Estimation of Markov models for economic models

Markov models play a key role in modelling the medium and longer term effects of policy interventions in both health and social science. They also feature prominently in cost-effectiveness analyses. At the same time policy makers and the public require that government strategies are "evidence based". The process by which "evidence" comes to inform the parameters of a Markov model is, however, far from straightforward and this was the subject of my PhD. Upon completion of the proposed series of papers readers should have the necessary methodological tools to perform evidence synthesis of a wide variety of data types to estimate Markov models correctly. The methods facilitate economic analysis and demonstrate how to perform estimation, cost-effectiveness analysis and value of information analysis within a single integrated program ensuring that uncertainty in the data is accurately propagated throughout the model.

Paper 1 will demonstrate how Markov models may be fit using WinBUGS including example code for data collected using a number of different common observation processes. WinBUGS is a Bayesian Markov Chain Monte Carlo (MCMC) package favoured for complicated evidence synthesis problems due to its tremendous flexibility 1. Paper 2 will provide a further example of how to compare the statistical fit of models representing different plausible mechanisms of action of treatments. The first example was presented in Price et al 2, but in this second paper the methods are extended to the situation where the data are subject to measurement error and available in the form of individual patient data. Paper 3 will demonstrate how to correctly adjust baseline progression parameters in Markov models using summary measures of treatment effect typically reported by trials. The potential impact on model outputs of using an incorrect approach that is commonly used in practice will be demonstrated. Paper 4 will demonstrate methods for meta-analysing trial data where the baseline disease progression rate is not constant over time. It will investigate what bias, if any, is introduced into the treatment effect estimate if a standard model assuming a constant baseline rate is used. The paper will report the results of both a simulation study and the analysis of a dataset provided by the Developmental, Psychosocial and Learning problems Cochrane review group. Paper 5 will provide guidance as to what data are required to estimate a Markov model from trial data. It will be argued that given the importance of cost-effectiveness analysis in the decision to adopt new health technologies more consideration should be given to these issues when reporting trial results. It will include example data tables to aid in the implementation of the suggestions. Finally, paper 6 will demonstrate how to perform an Expected Value of Partial Perfect Information (EVPPI) 3 analysis for a Markov model informed by an evidence synthesis of interval-censored trial data. The extreme non-linearity of the net-benefit function makes this a particularly challenging task.