PDB68 Maximum-Likelihood Estimation of Transition Probabilities between Fibrosis Stages in Nonalcoholic Steatohepatitis (NASH)

Abstract

NASH is a disease characterized by progression of hepatic fibrosis through five stages, from F0 (no fibrosis) to F4 (compensated cirrhosis). Singh, 2015 estimated a fibrosis progression rate (FPR) between fibrosis stages as the total number of stages progressed from any starting stage divided by the total number of person years of follow up. The FPR has been used in Markov cost-effectiveness models as a proxy for transition probabilities between fibrosis stages (Tapper, 2015; ICER, 2016; ICER, 2020). Gal, 2017 presented a method to calibrate model specific transition probabilities to match detailed study data that gives a better model of disease progression than FPR. This research improves on our previous methodology by leveraging the advantages of maximum-likelihood estimation (MLE). Our model restricted transitions by at most one stage per cycle. The observed data include the number of patients for all 25 combination of initial and final F-stages, and the total number of patient years for each initial stage. The elements of the transition probability matrix were considered as model parameters implying a multinomial distribution across the final stages for each starting stage. The lengths of follow-up periods were available on an aggregated level, therefore the MLE assumed an average follow-up time from each starting stage. The MLE achieved convergence and the resulting transition probabilities were found to be consistent with the estimated FPR, and the probabilities given by our prior calibration method. MLE is recommended to estimate transition probabilities over the use of FPR or the prior calibration method. The method incorporates all available information from the data source and benefits from the favorable statistical properties of MLE. In particular, the MLE method also provides covariance between the estimated parameters that can be used in probabilistic sensitivity analysis required in cost-effectiveness models for HTA submissions.