General Statistical Considerations for MTM models

Most MTM applications are carried out within a Bayesian framework. Bayesian methods are relevant in developing statements about key parameters in the presence of uncertainty, in estimation of parameters in the light of external evidence, and in making probabilistic statements about the role of all parameters involved. Bayesian framework requires prior distributions for all unknown model parameters which when combined with the likelihood (data), yield posterior distributions directly interpretable as the distributions of the quantities of interest. Therefore, it is possible to make direct probabilistic statements about the effectiveness of all treatments, the importance of risk factors or the contribution of genetic variants to the studied health status. Sensitivity to prior distributions should be considered and different underlying assumptions about the nature of the problem will be employed. Alternative modelling approaches will be evaluated using goodness of fit criteria, such as the Deviance Information Criterion (DIC).

Heterogeneity is a concern in MTM as in all meta-analyses. Methods to measure and account for heterogeneity do exist and shall be used throughout developing MTM models. To measure heterogeneity one can employ I2 (which shows the percentage of variability in a meta-analysis which can be attributed to heterogeneity rather than sampling error) and τ2 (the variance in the underlying distribution of the study-specific effects). Clinical evaluation of the heterogeneity on a case-by-case scenario shall complement the statistical approaches. To account for heterogeneity and encompass differences across studies in the meta-analysis result random effects models can be used. The most appropriate summary estimate to report from meta-analysis in the presence of heterogeneity is the predictive interval: the range of values within which the effect size of a future study is expected to be.

Changes in heterogeneity and inconsistency (the disagreement between the different sources of evidence) should be evaluated throughout any MTM application. The relative effect sizes, the ranking probabilities and predictive intervals for the effects of interventions are to be considered as the output of interest.

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