Extending methods for investigating the relationship between treatment effect and baseline risk from pairwise meta-analysis to network meta-analysis.

Baseline risk is a proxy for unmeasured but important patient-level characteristics, which may be modifiers of treatment effect, and is a potential source of heterogeneity in meta-analysis. Models adjusting for baseline risk have been developed for pairwise meta-analysis using the observed event rate in the placebo arm and taking into account the measurement error in the covariate to ensure that an unbiased estimate of the relationship is obtained. Our objective is to extend these methods to network meta-analysis where it is of interest to adjust for baseline imbalances in the non-intervention group event rate to reduce both heterogeneity and possibly inconsistency. This objective is complicated in network meta-analysis by this covariate being sometimes missing, because of the fact that not all studies in a network may have a non-active intervention arm. A random-effects meta-regression model allowing for inclusion of multi-arm trials and trials without a 'non-intervention' arm is developed. Analyses are conducted within a Bayesian framework using the WinBUGS software. The method is illustrated using two examples: (i) interventions to promote functional smoke alarm ownership by households with children and (ii) analgesics to reduce post-operative morphine consumption following a major surgery. The results showed no evidence of baseline effect in the smoke alarm example, but the analgesics example shows that the adjustment can greatly reduce heterogeneity and improve overall model fit.