Network meta-analysis of randomized controlled trials is increasingly used to combine both direct evidence comparing treatments within trials and indirect evidence comparing treatments across different trials. When the outcome is binary, the commonly used contrast-based network meta-analysis methods focus on relative treatment effects such as odds ratios comparing two treatments. As shown in a recent report, when using contrast-based network meta-analysis, the impact of excluding a treatment in the network can be substantial, suggesting a methodological limitation. In addition, relative treatment effects are sometimes not sufficient for patients to make decisions. For example, it can be challenging for patients to trade off efficacy and safety for two drugs if they only know the relative effects, not the absolute effects. A recently proposed arm-based network meta-analysis, based on a missing-data framework, provides an alternative approach. It focuses on estimating population-averaged treatment-specific absolute effects. This article examines the influence of treatment exclusion empirically using 14 published network meta-analyses, for both arm- and contrast-based approaches. The difference between these two approaches is substantial, and it is almost entirely due to single-arm trials. When a treatment is removed from a contrast-based network meta-analysis, it is necessary to exclude other treatments in two-arm studies that investigated the excluded treatment; such exclusions are not necessary in arm-based network meta-analysis, leading to substantial gain in performance.