Abstract
BackgroundMany reviews aim to compare numerous treatments and report results stratified by subgroups (eg, by disease severity). In such cases, a network meta‐analysis model including treatment by covariate interactions can estimate the relative effects of all treatment pairings for each subgroup of patients. Two key assumptions underlie such models: consistency of treatment effects and consistency of the regression coefficients for the interactions. Consistency may differ depending on the covariate value at which consistency is assessed. For valid inference, we need to be confident of consistency for the relevant range of covariate values. In this paper, we demonstrate how to assess consistency of treatment effects from direct and indirect evidence at various covariate values.MethodsConsistency is assessed using visual inspection, inconsistency estimates, and probabilities. The method is applied to an individual patient dataset comparing artemisinin combination therapies for treating uncomplicated malaria in children using the covariate age.ResultsThe magnitude of the inconsistency appears to be decreasing with increasing age for each comparison. For one comparison, direct and indirect evidence differ for age 1 (P = .05), and this brings results for age 1 for all comparisons into question.ConclusionWhen fitting models including interactions, the consistency of direct and indirect evidence must be assessed across the range of covariates included in the trials. Clinical inferences are only valid for covariate values for which results are consistent.
Highlights
Notation Let i denote the trial where the patient where be the trial arm where and NS is the number of independent trials; let j such that is the number of patients in trial i; and let k and is the number of arms in trial i
The model can be applied to datasets with multi-arm trials but the correlation between trial-specific treatment effects must be taken into account
For the same trial, if one wants to split node (3, 4) instead, we fix and the model is for treatment 1 where ~
Summary
The trial-specific log odds ratios, are assumed to be realisations from a normal distribution where and The model can be applied to datasets with multi-arm trials but the correlation between trial-specific treatment effects must be taken into account. NMA node-splitting model including treatment by covariate interaction When there are no multi-arm trials, the random-effects model is specified as follows: and where represents the difference in the log odds ratio of vs per unit increase in the covariate estimated using direct evidence; represents the difference in the log odds ratio of vs per unit increase in the covariate estimated using all trials that did not allocate and (i.e. using indirect evidence); and represents the trial-specific log odds ratio of vs .
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