Hatice IŞIK, Duru KARASOY, Uğur KARABEY

A new adjusted Bayesian method in Cox regression model with covariate subject to measurement error

An important bias can occur when estimating coefficients by maximizing the known partial likelihood function in the Cox regression model with the measurement error covariate. We focus here on Bayesian methods in order to adjust measurement error and aim to propose an adjusting Bayesian method. Constructing simulation studies using Markov Chain Monte Carlo simulation techniques to investigate the performance of models. We compare the proposed method with the existing method that used partial likelihood function, Bayesian Cox regression model ignoring measurement error, the adjusted Bayesian Cox regression model that exists in the literature by a simulation study which consists of different sample sizes, censoring rates, reliability levels, and regression coefficients. Simulation studies indicate that the proposed method outperformed others given some scenarios. A real data set is analyzed for an illustration of the findings.

Keywords:

Cox regression model Bayesian analysis, polygonal function prior, measurement error,

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[1] O.O. Aalen, Statistical inference for a family of counting processes, PhD thesis, University of California, 1975
[2] P.K. Andersen and R.D. Gill, Cox’s regression model for counting processes: A large sample study, Ann. Statist. 10 (4), 1100-1120, 1982.
[3] J.W. Bartlett and R.H. Keogh, Bayesian correction for covariate measurement error: A frequentist evaluation and comparison with regression calibration, Stat. Methods Med. Res. 27 (6), 1695-1708, 2018.
[4] E. Beamonte and J.D. Bermúdez, A Bayesian semiparametric analysis for additive hazard models with censored observations, Test 12 (2), 347-363, 2003.
[5] R. Bender, T. Augustin and M. Blettner, Generating survival times to simulate Cox proportional hazards models, Stat. Med. 24 (11), 1713-1723, 2005.
[6] R.J. Carroll, D. Ruppert, L.A. Stefanski and C.M. Crainiceanu, Measurement Error in Nonlinear Models: A Modern Perspective, 2nd ed., CRC Press, 2015.
[7] D. Collett, Modelling Survival Data in Medical Research, CRC Press, 2015.
[8] D.R. Cox, Regression models and life-tables, J. R. Stat. Soc. Ser. B. Stat. Methodol. 34 (2), 187-202, 1972.
[9] T.R. Fleming and D.P. Harrington, Counting Processes and Survival Analysis, John Wiley and Sons, 1991.
[10] D. Gamerman, Dynamic Bayesian models for survival data, J. R. Stat. Soc. Ser. C. Appl. Stat. 40 (1), 63-79, 1991.
[11] A. Gelman, J.B. Carlin, H.S. Stern, D.B. Dunson, A. Vehtari and D.B. Rubin, Bayesian Data Analysis, CRC Press, 2013.
[12] P. Gustafson, Measurement Error and Misclassification in Statistics and Epidemiology: Impacts and Bayesian Adjustments, CRC Press, 2003.
[13] G.B. Hamra, R.F. MacLehose and S.R. Cole, Sensitivity analyses for sparse-data problems - Using weakly informative Bayesian priors, Epidemiology 24 (2), 233-239, 2013.
[14] J.G. Ibrahim, M.H. Chen and D. Sinha, Bayesian Survival Analysis, Springer, 2005.
[15] H. Isik, Bayesian approach to Cox regression model with covariate subject to measurement error, PhD thesis, Hacettepe University, 2020.
[16] J.D. Kalbfleisch, Nonparametric Bayesian analysis of survival time data, J. R. Stat. Soc. Ser. B. Stat. Methodol. 40 (2), 214-221, 1978.
[17] R.H. Keogh and I.R. White, A toolkit for measurement error correction, with a focus on nutritional epidemiology, Stat. Med. 33 (12), 2137-2155, 2014.
[18] D.G. Kleinbaum and M. Klein, Survival Analysis, 3rd ed., Springer, 2010.
[19] E. Lesaffre and A.B. Lawson, Bayesian Biostatistics, Wiley, 2012.
[20] A.A. Mostafa and A. Ghorbal, Using WinBUGS to Cox model with changing from the baseline hazard function, Appl. Math. Sci. 5 (45), 2217-2240, 2011.
[21] S. Muff, A. Riebler, L. Held, H. Rue and P. Saner, Bayesian analysis of measurement error models using integrated nested Laplace approximations, J. R. Stat. Soc. Ser. C. Appl. Stat. 64 (2), 231-252, 2015.
[22] T. Nakamura, Proportional hazards model with covariates subject to measurement error, Biometrics 48 (3), 829-838, 1992.
[23] A. Ray, Primary biliary cirrhosis, https://Rstudio-Pubs-Static.S3.Amazonaws. com/159812_042b6e22b9cf44639fb26ae8b2df0a98.html, 2016.
[24] D. Sinha, J. G. Ibrahim and M. H. Chen, A Bayesian justification of Cox’s partial likelihood, Biometrika 90 (3), 629-641, 2003.
[25] G.Y. Yi and J.F. Lawless, A corrected likelihood method for the proportional hazards model with covariates subject to measurement error, J. Statist. Plann. Inference 137 (6), 1816-1828, 2007.