A Longitudinal Study of the Bladder Cancer Applying a State-Space Model with Non-Exponential Staying Time in States
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Bladder cancerMatrix-analytic methodsPhase-type distributionsState-space modelsSurvival
Montoro-Cazorla, D.; Pérez-Ocón, R.; Pereira das Neves-Yedig, A. A Longitudinal Study of the Bladder Cancer Applying a State-Space Model with Non-Exponential Staying Time in States. Mathematics 2021, 9, 363. [https://doi.org/10.3390/math9040363]
A longitudinal study for 847 bladder cancer patients for a period of fifteen years is presented. After the first surgery, the patients undergo successive ones (recurrences). A statemodel is selected for analyzing the evolution of the cancer, based on the distribution of the times between recurrences. These times do not follow exponential distributions, and are approximated by phase-type distributions. Under these conditions, a multidimensional Markov process governs the evolution of the disease. The survival probability and mean times in the different states (levels) of the disease are calculated empirically and also by applying the Markov model, the comparison of the results indicate that the model is well-fitted to the data to an acceptable significance level of 0.05. Two sub-cohorts are well-differenced: those reaching progression (the bladder is removed) and those that do not. These two cases are separately studied and performance measures calculated, and the comparison reveals details about the characteristics of the patients in these groups.