Fig. 2

Bar plot of the indirect methods using individual patient data (IPD) by year, method, and type of network. The frequencies of the identified methods (n = 33) were 17 (52 %) Bayesian hierarchical models†, 2 (6 %) Bucher methods‡, 8 (24 %) matching adjusted indirect comparisons (MAIC)^#, 1 (3 %) extended MAIC^#, 4 (12 %) meta-regression models*, 1 (3 %) mixed comparison**.

†Bayesian hierarchical models are multi-level models presented as a generalization of regression methods. Different levels account for the variation in patients between and within studies which form the hierarchical model. Network meta-analyses conducted in a Bayesian framework express the observed treatment effects via their ‘true’ underlying treatment effects. ‡The Bucher method (or adjusted indirect comparison) is the statistical approach to derive an indirect treatment effect estimate for two competing treatments that have been compared with a common intervention [68]. ^#Matching-adjusted indirect comparisons are indirect comparisons that use IPD from the active treatment trial(s) and aggregate data (AD) from the comparator treatment trial(s). The patient characteristics from the IPD trial(s) are weighted a priori and matched with the characteristics of the population in the AD trial(s) so that the baseline characteristics are similar between the two treatment groups. A recent extension of the method accounts for differences in endpoint definitions and missing data [46]. *A linear (or meta-regression) model with dummy variables reflecting the basic parameters (comparisons of all treatments vs. a common comparator), and with regression coefficients the NMA treatment effect estimates [69]. Under the consistency assumption, all treatment comparisons are written as functions of the basic parameters. **A mixed comparison between two treatments is the weighted average of direct and indirect estimates for the same treatment comparison, with weights the inverse of the variance of the estimated effects [69]