Methods: Data from the 57 epidemiologic studies (liver clinic series n=33, post-transfusion cohorts n=5, blood donor series n=10, and community-based cohorts n=9) from a published systematic review were used, including fibrosis distribution data (n=5) and cirrhosis data (n=52).
Liver fibrosis states F0-F4 were modeled using a continuous-time Markov tunnel model, with F4 denoting the absorbing cirrhosis state. Estimates of time-dependent transition probability, expressed as functions of annual transition rates, were derived using Kolmogorov's forward equation.
These estimates were used in a meta-analysis model incorporating both the multinomial-distributed fibrosis data and binomial-distributed cirrhosis data. Both fixed effects and random effects models (i.e., study-specific F0-F1 rates) without and with covariates (i.e., age, cohort type) were used. The fibrosis model was linked with the meta-analysis model using an MPES approach which explicitly reflected both the heterogeneity and uncertainty in the input data.
Vague priors were used for model parameters. Analytical solutions were obtained using WinBugs (2 chains n=21,000 with 1,000 burn-ins). Convergence was assessed via inspection of MCMC trace and autocorrelation plots and the Gelman-Rubin ratio. Standardized residuals were used for evidence consistency checking. Long-term predictions of fibrosis distribution were derived from the fitted model.
Results: Annual transition rates were F0-F1: 0.06 (95% CI: 0.04, 0.09); F1-F2: 0.10 (0.09, 0.103); F2-F3: 0.18 (0.16, 0.19), and F3-F4: 0.20 (0.17, 0.22). Large standardized residuals were observed for multinomial data relative to those from binomial data.
The cumulative probability of cirrhosis after 20 years was estimated to be 19% (95% CI: 14-25%) and varied by meta-analytic models. Patients from community clinics had better prognosis compared to those from liver clinics, rate ratio 0.08 (0.001, 0.18). Estimates of random effects model were generally consistent with or without baseline adjustment.
Conclusion: The MPES approach integrated a decision model with different meta-analytic models thus allowed the synthesis of the evidence base from vastly different study designs. For applications in HCV prognosis, this approach allowed for correction of bias due to study design and adjustment for clinical covariates.