Bayesian probabilistic sensitivity analysis of Markov models for natural history of a disease: an application for cervical cancer

Abstract

Background : parameter uncertainty in the Markov model’s description of a disease course was addressed. Probabilistic sensitivity analysis (PSA) is now considered the only tool that properly permits parameter uncertainty’s examination. This consists in sampling values from the parameter’s probability distributions. Methods : Markov models fitted with microsimulation were considered and methods for carrying out a PSA on transition probabilities were studied. Two Bayesian solutions were developed: for each row of the modeled transition matrix the prior distribution was assumed as a product of Beta or a Dirichlet. The two solutions differ in the source of information: several different sources for each transition in the Beta approach and a single source for each transition from a given health state in the Dirichlet. The two methods were applied to a simple cervical cancer’s model. Results : differences between posterior estimates from the two methods were negligible. Results showed that the prior variability highly influence the posterior distribution. Conclusions : the novelty of this work is the Bayesian approach that integrates the two distributions with a product of Binomial distributions likelihood. Such methods could be also applied to cohort data and their application to more complex models could be useful and unique in the cervical cancer context, as well as in other disease modeling.