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Keywords:

  • autoimmune hepatitis;
  • Child A and Child C cirrhosis;
  • decision analysis;
  • hepatitis C virus infection;
  • Markov chain;
  • stochastic modelling

Abstract

Background & Aims:

Liver disease is often characterized by an intricate network of multiple, simultaneously interacting factors with organ-specific, as well as systemic effects. The aim of the present study is to introduce a new mathematical model on how to weigh a variety of factors contributing to chronic liver disease by the relevance of their influence on the overall disease processes.

Methods: Liver disease is modelled as the interaction of multiple internal and external factors. Each factor can potentially interact with any of the other factors in the model. The strength of interactions is expressed as per cent. The sum of all interactions contributing to each individual factor adds up to 100%. This model corresponds mathematically to a transposed Markov matrix. The analysis uses the two examples of hepatitis C virus (HCV) and autoimmune hepatitis (AIH).

Results: Impaired liver function is the most influential factor and increases in relevance as the degree of hepatic fibrosis increases. The relative importance of treating the primary disease process (HCV or AIH) diminishes as fibrosis develops. Similarly, psychosocial factors become less important with disease progression. Liver transplant is most important for Child's C cirrhosis. It is relatively influential for the early phase of AIH but not HCV, reflecting the fact that some cases of non-cirrhotic AIH can progress rapidly to acute liver failure.

Conclusion: In a disease process characterized by a large array of multiple interacting factors, the decision tool of a transposed Markov chain helps to sort the contributing factors by the magnitude of their influence.