008) Semiparametric maximum likelihood estimation in normal transformation models for bivariate survival data. Biometrika 95:947–960CrossRefMATHMathSciNet
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 100:484–492CrossRefMATHMathSciNet Martin EC, Betensky RA (2005) Testing quasi-independence of failure and truncation times via conditional Kendall’s tau. J Am Stat Assoc 100:484–492CrossRefMATHMathSciNet
Zurück zum Zitat Nan B, Lin X, Lisabeth LD, Harlow S (2006) Piecewise constant cross-ratio estimation for association of age at a marker event and age at menopause. J Am Stat Assoc 101:65–77CrossRefMATHMathSciNet Nan B, Lin X, Lisabeth LD, Harlow S (2006) Piecewise constant cross-ratio estimation for association of age at a marker event and age at menopause. J Am Stat Assoc 101:65–77CrossRefMATHMathSciNet
Zurück zum Zitat Oakes D (1982) A model for association in bivariate survival data. J R Stat Soc B 44:414–422MATHMathSciNet Oakes D (1982) A model for association in bivariate survival data. J R Stat Soc B 44:414–422MATHMathSciNet
Zurück zum Zitat Oakes D (1986) Semiparametric inference in a model for association in bivariate survival data. Biometrika 73:353–361MATHMathSciNet Oakes D (1986) Semiparametric inference in a model for association in bivariate survival data. Biometrika 73:353–361MATHMathSciNet
Zurück zum Zitat Prentice RL, Hsu L (1997) Regression on hazard ratios and cross ratios in multivariate failure time analysis. Biometrika 84:349–363CrossRefMATHMathSciNet Prentice RL, Hsu L (1997) Regression on hazard ratios and cross ratios in multivariate failure time analysis. Biometrika 84:349–363CrossRefMATHMathSciNet
Zurück zum Zitat Shih J, Louis TA (1995) Inference on the association parameter in copula models for bivariate survival data. Biometrics 51:1384–1399CrossRefMATHMathSciNet Shih J, Louis TA (1995) Inference on the association parameter in copula models for bivariate survival data. Biometrics 51:1384–1399CrossRefMATHMathSciNet
Zurück zum Zitat van der Laan MJ (1996) Nonparametric estimation of the bivariate survival function with truncated data. J Multivar Anal 58:107–131CrossRefMATH van der Laan MJ (1996) Nonparametric estimation of the bivariate survival function with truncated data. J Multivar Anal 58:107–131CrossRefMATH
Zurück zum Zitat van der Vaart A, Wellner JA (1996) Weak convergence and empirical processes. Springer, New YorkCrossRefMATH van der Vaart A, Wellner JA (1996) Weak convergence and empirical processes. Springer, New YorkCrossRefMATH
Metadaten
Titel
Cross-ratio estimation for bivariate failure times with left truncation
verfasst von
Tianle Hu
Xihong Lin
Bin Nan
Publikationsdatum
01.01.2014
Verlag
Springer US
Erschienen in
Lifetime Data Analysis / Ausgabe 1/2014
Print ISSN: 1380-7870
Elektronische ISSN: 1572-9249
DOI
https://doi.org/10.1007/s10985-013-9263-7

Weitere Artikel der Ausgabe 1/2014

Lifetime Data Analysis 1/2014 Zur Ausgabe