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Correlated Frailty Model: an Advantageous Approach for Covariate Analysis of Tuberculosis Data


Affiliations
1 Tuberculosis Research Centre (ICMR), Chennai-600 031, India
 

The demonstration of varying treatment effects among different subjects of patients is an important part of the analysis of clinical trials. But issues of censoring, truncation and inclusion criteria complicate the analysis of clinical trial data. Recent advances in proportional hazard methodologies provide regression diagnostics, improved point and interval estimates of the parameters of survival functions, handling of time dependent covariates in the analysis. This paper discusses the interactions between treatment and patient in the presence of censoring and to account heterogeneity using frailty model. The application of the frailty model with respect to pulmonary tuberculosis data are presented and discussed.

Keywords

Tuberculosis, Cox Proportional Hazard Model, Time-dependent Covariates, Gamma Shared Frailty Model
User

  • Aalen (1988) Heterogeneity in survival analysis. Stat. in Medicine. 7, 1121-1137.

  • Altman and De Stavola B (1994) Practical problems in fitting a proportional hazards model to data with updated measurements of covariates. Stat. Med. 13, 301-341.

  • Andersen PK (1986) Time-dependent covariates and Markov processes. In: Modern statistical methods in chronic disease epidemiology. Moolgavkar SH & Prentice RL (eds), Wiley, NY. pp: 82–103.

  • Andersen PK, Klein JP and Zhang MJ (1999) Testing for centre effects in multi-centre survival studies: a Monte Carlo comparison of fixed and random effects tests. Stat. Med. 18, 1489- 1500.

  • Andersen PK, Klein JP, Knudsen KM and Palacios RT (1997) Estimation of variance in Cox’s regression model with shared gamma frailties. Biometrics. 53,1475–1484.

  • Aydemir O, Aydemir S and Dirschedl P (1999) Analysis of time-dependent covariates in failure time data. Stat. Med. 18, 2123-2134.

  • Clayton D (1978) A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika. 65,141–151

  • Clayton D (1991) A Monte Carlo method for Bayesian inference in frailty models. Biometrics. 47, 467–485.

  • Clayton D and Cuzick J (1985) Multivariate generalization of the proportional hazards model (with Discussion). J. Royal Stat. Soc. 148, 82–117.

  • Cox DR (1972) Regression model and life tables (with discussion). J. Royal Stat. Soc.(B), 34, 187–220.

  • Cox DR (1975) Partial likelihood. Biometrika. 62, 269- 276.

  • Cox DR and Oakes D (1984) Analysis of survival data. London Chapman & Hall.

  • Crowley J and Hu M (1977) Covariate analysis of heart transplant survival data. J. Am. Stat. Ass. 78, 27-36.

  • Duchateau L, Janssen P, Lindsey P, Legrand C, Nguti R and Sylvester R (2002) The shared frailty model and the power for heterogeneity tests in multicenter trails. Comp. Stat. Data Analysis. 40, 603–620.

  • Fisher LD and Lin DY (1999) Time-dependent covariates in the cox proportional-hazards regression model. Ann. Rev. Pub. Health. 20,145–57.

  • Hougaard P (1986) A class of multivariate failure time distributions. Biometrika. 73, 671–678.

  • Hougaard P (2000) Analysis of multivariate survival data. Springer: NY. pp: 312–381.

  • Jenkins SP (1997) Discrete time proportional hazard regression. STATA Tech. Bull. 39, 17-32.

  • Klein JP and Moeschberger ML (1997) Survival Analysis Techniques for Censored and truncated data, Springer-Verlag: NY.

  • Klein JP (1992) Semi-parametric estimation of random effects using the Cox model based on the EM algorithm. Biometrics. 48, 795–806.

  • Liang KY, Self SG, Bandeen-Roche KJ and Zeger SL (1995) Some recent developments for regression analysis of multivariate failure time data. Lifetime Data Anal. 1, 403-415.

  • Manton K and Stallard E (1981) Methods for evaluating the heterogeneity of aging processes in human populations using vital statistics data: explaining the black/white mortality crossover by a model of mortality selection. Human Bio. 53, 47–67.

  • Murphy SA (1992) Consistency in a proportional hazards model incorporating a random effect. Annals Stat. 22, 712–731.

  • Parner E (1998) Asymptotic theory for the correlated gamma frailty model. Ann. Stat. 26, 183–214.

  • Rahgozar M, Faghihzadeh S, Rouchi GB and Peng Y (2008) The power of testing a semi-parametric shared gamma frailty parameter in failure time data. Stat. Med. 27, 4328-4339.

  • Tuberculosis Research Centre, ICMR, Chennai, India (2004) Split-drug regimens for the treatment of patients with sputum smear-positive pulmonary tuberculosis- a unique approach. Trop. Med. Int. Health. 9, 551-58.

  • Vaupel JW, Manton K and Stallard E (1979) The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography. 16, 439–454.

  • Vu H, Segal MR, Knuiman MW and James IR (2001) Asymptotic and small sample statistical properties of random frailty variance estimates for shared gamma frailty models. Comm. Stat—Simulation Comp. 30, 581–595


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  • Correlated Frailty Model: an Advantageous Approach for Covariate Analysis of Tuberculosis Data

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Authors

C. Ponnuraja
Tuberculosis Research Centre (ICMR), Chennai-600 031, India
P. Venkatesan
Tuberculosis Research Centre (ICMR), Chennai-600 031, India

Abstract


The demonstration of varying treatment effects among different subjects of patients is an important part of the analysis of clinical trials. But issues of censoring, truncation and inclusion criteria complicate the analysis of clinical trial data. Recent advances in proportional hazard methodologies provide regression diagnostics, improved point and interval estimates of the parameters of survival functions, handling of time dependent covariates in the analysis. This paper discusses the interactions between treatment and patient in the presence of censoring and to account heterogeneity using frailty model. The application of the frailty model with respect to pulmonary tuberculosis data are presented and discussed.

Keywords


Tuberculosis, Cox Proportional Hazard Model, Time-dependent Covariates, Gamma Shared Frailty Model

References





DOI: https://doi.org/10.17485/ijst%2F2010%2Fv3i2%2F29668