nach oben

Lifetime Data Analysis

Erschienen in:

01.01.2014

Proportional hazards model with varying coefficients for length-biased data

verfasst von: Feipeng Zhang, Xuerong Chen, Yong Zhou

Erschienen in: Lifetime Data Analysis | Ausgabe 1/2014

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

Length-biased data arise in many important applications including epidemiological cohort studies, cancer prevention trials and studies of labor economics. Such data are also often subject to right censoring due to loss of follow-up or the end of study. In this paper, we consider a proportional hazards model with varying coefficients for right-censored and length-biased data, which is used to study the interact effect nonlinearly of covariates with an exposure variable. A local estimating equation method is proposed for the unknown coefficients and the intercept function in the model. The asymptotic properties of the proposed estimators are established by using the martingale theory and kernel smoothing techniques. Our simulation studies demonstrate that the proposed estimators have an excellent finite-sample performance. The Channing House data is analyzed to demonstrate the applications of the proposed method.

Vorheriger Artikel On computing standard errors for marginal structural Cox models

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!

Jetzt informieren

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!

Jetzt informieren

Nur mit Berechtigung zugänglich

Addona V, Wolfson D (2006) A formal test for the stationarity of the incidence rate using data from a prevalent cohort study with follow-up. Lifetime Data Anal 12:267–284CrossRefMathSciNet

Andersen P, Gill R (1982) Cox’s regression model for counting processes: a large sample study. Ann Stat 10:1100–1120CrossRefMATHMathSciNet

Asgharian M, Wolfson D (2005) Asymptotic behavior of the unconditional npmle of the length-biased survivor function from right censored prevalent cohort data. Ann Stat 33:2109–2131CrossRefMATHMathSciNet

Asgharian M, M’Lan C, Wolfson D (2002) Length-biased sampling with right censoring. J Am Stat Assoc 97:201–209CrossRefMATHMathSciNet

Cai J, Fan J, Zhou H, Zhou Y (2007) Hazard models with varying coefficients for multivariate failure time data. Ann Stat 35:324–354CrossRefMATHMathSciNet

Cai Z, Sun Y (2003) Local linear estimation for time-dependent coefficients in Cox’s regression models. Scand J Stat 30:93–111CrossRefMATHMathSciNet

Cai Z, Fan J, Li R (2000a) Efficient estimation and inferences for varying-coefficient models. J Am Stat Assoc 95:888–902CrossRefMATHMathSciNet

Cai Z, Fan J, Yao Q (2000b) Functional-coefficient regression models for nonlinear time series. J Am Stat Assoc 95:941–956CrossRefMATHMathSciNet

Carroll R, Ruppert D, Welsh A (1998) Local estimating equations. J Am Stat Assoc 93:214–227CrossRefMATHMathSciNet

Chen R, Tsay R (1993) Functional-coefficient autoregressive models. J Am Stat Assoc 88:298–308MATHMathSciNet

Cox D (1972) Regression models and life-tables. J Royal Stat Soc Ser B 34:187–220MATH

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

Fan J, Zhang W (1999) Statistical estimation in varying coefficient models. Ann Stat 27:1491–1518CrossRefMATHMathSciNet

Fan J, Lin H, Zhou Y (2006) Local partial-likelihood estimation for lifetime data. Ann Stat 34:290–325CrossRefMATHMathSciNet

Ghosh D (2008) Proportional hazards regression for cancer studies. Biometrics 64:141–148CrossRefMATHMathSciNet

Gill R, Vardi Y, Wellner J (1988) Large sample theory of empirical distributions in biased sampling models. Ann Stat 16:1069–1112CrossRefMATHMathSciNet

Gretton A, Györfi L (2010) Consistent nonparametric tests of independence. J Mach Learn Res 11:1391–1423MATHMathSciNet

Hastie T, Tibshirani R (1993) Varying-coefficient models. J Royal Stat Soc Ser B 55:757–796MATHMathSciNet

Hoover D, Rice J, Wu C, Yang L (1998) Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika 85:809–822CrossRefMATHMathSciNet

Huang Y, Wang M (1995) Estimating the occurrence rate for prevalent survival data in competing risks models. J Am Stat Assoc 80:1406–1415CrossRef

Hyde J (1980) Survival analysis with incomplete observations. Biostatistics 30:31–46

Kalbfleisch J, Lawless J (1991) Regression models for right truncated data with applications to AIDS incubation times and reporting lags. Stat Sinica 1:19–32MATH

Keiding N (1992) Independent delayed entry. In: Klein JP, Goel P (eds) Survival analysis: state of the art. Kluwer, Dordrecht, pp 309–326CrossRef

Klein J, Moeschberger M (2003) Survival analysis: techniques for censored and truncated data, 2nd edn. Springer, New York

Lagakos S, Barraj L, De Gruttola V (1988) Nonparametric analysis of truncated survival data, with application to AIDS. Biometrika 75:515–523CrossRefMATHMathSciNet

Lancaster T (1979) Econometric methods for the duration of unemployment. Econometrica 47:939–956CrossRefMATHMathSciNet

Luo X, Tsai W (2009) Nonparametric estimation for right-censored length-biased data: a pseudo-partial likelihood approach. Biometrika 96:873–886CrossRefMATHMathSciNet

Martinussen T, Scheike T, Skovgaard I (2002) Efficient estimation of fixed and time-varying covariate effects in multiplicative intensity models. Scand J Stat 29:57–74CrossRefMATHMathSciNet

Marzec L, Marzec P (1997) On fitting Cox’s regression model with time-dependent coefficients. Biometrika 84:901–908CrossRefMATHMathSciNet

Murphy S (1993) Testing for a time dependent coefficient in Cox’s regression model. Scand J Stat 20:35–50MATH

Muttlak H, McDonald L (1990) Ranked set sampling with size-biased probability of selection. Biometrics 46:435–445CrossRefMATHMathSciNet

Pepe M, Fleming T (1991) Weighted Kaplan-Meier statistics: large sample and optimality considerations. J Roy Statist Soc Ser B 53:341–352

Qin J, Shen Y (2010) Statistical methods for analyzing right-censored length-biased data under Cox model. Biometrics 66:382–392CrossRefMATHMathSciNet

Tian L, Zucker D, Wei L (2005) On the Cox model with time-varying regression coefficients. J Am Stat Assoc 100:172–183CrossRefMATHMathSciNet

Tsai W (2009) Pseudo-partial likelihood for proportional hazards models with biased-sampling data. Biometrika 96:601–615CrossRefMATHMathSciNet

Turnbull B (1976) The empirical distribution function with arbitrarily grouped, censored and truncated data. J Royal Stat Soc Ser B 38:290–295MATHMathSciNet

Vardi Y (1982) Nonparametric estimation in the presence of length bias. Ann Stat 10:616–620CrossRefMATHMathSciNet

Vardi Y (1989) Multiplicative censoring, renewal processes, deconvolution and decreasing density: nonparametric estimation. Biometrika 76:751–761CrossRefMATHMathSciNet

Wang M (1989) A semiparametric model for randomly truncated data. J Am Stat Assoc 84:742–748CrossRefMATH

Wang M (1991) Nonparametric estimation from cross-sectional survival data. J Am Stat Assoc 86:130–143CrossRefMATH

Wang M (1996) Hazards regression analysis for length-biased data. Biometrika 83:343–354CrossRefMATHMathSciNet

Wang M, Brookmeyer R, Jewell N (1993) Statistical models for prevalent cohort data. Biometrics 49:1–11CrossRefMATHMathSciNet

Winter B, Földes A (1988) A product-limit estimator for use with length-biased data. Can J Stat 16:337–355CrossRefMATH

Wu C, Chiang C (2000) Kernel smoothing on varying coefficient models with longitudinal dependent variable. Stat Sinica 10:433–456MATHMathSciNet

Wu C, Chiang C, Hoover D (1998) Asymptotic confidence regions for kernel smoothing of a varying-coefficient model with longitudinal data. J Am Stat Assoc 93:1388–1402CrossRefMATHMathSciNet

Ying Z, Jung S, Wei L (1995) Survival analysis with median regression models. J Am Stat Assoc 90:178–184CrossRefMATHMathSciNet

Zelen M (2004) Forward and backward recurrence times and length biased sampling: age specific models. Lifetime Data Anal 10:325–334CrossRefMATHMathSciNet

Zelen M, Feinleib M (1969) On the theory of screening for chronic diseases. Biometrika 56:601–614CrossRefMATHMathSciNet

Titel: Proportional hazards model with varying coefficients for length-biased data
verfasst von: Feipeng Zhang
Xuerong Chen
Yong Zhou
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/s10985-013-9257-5

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

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

Springer Professional "Wirtschaft"

Springer Professional "Wirtschaft+Technik"

Weitere Artikel der Ausgabe 1/2014

Case-cohort analysis of clusters of recurrent events

The versatility of multi-state models for the analysis of longitudinal data with unobservable features

Matched survival data in a co-twin control design

On computing standard errors for marginal structural Cox models

Survival analysis with incomplete genetic data

Cross-ratio estimation for bivariate failure times with left truncation