Appendix: Visualizing the target estimand in comparative effectiveness studies with multiple treatments

<b>These are peer-reviewed supplementary materials for the article '</b><b>Visualizing the target estimand in comparative effectiveness studies with multiple treatments</b><b>' published in the</b><b> </b><b><i>Journal of Comparative Effectiveness Research</i></b><b>.</b><br>Data-generating mechanismAdditional resultsAdditional Multiple Sclerosis Case Study Methods and ResultsAdditional methodsCohort DefinitionDetails on baseline covariatesMissing data imputationMatchingAdditional resultsMissing data patternBaseline Characteristics Before ImputationBaseline characteristics after imputationAdditional bivariate ellipsesTreatment effect heterogeneity explorationAssessment of matching implementationJoy plotsReferences<b>Aim: </b>Comparative effectiveness research using real-world data often involves pairwise propensity score matching to adjust for confounding bias. We show that corresponding treatment effect estimates may have limited external validity, and propose two visualization tools to clarify the target estimand. <b>Materials &amp; methods:</b> We conduct a simulation study to demonstrate, with bivariate ellipses and joy plots, that differences in covariate distributions across treatment groups may affect the external validity of treatment effect estimates. We showcase how these visualization tools can facilitate the interpretation of target estimands in a case study comparing the effectiveness of teriflunomide (TERI), dimethyl fumarate (DMF) and natalizumab (NAT) on manual dexterity in patients with multiple sclerosis. <b>Results:</b> In the simulation study, estimates of the treatment effect greatly differed depending on the target population. For example, when comparing treatment B with C, the estimated treatment effect (and respective standard error) varied from -0.27 (0.03) to -0.37 (0.04) in the type of patients initially receiving treatment B and C, respectively. Visualization of the matched samples revealed that covariate distributions vary for each comparison and cannot be used to target one common treatment effect for the three treatment comparisons. In the case study, the bivariate distribution of age and disease duration varied across the population of patients receiving TERI, DMF or NAT. Although results suggest that DMF and NAT improve manual dexterity at 1 year compared with TERI, the effectiveness of DMF versus NAT differs depending on which target estimand is used. <b>Conclusion:</b> Visualization tools may help to clarify the target population in comparative effectiveness studies and resolve ambiguity about the interpretation of estimated treatment effects.