Predicting Advanced Fibrosis and Examing Fibrosis Stage Transitions using a Transition Markov Model

Specialeforsvar ved Pernille Juul Jørgensen

Titel: Predicting Advanced Fibrosis and Examing Fibrosis Stage Transitions using a Transition Markov Model

Abstract:  The topic of this thesis is NALFD more specifically liver fibrosis, which has shown to be the most prognostic and predictive histological feature. The aim of this thesis was twofold. The first aim was to develop a predictive model for advanced fibrosis (stage 3-4) that had a higher predictive ability than previous developed scores. The variable encoding a merged version of the fibrosis stages (0-2 vs 3-4) was therefore modelled as the response in a logistic regression model with predictors chosen through a backward model selection procedure using the AIC criteria. In the evaluation of the model two validation methods were applied and in both, the model was compared with three previous developed scores (ADAPT, FIB-4 and PRO-C3). Efron’s enhanced bootstrap was used as internal validation method and an independent validation dataset was used as external validation method. The internal validation was included since often an independent validation data is not available and the difference in results between the two methods of evaluation was therefore of interest. The AUC was used together with specificity and sensitivity as accuracy metrics to assess and compare the model’s and scores’ predictive ability. The two validation methods agreed on the overall result, namely that the developed model had the highest AUC, however it was only a tiny bit higher than the second highest AUC belonging to ADAPT. Also, the developed model had the highest specificity but in return one of the lowest sensitivities amongst all the models.
The second aim was more prognostic with a first order Markov assumption and Markov theory used to examine how subjects move between fibrosis stages. The transition probabilities gotten directly from the data revealed no significant difference between the treatment and placebo group in the cohort. To investigate which covariates in the data had the most influence on the transitions, a Transition Markov Model (TMM) was developed using ordinal logistic regression. This ordinal model had present fibrosis stage as response and previous fibrosis stage as one of the predictor variables to uphold the first order Markov assumption. The rest of the predictors were chosen through a forward model selection procedure using the AIC criteria. From the TMM was calculated transition probability estimates for two low risk and two high risk subjects, respectively. Both risk groups included a subject from each treatment group (treatment vs placebo). Using a method relying on the permutation of the treatment variable and the Kullback-Liebler divergence for probability vectors no significant difference was found between the transitions for the two treatments.
Keywords: NAFLD, Liver fibrosis, Logistic regression, Efron’s advanced bootstrap, Cumulative residuals, Ordinal regression, Markov theory, Kullback-Liebler divergence.


Vejleder: Helle Sørensen
Censor:   Sören Muller, SDU