A flowgraph model for bladder carcinoma

Theoretical Biology and Medical Modelling - Tập 11 - Trang 1-11 - 2014
Gregorio Rubio1, Belén García-Mora1, Cristina Santamaría1, José Luis Pontones2
1Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Spain
2Departamento de Urología, Hospital Politécnico La Fe, Valencia, Spain

Tóm tắt

Superficial bladder cancer has been the subject of numerous studies for many years, but the evolution of the disease still remains not well understood. After the tumor has been surgically removed, it may reappear at a similar level of malignancy or progress to a higher level. The process may be reasonably modeled by means of a Markov process. However, in order to more completely model the evolution of the disease, this approach is insufficient. The semi-Markov framework allows a more realistic approach, but calculations become frequently intractable. In this context, flowgraph models provide an efficient approach to successfully manage the evolution of superficial bladder carcinoma. Our aim is to test this methodology in this particular case. We have built a successful model for a simple but representative case. The flowgraph approach is suitable for modeling of superficial bladder cancer.

Tài liệu tham khảo

van Rhijn BW, Burger M, Lotan Y, Solsona E, Stief CG, Sylvester RJ, Witjes JA, Zlotta AR: Recurrence and progression of disease in non-muscle-invasive bladder cancer: from epidemiology to treatment strategy. Eur Urol. 2009, 56: 430-42. 10.1016/j.eururo.2009.06.028. Sylvester RJ, van der Meijden AP, Oosterlinck W, Witjes JA, Bouffioux C, Denis L, Newling DW, Kurth K: Predicting recurrence and progression in individual patients with stage Ta T1 bladder cancer using EORTC risk tables: a combined analysis of 2596 patients from seven EORTC trials. Eur Urol. 2006, 49: 475-7. Fernández-Gómez J, Madero R, Solsona E, Unda M, neiro LMP, González M, Portillo J, Ojea A, Pertusa C, Rodríguez-Molina J, Camacho J, Rabadan M, Astobieta A, Montesinos M, Isorna S, nola PM, Gimeno A, Blas M, neiro JAMP: The EORTC Tables Overestimate the Risk of Recurrence and Progression in Patients with Non-Muscle-Invasive Bladder Cancer Treated with Bacillus Calmette-Guerin: External Validation of the EORTC Risk Tables. Eur Urol. 2011, 60: 423-30. 10.1016/j.eururo.2011.05.033. Butler RW, Huzurbazar AV: Stochastic network models for survival analysis. J Am Statist Assoc. 1997, 92: 246-57. 10.1080/01621459.1997.10473622. Klein JP, Moeschberger ML: Suvival Analysis Techniques for Censored and Truncated Data. 2003, Springer, segunda Neuts MF: Matrix Geometric Solutions in Stocastic Models An Algoritmic Approach. 1981, Baltimore: The Johns Hopkins University Press Latouche G, Ramaswami V: Introduction to Matrix Analytic Methods in Stochastic Modeling. 1999, Philadelphia: SIAM Pérez-Ocón R, Segovia MC: Modeling lifetimes using phase-type distributions. Risk, Reliability and Societal Safety, Proceedings of the European Safety and Reliability Conference 2007 (ESREL 2007). Edited by: Taylor & Francis re. 2007 Huzurbazar A, Williams B: Incorporating Covariates in Flowgraph Models: Applications to Recurrent Event Data. Thecnometrics. 2010, 52: 198-208. 10.1198/TECH.2010.08044. Collins DH, Huzurbazar AV: System reliability and safety assessment using non-parametric flowgraph models. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability December 1, 2008 vol 222 no 4. 2008, 667-664. Huzurbazar A: Multistate Models, Flowgraph Models, and Semi-Markov Processes. Communications in Statistics - Theory and Methods. 2004, 33: 457-474. 10.1081/STA-120028678. Huzurbazar A: Flowgraph Models for Multistate Time-To-Event Data. 2005, New York: Wiley Mullen KM, van Stokkum IHM: nnls: The Lawson-Hanson algorithm for non-negative least squares (NNLS). 2012, [R package version 1.4], http://CRAN.R-project.org/package=nnls Abate J, Whitt W: The Fourier-Series Method For Inverting Transforms Of Probability Distributions. Queueing Syst. 1992, 5-88. Collins DH, Huzurbazar AV: Prognostic models based on statistical flowgraphs. Appl Stochastic Models Bus Ind. 2012, 28: 141-51. 10.1002/asmb.884. OMS: International Classification of Tumours. 1999, 2™, World Health Organization, Histological typing of urinary bladder tumours, Volumen 10, Geneva Lujan S: Modelización matemática de la multirrecidiva y heterogeneidad individual para el cálculo del riesgo biológico de recidiva y progresión del tumor vesical no músculo invasivo. PhD thesis. 2012, Universitat de València Team RDC: R: A Language and Environment for Statistical Computing. 2010, R Foundation for Statistical Computing, Vienna, Austria, Goulet V, Dutang C, Maechler M, Firth D, Shapira M, Stadelmann M, expm-developers@listsR-forgeR-projectorg: expm: Matrix exponential. 2011, [R package version 0.98-5], http://CRAN.R-project.org/package=expm Bates D, Maechler M: Matrix: Sparse and Dense Matrix Classes and Methods. 2011, R package version 1.0-1. Therneau T: survival: Survival analysis, including penalised likelihood. 2011, original Splus: R port by Thomas Lumley, [R package version 2.36-10], http://CRAN.R-project.org/package=survival Jackson CH: Multi-State Models for Panel Data: The msm Package for R. Journal of Statistical Software. 2011, 38 (8): 1-29.http://www.jstatsoft.org/v38/i08/