Fig. 6

Pairwise comparison of confidence intervals yielded by combinations of ITS analysis (OLS or REML) and meta-analysis methods (fixed, DL + WT, DL + HKSJ, REML + WT or REML + HKSJ). Each plot contains the 17 meta-analyses’ absolute difference in meta-analytic effect estimates and scaled relative confidence intervals, ranked in order of scaled relative confidence interval width. The top triangle (green points) presents the immediate level-change, while the bottom triangle (blue points) presents the slope-change per month. The scaled relative confidence interval widths for the level-change were calculated as column method confidence interval width divided by row method confidence interval width (and row method / column method for slope-change per month), scaled such that the row method (column method in the case of slope-change per month) spans -0.5 to 0.5 (indicated by the horizontal grey lines, which form the ‘reference rectangle’). Confidence intervals entirely within the reference rectangle (i.e., between the horizontal grey lines) have smaller confidence intervals than the comparison (left of the vertical red line), while the confidence intervals extending beyond the reference rectangle have larger confidence intervals than the comparison (right of the vertical red line). The black confidence intervals indicate where one or both of the confidence limits were beyond the limits y-axis scale. The coloured boxes indicate cells that compare meta-analysis models (i.e., fixed- vs random-effects models)[yellow boxes], ITS analysis methods when random-effects meta-analysis was used (black boxes), between-study variance estimators (blue boxes) and confidence interval methods (red boxes). The solid coloured boxes indicate comparisons of level-change and dashed boxes indicate slope-change per month. See Additional file 1: Figure S3 for random-effect meta-analysis comparisons only. DL DerSimonian and Laird, HKSJ Hartung-Knapp/Sidik-Jonkman, ITS interrupted time series, OLS ordinary least squares, REML restricted maximum likelihood, WT Wald-type