Application of Parametric Survival Model and Multinomial-Dirichlet Bayesian Model within a Multi-state Setup for Cost-Effectiveness Analysis of Two Alternative Chemotherapies for Patients with Chronic Lymphocytic Leukaemia

Estimation of transition probabilities between disease states and determination of length of stay in each state are two major concerns underlying the multi-state model based approach for cost-effectiveness analysis (CEA). The objective of this study is to apply and compare two different methods to estimate transition probabilities between three disease states viz., progression-free, progression, and death, for performing CEA of chemoimmunotherapy, as compared to chemotherapy, for treating patients suffering from Lymphocytic Leukaemia. In the first method, we fit a parametric survival model to the events progression and death, and as an alternative approach, we fit a Multinomial-Dirichlet Bayesian model to the number of transitions between different states. In the first method a Weibull clock-forward time-inhomogeneous semi-markov model is used, while in the second method the transition probabilities are assumed to be time-independent and are estimated through simulations from their posterior distributions using MCMC implementation. Results from both methods suggest that chemoimmunotherapy is cost-effective over chemotherapy. However, a comparison between the predictions of long term transitions from the two methods suggests that the method based on Weibull time-inhomogeneous semi-markov model provides more reliable estimates, especially when the time horizon of the study is long. Chemoimmunotherapy is cost effective when patients are willing to pay an additional cut off cost of around 13,000-15,000 GBP (by first method) for per unit additional gain in QALY.