Skip to main content
Top
Published in: Lifetime Data Analysis 4/2023

07-05-2023

Improving marginal hazard ratio estimation using quadratic inference functions

Authors: Hongkai Liang, Xiaoguang Wang, Yingwei Peng, Yi Niu

Published in: Lifetime Data Analysis | Issue 4/2023

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Clustered and multivariate failure time data are commonly encountered in biomedical studies and a marginal regression approach is often employed to identify the potential risk factors of a failure. We consider a semiparametric marginal Cox proportional hazards model for right-censored survival data with potential correlation. We propose to use a quadratic inference function method based on the generalized method of moments to obtain the optimal hazard ratio estimators. The inverse of the working correlation matrix is represented by the linear combination of basis matrices in the context of the estimating equation. We investigate the asymptotic properties of the regression estimators from the proposed method. The optimality of the hazard ratio estimators is discussed. Our simulation study shows that the estimator from the quadratic inference approach is more efficient than those from existing estimating equation methods whether the working correlation structure is correctly specified or not. Finally, we apply the model and the proposed estimation method to analyze a study of tooth loss and have uncovered new insights that were previously inaccessible using existing methods.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

Appendix
Available only for authorised users
Literature
go back to reference Cai J, Prentice RL (1995) Estimating equations for hazard ratio parameters based on correlated failure time data. Biometrika 82:151–164MathSciNetCrossRefMATH Cai J, Prentice RL (1995) Estimating equations for hazard ratio parameters based on correlated failure time data. Biometrika 82:151–164MathSciNetCrossRefMATH
go back to reference Cai J, Prentice RL (1997) Regression analysis for correlated failure time data. Biometrika 3:197–213MATH Cai J, Prentice RL (1997) Regression analysis for correlated failure time data. Biometrika 3:197–213MATH
go back to reference Chien LC, Chang LY, Shen CW (2022) A model selection criterion for clustered survival analysis with informative cluster size. Pharm Stat 1–17 Chien LC, Chang LY, Shen CW (2022) A model selection criterion for clustered survival analysis with informative cluster size. Pharm Stat 1–17
go back to reference 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 65:141–151MathSciNetCrossRefMATH 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 65:141–151MathSciNetCrossRefMATH
go back to reference Crowder MJ (1995) On the use of a working correlation matrix in using generalized linear models for repeated measurements. Biometrika 82:407–410CrossRefMATH Crowder MJ (1995) On the use of a working correlation matrix in using generalized linear models for repeated measurements. Biometrika 82:407–410CrossRefMATH
go back to reference Gray RJ, Li Y (2002) Optimal weight functions for marginal proportional hazards analysis of clustered failure time data. Lifetime Data Anal 8:5–19MathSciNetCrossRefMATH Gray RJ, Li Y (2002) Optimal weight functions for marginal proportional hazards analysis of clustered failure time data. Lifetime Data Anal 8:5–19MathSciNetCrossRefMATH
go back to reference Hougaard P (1995) Frailty models for survival data. Lifetime Data Anal 1:255–273CrossRef Hougaard P (1995) Frailty models for survival data. Lifetime Data Anal 1:255–273CrossRef
go back to reference Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data. Wiley, HobokenCrossRefMATH Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data. Wiley, HobokenCrossRefMATH
go back to reference Lee EW, Wei LJ, Amato DA, Leurgans S (1992) Cox-type regression analysis for large numbers of small groups of correlated failure time observations. Surviv Anal State Art 211:237–247MathSciNetCrossRefMATH Lee EW, Wei LJ, Amato DA, Leurgans S (1992) Cox-type regression analysis for large numbers of small groups of correlated failure time observations. Surviv Anal State Art 211:237–247MathSciNetCrossRefMATH
go back to reference Lin DY (1994) Cox regression analysis of multivariate failure time data: the marginal approach. Stat Med 13:2233–2247CrossRef Lin DY (1994) Cox regression analysis of multivariate failure time data: the marginal approach. Stat Med 13:2233–2247CrossRef
go back to reference McGilchrist CA, Aisbett CW (1991) Regression with frailty in survival analysis. Biometrics 47:461–466CrossRef McGilchrist CA, Aisbett CW (1991) Regression with frailty in survival analysis. Biometrics 47:461–466CrossRef
go back to reference Prentice RL, Hsu L (1997) Regression on hazard ratios and cross ratios in multivariate failure time analysis. Biometrika 84:349–363MathSciNetCrossRefMATH Prentice RL, Hsu L (1997) Regression on hazard ratios and cross ratios in multivariate failure time analysis. Biometrika 84:349–363MathSciNetCrossRefMATH
go back to reference Qu A, Lindsay BG, Li B (2000) Improving generalised estimating equations using quadratic inference functions. Biometrika 87:823–836MathSciNetCrossRefMATH Qu A, Lindsay BG, Li B (2000) Improving generalised estimating equations using quadratic inference functions. Biometrika 87:823–836MathSciNetCrossRefMATH
go back to reference Segal MR, Neuhaus JM (1993) Robust inference for multivariate survival data. Stat Med 12:1019–1031CrossRef Segal MR, Neuhaus JM (1993) Robust inference for multivariate survival data. Stat Med 12:1019–1031CrossRef
go back to reference Therneau T, Grambsch PM (2000) Modeling survival data: extending the cox model. Springer-Verlag, New YorkCrossRefMATH Therneau T, Grambsch PM (2000) Modeling survival data: extending the cox model. Springer-Verlag, New YorkCrossRefMATH
go back to reference Wei LJ, Lin DY, Weissfeld L (1989) Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. J Am Stat Assoc 84:1065–1073MathSciNetCrossRef Wei LJ, Lin DY, Weissfeld L (1989) Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. J Am Stat Assoc 84:1065–1073MathSciNetCrossRef
go back to reference Xue L, Wang L, Qu A (2010) Incorporating correlation for multivariate failure time data when cluster size is large. Biometrics 66:393–404MathSciNetCrossRefMATH Xue L, Wang L, Qu A (2010) Incorporating correlation for multivariate failure time data when cluster size is large. Biometrics 66:393–404MathSciNetCrossRefMATH
go back to reference Yan F, Zhu L, Liu Y, Cai J, Zhou H (2021) Semiparametric regression based on quadratic inference function for multivariate failure time data with auxiliary information. Lifetime Data Anal 27:269–299MathSciNetCrossRefMATH Yan F, Zhu L, Liu Y, Cai J, Zhou H (2021) Semiparametric regression based on quadratic inference function for multivariate failure time data with auxiliary information. Lifetime Data Anal 27:269–299MathSciNetCrossRefMATH
Metadata
Title
Improving marginal hazard ratio estimation using quadratic inference functions
Authors
Hongkai Liang
Xiaoguang Wang
Yingwei Peng
Yi Niu
Publication date
07-05-2023
Publisher
Springer US
Published in
Lifetime Data Analysis / Issue 4/2023
Print ISSN: 1380-7870
Electronic ISSN: 1572-9249
DOI
https://doi.org/10.1007/s10985-023-09598-4

Other articles of this Issue 4/2023

Lifetime Data Analysis 4/2023 Go to the issue