PARAMETRIC MODELLING USING BAYESIAN APPROACH

Juliana  Consul; Evans  Osaisai; Japheth Bunakiye; Joseph  Erho

Juliana Consul
Evans Osaisai
Japheth Bunakiye
Joseph Erho

Keywords: prognosis index, modelling, parameters, variables, rjags

Abstract

In this paper, we focus on the applicability of a Bayesian analysis to survival time of breast cancer data by assuming that the survival times
follow a Weibull distribution. This study determines a method of estimating the model parameters in survival analysis. The proportional hazard model is
used to relate the hazard function to the covariate values for an individual. The scale parameter of a Weibull distribution is used to incorporate the covariates of the individual and the linear predictor is expressed as a logarithmic link function of the hazard multiplier. The Bayesian approach to survival analysis is used via the Just another Gibbs sampler (RJAGS) program in R language and R functions was used to calculate the prognostic index as a linear predictor on an index from 0 to 100 which is used for predicting the outcome of the patients on the basis of the clinical information. The posterior summaries of interest which were derived from the posterior distribution are provided. The results from the posterior distribution obtained from this study can be used in the calculation of the risk value of the breast cancer patient. Thus, the risk value helps the researcher to have an assess to the patients exposure to breast cancer. The Parametric model was seen to be a very attractive option of modelling and the ease of interpretation of parameters is of benefit especially for clinicians.

References

K. Abrams, D. Ashby, D. Errington. A Bayesian approach to Weibull survival models Application to a cancer clinical trial. Lifetime Data Analysis 2 (1996), 159–174.

D. Alvares, E. Lzaro, V. Gmez-Rubio, C. Armero. Bayesian survival analysis with BUGS. Statistics in Medicine 40 (2021), 2975–3020.

E. Avc17. Bayesian survival analysis: Comparison of survival probability of hormone receptor status for breast cancer data. International Journal of Data Analysis Techniques and Strategies 9 (2017), 63–74.

S. Banerjee, D. K. Dey. Semiparametric proportional odds models for spatially correlated survival data. Lifetime Data Analysis 11 (2005), 175–191.

S. Banerjee, M. M. Wall, B. P. Carlin. Frailty modeling for spatially correlated survival data, with application to infant mortality in Minnesota. Biostatistics 4 (2003), 123–142.

L. Biard, A. Bergeron, V. Lvy, S. Chevret. Bayesian survival analysis for early detection of treatment effects in phase 3 clinical trials. Contemporary Clinical Trials Communications 21 (2021).

C. Chatfield. The Analysis of Time Series, 6th Edition. Chapman and Hall (2004).

D. R. Cox. Regression Models and Life-Tables. Journal of the Royal Statistical Society B 34(1972), 187–220.

M. J. Crowder. Multivariate survival analysis and competing risks. Chapman and Hall/CRC, Boca Raton (2012).

M. Farrow. MAS 8303, Modern Bayesian inference. Lecture notes, Newcastle University (2011).

P. H. Garthwaite, J. B. Kadane, A. O’Hagan. Statistical Methods for Eliciting Probability Distributions. Journal of the American Statistical Association 100(2005), 680–701.

W. R. Gilks. Markov chain Monte Carlo. John Wiley and Sons, Ltd (2005).

P. Groeneboom, G. Jongbloed, B. I. Witte. Maximum smoothed likelihood estimation and smoothed maximum likelihood estimation in the current status model. Annals of Statistics 38(2010), 352–387.

J. Ibrahim, M. Chen, D. Sinha. Bayesian survival analysis. Journal of The American Statistical Association 99(2005).

J. D. Kalbfleisch, R. L. Prentice. The Statistical Analysis of Failure Time Data. 2nd edition. New York: John Wiley and Sons (2011).

P. Groeneboom, G. Jongbloed, B. I. Witte. Analysis of type I and II error rates of Bayesian and frequentist parametric and nonparametric two-sample hypothesis tests under preliminary assessment of normality. computational Statistics 22(2020), 101–109.

J. P. Klein, M. L. Moeschberger. Survival Analysis: Techniques for Censored and Truncated Data. 2nd edition. New York, Springer (2010).

J. P. Klein, H. C. Van Houwelingen, J. G. Ibrahim, T. H. Scheike. Handbook of Survival Analysis. 1st ed. Boca Raton, FL: Chapman & Hall/CRC Press (2013).

Y. Khan, A. A Khan. Bayesian survival analysis of regression model using Weibull. International Journal of Innovative Research in Science, Engineering and Technology 2(12),(2013), 7199–7204.

G. Lawrence, M. Wallis, P. Allgood, I. Nagtegaal, J. Warwick, F. Cafferty, N. Houssami, O. Kearins, N. Tappenden, E. O. Sullivan, S. Duffy. Population estimates of survival in women with screen-detected and symptomatic breast cancer taking account of lead time and length bias. Breast Cancer Research Treatment 116,(2009), 179–185.

S. Lee, H. Lim. Review of statistical methods for survival analysis using genomic data. Genomics and informatics 17(4),(2019).