Novel Approach of Multistate Markov Chains to Evaluate Progression in the Expanded Model of Non-alcoholic Fatty Liver Disease
A global increase in the prevalence of obesity and type 2 diabetes is strongly connected to an increased prevalence of non-alcoholic fatty liver disease (NAFLD) worldwide. In this article, the progression of the NAFLD process is modeled by continuous time Markov chains (CTMCs) with nine states. Maxi...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2022-02-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2021.766085/full |
| _version_ | 1818284008316862464 |
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| author | Iman M. Attia |
| author_facet | Iman M. Attia |
| author_sort | Iman M. Attia |
| collection | DOAJ |
| description | A global increase in the prevalence of obesity and type 2 diabetes is strongly connected to an increased prevalence of non-alcoholic fatty liver disease (NAFLD) worldwide. In this article, the progression of the NAFLD process is modeled by continuous time Markov chains (CTMCs) with nine states. Maximum likelihood is used to estimate the transition intensities among the states. Once the transition intensities are obtained, the mean sojourn time and its variance are estimated, and the state probability distribution and its asymptotic covariance matrix are also estimated. A hypothetical example based on a longitudinal study assessing patients with NAFLD in various stages is discussed. The mean time to absorption is estimated, and the other abovementioned statistical indices are examined. In this article, the maximum likelihood estimation (MLE) function is utilized in a new approach to compensate for the missing values in the follow-up period of patients evaluated in longitudinal studies. A MATLAB code link is provided, at the end of the article, for the estimation of the transition rate matrix and transition probability matrix. |
| first_indexed | 2024-12-13T00:45:58Z |
| format | Article |
| id | doaj.art-e2f4ca4136314044bc5bac152c6a1100 |
| institution | Directory Open Access Journal |
| issn | 2297-4687 |
| language | English |
| last_indexed | 2024-12-13T00:45:58Z |
| publishDate | 2022-02-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj.art-e2f4ca4136314044bc5bac152c6a11002022-12-22T00:05:02ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872022-02-01710.3389/fams.2021.766085766085Novel Approach of Multistate Markov Chains to Evaluate Progression in the Expanded Model of Non-alcoholic Fatty Liver DiseaseIman M. AttiaA global increase in the prevalence of obesity and type 2 diabetes is strongly connected to an increased prevalence of non-alcoholic fatty liver disease (NAFLD) worldwide. In this article, the progression of the NAFLD process is modeled by continuous time Markov chains (CTMCs) with nine states. Maximum likelihood is used to estimate the transition intensities among the states. Once the transition intensities are obtained, the mean sojourn time and its variance are estimated, and the state probability distribution and its asymptotic covariance matrix are also estimated. A hypothetical example based on a longitudinal study assessing patients with NAFLD in various stages is discussed. The mean time to absorption is estimated, and the other abovementioned statistical indices are examined. In this article, the maximum likelihood estimation (MLE) function is utilized in a new approach to compensate for the missing values in the follow-up period of patients evaluated in longitudinal studies. A MATLAB code link is provided, at the end of the article, for the estimation of the transition rate matrix and transition probability matrix.https://www.frontiersin.org/articles/10.3389/fams.2021.766085/fullmultistate Markov chainsnon-alcoholic fatty liver diseasecontinuous time Markov chainsmaximum likelihood estimationmean sojourn timelongitudinal study |
| spellingShingle | Iman M. Attia Novel Approach of Multistate Markov Chains to Evaluate Progression in the Expanded Model of Non-alcoholic Fatty Liver Disease Frontiers in Applied Mathematics and Statistics multistate Markov chains non-alcoholic fatty liver disease continuous time Markov chains maximum likelihood estimation mean sojourn time longitudinal study |
| title | Novel Approach of Multistate Markov Chains to Evaluate Progression in the Expanded Model of Non-alcoholic Fatty Liver Disease |
| title_full | Novel Approach of Multistate Markov Chains to Evaluate Progression in the Expanded Model of Non-alcoholic Fatty Liver Disease |
| title_fullStr | Novel Approach of Multistate Markov Chains to Evaluate Progression in the Expanded Model of Non-alcoholic Fatty Liver Disease |
| title_full_unstemmed | Novel Approach of Multistate Markov Chains to Evaluate Progression in the Expanded Model of Non-alcoholic Fatty Liver Disease |
| title_short | Novel Approach of Multistate Markov Chains to Evaluate Progression in the Expanded Model of Non-alcoholic Fatty Liver Disease |
| title_sort | novel approach of multistate markov chains to evaluate progression in the expanded model of non alcoholic fatty liver disease |
| topic | multistate Markov chains non-alcoholic fatty liver disease continuous time Markov chains maximum likelihood estimation mean sojourn time longitudinal study |
| url | https://www.frontiersin.org/articles/10.3389/fams.2021.766085/full |
| work_keys_str_mv | AT imanmattia novelapproachofmultistatemarkovchainstoevaluateprogressionintheexpandedmodelofnonalcoholicfattyliverdisease |