Parameterization of treatment effects for meta-analysis in multi-state Markov models

Malcolm Price, Nicky Welton and Tony Ades have a new paper in Statistics in Medicine. This considers how to parameterize Markov models of clinical trials, so that meta-analysis can be performed. They consider data that is panel observed (at regular time intervals) but aggregated into the number of transitions of each type among all patients between two consecutive observations. As a result, it is necessary to assume a time homogeneous Markov model, since there is no information to consider time inhomogeneity or patient inhomogeneity. These types of cost-effectiveness trials are usually analyzed using a discrete time framework (Markov transition model), with the assumption that only one transition is allowed between observations. Price et al advocate using a continuous time method. The main advantage of this is that fewer parameters are required e.g. rare jumps to distant states can be explained by the presence of multiple jumps rather than having to include the transition probability as an extra parameter in the model.

Price et al consider asthma trial data where they are interested in combining data from 5 distinct two-arm RCTs, there is some overlap between the treatments tested so evidence networks comparing treatments can be constructed.

The main weakness of the approach is the reliance on the DIC. Different models for the set of non-zero transition intensities are considered using the DIC, with the models allowing different intensities for each trial treatment arm. While later in the paper there are benefits of adopting the Bayesian paradigm, here it doesn't seem useful. For these fixed effects models and given the flat priors chosen, DIC should (asymptotically) be the same as AIC. However, AIC is dubious here also because of the aspect of testing on the boundary of the parameter space and is likely to put too much favour on simpler models in this context. Likelihood ratio tests based on mixtures of Chi-squared distributions (Self and Liang, 1987) could be applied as in Gentleman et al 1994. However, judging from the example data given for treatments A and D, the real issue is lack of data, e.g. there are very few transitions to and from state X.