A shiny app for modeling the lifetime in primary breast cancer patients through phase-type distributions

Christian Acal; Elena Contreras; Ismael Montero; Juan Eloy Ruiz-Castro; Christian Acal; Elena Contreras; Ismael Montero; Juan Eloy Ruiz-Castro

doi:10.3934/mbe.2024065

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 1: 1508-1526. doi: 10.3934/mbe.2024065

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A shiny app for modeling the lifetime in primary breast cancer patients through phase-type distributions

1.
Department of Statistics and O.R. and IMAG, University of Granada, 18071 Granada, Spain
2.
University of Granada, 18071 Granada, Spain
3.
Department of Statistics and O.R., University of Cádiz, 11510 Cádiz, Spain

Received: 21 November 2023 Revised: 13 December 2023 Accepted: 19 December 2023 Published: 29 December 2023

Phase-type distributions (PHDs), which are defined as the distribution of the lifetime up to the absorption in an absorbent Markov chain, are an appropriate candidate to model the lifetime of any system, since any non-negative probability distribution can be approximated by a PHD with sufficient precision. Despite PHD potential, friendly statistical programs do not have a module implemented in their interfaces to handle PHD. Thus, researchers must consider others statistical software such as R, Matlab or Python that work with the compilation of code chunks and functions. This fact might be an important handicap for those researchers who do not have sufficient knowledge in programming environments. In this paper, a new interactive web application developed with shiny is introduced in order to adjust PHD to an experimental dataset. This open access app does not require any kind of knowledge about programming or major mathematical concepts. Users can easily compare the graphic fit of several PHDs while estimating their parameters and assess the goodness of fit with just several clicks. All these functionalities are exhibited by means of a numerical simulation and modeling the time to live since the diagnostic in primary breast cancer patients.
- phase-type distributions,
- modelling,
- lifetime,
- shiny,
- interactive app,
- breast cancer
Citation: Christian Acal, Elena Contreras, Ismael Montero, Juan Eloy Ruiz-Castro. A shiny app for modeling the lifetime in primary breast cancer patients through phase-type distributions[J]. Mathematical Biosciences and Engineering, 2024, 21(1): 1508-1526. doi: 10.3934/mbe.2024065

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Abstract

Phase-type distributions (PHDs), which are defined as the distribution of the lifetime up to the absorption in an absorbent Markov chain, are an appropriate candidate to model the lifetime of any system, since any non-negative probability distribution can be approximated by a PHD with sufficient precision. Despite PHD potential, friendly statistical programs do not have a module implemented in their interfaces to handle PHD. Thus, researchers must consider others statistical software such as R, Matlab or Python that work with the compilation of code chunks and functions. This fact might be an important handicap for those researchers who do not have sufficient knowledge in programming environments. In this paper, a new interactive web application developed with shiny is introduced in order to adjust PHD to an experimental dataset. This open access app does not require any kind of knowledge about programming or major mathematical concepts. Users can easily compare the graphic fit of several PHDs while estimating their parameters and assess the goodness of fit with just several clicks. All these functionalities are exhibited by means of a numerical simulation and modeling the time to live since the diagnostic in primary breast cancer patients.

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