PARAMETRIC MODELLING USING BAYESIAN APPROACH

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.