Yıl 2023,
Cilt: 52 Sayı: 5, 1263 - 1281, 31.10.2023
Habbiburr Rehman
N. Chandra
,
Ali Abuzaid
Kaynakça
- [1] O.O. Aalen, A linear regression model for the analysis of life times, Stat. Med. 8
(8), 907-925, 1989.
- [2] S. Anjana and P. Sankaran, Parametric analysis of lifetime data with multiple causes
of failure using cause-specific reversed hazard rates, Calcutta Stat. Assoc. Bull. 67
(3-4), 129-142, 2015.
- [3] J. Beyersmann, A. Allignol and M. Schumacher, Competing Risks and Multistate
Models with R, Springer Science & Business Media, New York, 2012.
- [4] D.R. Cox, Regression models and life-tables, J. R. Stat. Soc. Ser. B (Methodol.)
34(2), 187-220, 1972.
- [5] A. Gelman, Prior distributions for variance parameters in hierarchical models (comment
on article by Browne and Draper), Bayesian Anal. 1 (3) 515-534, 2006.
- [6] S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions, and the
Bayesian restoration of images, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-
6 (6), 721-741, 1984.
- [7] W.R. Gilks, R. Sylvia and S. David, Markov Chain Monte Carlo in Practice, CRC
press, Boca Raton, 1996
- [8] C.B. Guure and N.A. Ibrahim, Bayesian analysis of the survival function and failure
rate of Weibull distribution with censored data, Math. Probl. Eng. 2012.
- [9] B. Haller, G. Schmidt and K. Ulm, Applying competing risks regression models: an
overview, Lifetime Data Anal. 19 (1), 33-58, 2013.
- [10] W.K. Hastings, Monte Carlo sampling methods using Markov chains and their applications,
Biometrika 57 (1), 97-109, 1970.
- [11] J.H. Jeong and J. Fine, Direct parametric inference for the cumulative incidence
function, J. R. Stat. Soc. Ser. C (Applied Stat.) 55 (2), 187-200, 2006.
- [12] H. Jiang, M. Xie and L. Tang, Markov chain monte Carlo methods for parameter
estimation of the modified Weibull distribution , J. Appl. Stat. 35 (6), 647-658, 2008.
- [13] J.D. Kalbeisch and R.L. Prentice, The Statistical Analysis of Failure Time Data,
volume 360, John Wiley & Sons, New Jersey, 2002.
- [14] J.P. Klein and M.L. Moeschberger, Survival Analysis: Techniques for Censored and
Truncated Data, Springer-Verlag, New York, 2003.
- [15] C. Lai, M. Xie and D. Murthy, A modified Weibull distribution, IEEE Trans. Reliab.
52 (1), 33-37, 2003.
- [16] X. Lai, K.K. Yau and L. Liu, Competing risk model with bivariate random eects for
clustered survival data, Comput. Stat. Data Anal. 112, 215-223, 2017.
- [17] J.F. Lawless, Statistical Models and Methods for Lifetime Data, volume 362, John
Wiley & Sons, New Jersey, 2003.
- [18] M. Lee, Parametric inference for quantile event times with adjustment for covariates
on competing risks data, J. Appl. Stat. 46 (12), 2128-2144, 2019.
- [19] W. Li, X. Xue and Y. Long, Long. An additive subdistribution hazard model for
competing risks data, Commun. Stat. - Theory Methods 46 (23), 11667-11687, 2017.
- [20] D. Lin and Z. Ying, Semiparametric analysis of general additive-multiplicative hazard
models for counting processes, Ann. Stat. 23 (5), 1712-1734, 1995.
- [21] D. Lin and Z. Ying, Semiparametric analysis of the additive risk model, Biometrika
81 (1), 61-71, 1994.
- [22] D. Lunn, C. Jackson, N. Best, D. Spiegelhalter and A. Thomas, The BUGS book: A
Practical Introduction to Bayesian Analysis, Chapman and Hall/CRC, Boca Raton,
2012.
- [23] J.A. Nelder and R. Mead, A simplex method for function minimization, Comput. J.
7 (4), 308-313, 1965.
- [24] H.K.T. Ng, Parameter estimation for a modified Weibull distribution, for progressively
type-II censored samples, IEEE Trans. Reliab. 54 (3), 374-380, 2005.
- [25] M. Pintilie, Competing Risks: A Practical Perspective, volume 58, John Wiley &
Sons, England, 2006.
- [26] N. Porta Bleda, G. Gómez Melis and M.L. Calle Rosingana, The role of survival
functions in competing risks, Technical report, Universitat Politùcnica de Catalunya,
2008.
- [27] R.L. Prentice, J.D. Kalbeisch, A.V. Peterson Jr, N. Flournoy, V.T. Farewell and N.E.
Breslow, The analysis of failure times in the presence of competing risks, Biometrics
34 (4), 541–554, 1978.
- [28] H. Rehman, N. Chandra, T. Emura and M. Pandey, Estimation of the modified
Weibull additive hazards regression model under competing risks, Symmetry, 15
(485), 2023, https://doi.org/10.3390/sym15020485.
- [29] H. Rehman, N. Chandra, F.S. Hosseini-Baharanchi, A.R. Baghestani and M.A.
Pourhoseingholi, Cause-specific hazard regression estimation for modified Weibull
distribution under a class of non-informative priors, J. Appl. Stat. 49 (7), 1784–
1801, 2022.
- [30] C.P. Robert, G. Casella and G. Casella, Introducing Monte Carlo methods with R,
volume 18, Springer Science & Business Media, New York, 2010.
- [31] P. Sankaran and S. Prasad, Additive risks regression model for middle censored
exponentiated-exponential lifetime data, Commun. Stat. Simul. Comput. 47 (7),
1963-1974, 2018.
- [32] Y. Shen and S. Cheng, Confidence bands for cumulative incidence curves under the
additive risk model, Biometrics 55(4), 1093-1100, 1999.
- [33] C. Siddhartha and G. Edward, Understanding the metropolis-hastings algorithm,
Stat. Methods Appt. 49 (4), 327-335, 1995.
- [34] S. Sinha, Bayesian Estimation, New Age International (P) Limited Publisher, New
Delhi, 1998.
- [35] J. Sun, L. Sun and N. Flournoy, Additive hazards model for competing risks analysis
of the case-cohort design, Commun. Stat. - Theory Methods 33 (2), 351-366, 2004.
- [36] T.M. Therneau and P.M. Grambsch, Modeling Survival Data: Extending the Cox
Model, Springer Science & Business Media, New York, 2000.
- [37] S. Upadhyay and A. Gupta, A Bayes analysis of modified Weibull distribution via
Markov chain Monte Carlo simulation, J. Stat. Comput. Simul. 80 (3), 241-254,
2010.
- [38] X. Zhang, H. Akcin and H.J. Lim, Regression analysis of competing risks data via
semi-parametric additive hazard model, Stat. Methods Appt. 20 (3), 357-381, 2011.
Analysis and modelling of competing risks survival data using modified Weibull additive hazards regression approach
Yıl 2023,
Cilt: 52 Sayı: 5, 1263 - 1281, 31.10.2023
Habbiburr Rehman
N. Chandra
,
Ali Abuzaid
Öz
The cause-specific hazard function plays an important role in developing the regression models for competing risks survival data. Proportional hazards and additive hazards are the commonly used regression approaches in survival analysis. Mostly, in literature, the proportional hazards model was used for parametric regression modelling of survival data. In this article, we introduce a parametric additive hazards regression model for survival analysis with competing risks. For employing a parametric model we consider the modified Weibull distribution as a baseline model which is capable to model survival data with non-monotonic behaviour of hazard rate. The estimation process is carried out via maximum likelihood and Bayesian approaches. In addition to Bayesian methods, a class of non-informative types of prior is introduced with squared error (symmetric) and linear-exponential (asymmetric) loss functions. The relative performance of the different estimators is assessed using Monte Carlo simulation. Finally, using the proposed methodology, a real data analysis is performed.
Kaynakça
- [1] O.O. Aalen, A linear regression model for the analysis of life times, Stat. Med. 8
(8), 907-925, 1989.
- [2] S. Anjana and P. Sankaran, Parametric analysis of lifetime data with multiple causes
of failure using cause-specific reversed hazard rates, Calcutta Stat. Assoc. Bull. 67
(3-4), 129-142, 2015.
- [3] J. Beyersmann, A. Allignol and M. Schumacher, Competing Risks and Multistate
Models with R, Springer Science & Business Media, New York, 2012.
- [4] D.R. Cox, Regression models and life-tables, J. R. Stat. Soc. Ser. B (Methodol.)
34(2), 187-220, 1972.
- [5] A. Gelman, Prior distributions for variance parameters in hierarchical models (comment
on article by Browne and Draper), Bayesian Anal. 1 (3) 515-534, 2006.
- [6] S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions, and the
Bayesian restoration of images, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-
6 (6), 721-741, 1984.
- [7] W.R. Gilks, R. Sylvia and S. David, Markov Chain Monte Carlo in Practice, CRC
press, Boca Raton, 1996
- [8] C.B. Guure and N.A. Ibrahim, Bayesian analysis of the survival function and failure
rate of Weibull distribution with censored data, Math. Probl. Eng. 2012.
- [9] B. Haller, G. Schmidt and K. Ulm, Applying competing risks regression models: an
overview, Lifetime Data Anal. 19 (1), 33-58, 2013.
- [10] W.K. Hastings, Monte Carlo sampling methods using Markov chains and their applications,
Biometrika 57 (1), 97-109, 1970.
- [11] J.H. Jeong and J. Fine, Direct parametric inference for the cumulative incidence
function, J. R. Stat. Soc. Ser. C (Applied Stat.) 55 (2), 187-200, 2006.
- [12] H. Jiang, M. Xie and L. Tang, Markov chain monte Carlo methods for parameter
estimation of the modified Weibull distribution , J. Appl. Stat. 35 (6), 647-658, 2008.
- [13] J.D. Kalbeisch and R.L. Prentice, The Statistical Analysis of Failure Time Data,
volume 360, John Wiley & Sons, New Jersey, 2002.
- [14] J.P. Klein and M.L. Moeschberger, Survival Analysis: Techniques for Censored and
Truncated Data, Springer-Verlag, New York, 2003.
- [15] C. Lai, M. Xie and D. Murthy, A modified Weibull distribution, IEEE Trans. Reliab.
52 (1), 33-37, 2003.
- [16] X. Lai, K.K. Yau and L. Liu, Competing risk model with bivariate random eects for
clustered survival data, Comput. Stat. Data Anal. 112, 215-223, 2017.
- [17] J.F. Lawless, Statistical Models and Methods for Lifetime Data, volume 362, John
Wiley & Sons, New Jersey, 2003.
- [18] M. Lee, Parametric inference for quantile event times with adjustment for covariates
on competing risks data, J. Appl. Stat. 46 (12), 2128-2144, 2019.
- [19] W. Li, X. Xue and Y. Long, Long. An additive subdistribution hazard model for
competing risks data, Commun. Stat. - Theory Methods 46 (23), 11667-11687, 2017.
- [20] D. Lin and Z. Ying, Semiparametric analysis of general additive-multiplicative hazard
models for counting processes, Ann. Stat. 23 (5), 1712-1734, 1995.
- [21] D. Lin and Z. Ying, Semiparametric analysis of the additive risk model, Biometrika
81 (1), 61-71, 1994.
- [22] D. Lunn, C. Jackson, N. Best, D. Spiegelhalter and A. Thomas, The BUGS book: A
Practical Introduction to Bayesian Analysis, Chapman and Hall/CRC, Boca Raton,
2012.
- [23] J.A. Nelder and R. Mead, A simplex method for function minimization, Comput. J.
7 (4), 308-313, 1965.
- [24] H.K.T. Ng, Parameter estimation for a modified Weibull distribution, for progressively
type-II censored samples, IEEE Trans. Reliab. 54 (3), 374-380, 2005.
- [25] M. Pintilie, Competing Risks: A Practical Perspective, volume 58, John Wiley &
Sons, England, 2006.
- [26] N. Porta Bleda, G. Gómez Melis and M.L. Calle Rosingana, The role of survival
functions in competing risks, Technical report, Universitat Politùcnica de Catalunya,
2008.
- [27] R.L. Prentice, J.D. Kalbeisch, A.V. Peterson Jr, N. Flournoy, V.T. Farewell and N.E.
Breslow, The analysis of failure times in the presence of competing risks, Biometrics
34 (4), 541–554, 1978.
- [28] H. Rehman, N. Chandra, T. Emura and M. Pandey, Estimation of the modified
Weibull additive hazards regression model under competing risks, Symmetry, 15
(485), 2023, https://doi.org/10.3390/sym15020485.
- [29] H. Rehman, N. Chandra, F.S. Hosseini-Baharanchi, A.R. Baghestani and M.A.
Pourhoseingholi, Cause-specific hazard regression estimation for modified Weibull
distribution under a class of non-informative priors, J. Appl. Stat. 49 (7), 1784–
1801, 2022.
- [30] C.P. Robert, G. Casella and G. Casella, Introducing Monte Carlo methods with R,
volume 18, Springer Science & Business Media, New York, 2010.
- [31] P. Sankaran and S. Prasad, Additive risks regression model for middle censored
exponentiated-exponential lifetime data, Commun. Stat. Simul. Comput. 47 (7),
1963-1974, 2018.
- [32] Y. Shen and S. Cheng, Confidence bands for cumulative incidence curves under the
additive risk model, Biometrics 55(4), 1093-1100, 1999.
- [33] C. Siddhartha and G. Edward, Understanding the metropolis-hastings algorithm,
Stat. Methods Appt. 49 (4), 327-335, 1995.
- [34] S. Sinha, Bayesian Estimation, New Age International (P) Limited Publisher, New
Delhi, 1998.
- [35] J. Sun, L. Sun and N. Flournoy, Additive hazards model for competing risks analysis
of the case-cohort design, Commun. Stat. - Theory Methods 33 (2), 351-366, 2004.
- [36] T.M. Therneau and P.M. Grambsch, Modeling Survival Data: Extending the Cox
Model, Springer Science & Business Media, New York, 2000.
- [37] S. Upadhyay and A. Gupta, A Bayes analysis of modified Weibull distribution via
Markov chain Monte Carlo simulation, J. Stat. Comput. Simul. 80 (3), 241-254,
2010.
- [38] X. Zhang, H. Akcin and H.J. Lim, Regression analysis of competing risks data via
semi-parametric additive hazard model, Stat. Methods Appt. 20 (3), 357-381, 2011.