Computing survival functions of the sum of two independent Markov processes: an application to bladder carcinoma treatment

Abstract

The study of the sum of two independent phase-type (PH)-distributed variables, each of them being associated with a Markovian process with one absorbing state, is considered in this paper. The distribution function of the variable sum is computed, obtaining a new PH-distributed function of higher order. As the order increases in the new function, the exponential function of a block upper triangular matrix is calculated in terms of its respective blocks to reduce the dimension of the problem. The obtained results are applied to bladder carcinoma data.

Keywords:

• Markov process
• Fréchet derivative
• Kronecker product
• phase-type distribution
• bladder carcinoma

2010 AMS Subject Classification::

• 60J22

Acknowledgement

This study has been funded by the Vicerrectorado de Investigación de la Universitat Politècnica de València. Code 2406.