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Computing survival functions of the sum of two independent Markov processes: an application to bladder carcinoma treatment. (English) Zbl 1311.60084

The framework of the paper is continuous time Markov processes on a finite discrete state space with all but one states transient and one absorbing state. The authors are concerned with the (random) time until absorption, the distribution of which is a phase-type (PH) distribution. In particular the authors calculate and compute the sum of two independent distributions of such type, which is again a phase-type distribution. The result is applied to study the evolution of bladder cancer based on a real data set.

MSC:

60J27 Continuous-time Markov processes on discrete state spaces
60J28 Applications of continuous-time Markov processes on discrete state spaces
60J22 Computational methods in Markov chains
92C50 Medical applications (general)
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[1] DOI: 10.1017/S0269964801153076 · Zbl 0982.62084 · doi:10.1017/S0269964801153076
[2] Graham A., Kronecker Products and Matrix Calculus with Applications (1981) · Zbl 0497.26005
[3] DOI: 10.3322/canjclin.50.1.7 · doi:10.3322/canjclin.50.1.7
[4] DOI: 10.1016/S0022-5347(01)67321-X · doi:10.1016/S0022-5347(01)67321-X
[5] Jackson C., msm (Multi-state Markov and Hidden Markov Models in Continuous Time)
[6] DOI: 10.1002/sim.886 · doi:10.1002/sim.886
[7] DOI: 10.1002/9781118032985 · doi:10.1002/9781118032985
[8] Kenny C.S., SIAM J. Matrix Anal. Appl 10 (3) pp 191– (1998)
[9] Neuts M.F., Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach (1981) · Zbl 0469.60002
[10] DOI: 10.1007/978-3-642-59871-5 · doi:10.1007/978-3-642-59871-5
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