EURO 2024 Copenhagen
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3918. The Clustered-State Markovian Arrival Process: A Framework for Dependent Recurrence and Mortality Modeling

Invited abstract in session TD-39: Analysis of Stochastic Models I, stream Stochastic Modelling.

Tuesday, 14:30-16:00
Room: 35 (building: 306)

Authors (first author is the speaker)

1. Álvaro Díaz Pérez
uc3m-Santander Big Data Institute, Universidad Carlos III de Madrid
2. Rosa Elvira Lillo Rodríguez
Statstics, Universidad Carlos III de Madrid
3. Pepa Ramírez-Cobo
Universidad de Cádiz

Abstract

The Clustered-State Markovian Arrival Process (CS-MAP) is introduced as an extension of the Markovian Arrival Process (MAP). This new model can be employed to model marked point processes with a finite mark space, but our focus lies in its application for modeling recurrent processes with terminal events, which are prevalent in the biomedical context where temporal sequences of recurrences are observed, preceded by the death of the patient. We present novel results regarding this stochastic process, including explicit expressions for the marginal and joint densities and for the moments and correlations of the inter-event times, as well as for the probability mass function of the number of recurrences before death. Furthermore, we provide an explicit expression for the likelihood function, incorporating right-censoring, which is common in survival analysis. Maximizing the log-likelihood function poses a challenge due to the large number of parameters in the model; however, we propose a heuristic approach for this purpose and we employ an appropriate local maximization algorithm. Additionally, we introduce some methods to enhance computational efficiency, such as a simplification of the likelihood function. Finally, we demonstrate the effectiveness of the proposed maximum likelihood approach using simulated data and apply it to model real data concerning patients with oncological diseases.

Keywords

Status: accepted

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