Isaac Scientific Publishing

Journal of Advanced Statistics

Proportional Hazard Regression Model with Bayesian Approach

Download PDF (658.1 KB) PP. 38 - 51 Pub. Date: March 1, 2016

DOI: 10.22606/jas.2016.11005

Author(s)

  • Rashmi Aggarwal
    Department of Statistics, Panjab University, Chandigarh, India
  • Suresh Kumar Sharma*
    Department of Statistics, Panjab University, Chandigarh, India
  • Kanchan Jain
    Department of Statistics, Panjab University, Chandigarh, India

Abstract

The purpose of survival analysis is to model the underlying distribution of the failure time variable and to assess the dependence of the failure time variable on independent variables. In this paper, we explored PHREG procedure for different models using Bayesian approach. PHREG procedure not only fits COX model but also allows us to fit a piecewise exponential model. The Bayesian analysis treats model parameters as random variables and the inference about these parameters is based on posterior distribution of the parameters. A posterior distribution is a weighted likelihood function of the data with a prior distribution of the parameters using the Bayes’ theorem. Generally, for model regression coefficients, normal or uniform prior distributions are used in PHREG procedure. In addition to this, one may specify gamma or improper prior distribution for the scale or variance parameters as well as for hazard parameters in piecewise exponential model. PHREG procedure have been demonstrated with application to real life dataset. Bayesian analysis with PHREG procedure and piecewise constant Bayesian hazard model is also explored along with diagnostic test.

Keywords

Piecewise polynomial, PHREG procedure, Hazard model, Geweke diagnostics.

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