The validity of mixed treatment comparisons (MTCs), also called network meta-analysis, relies on whether it is reasonable to accept the underlying assumptions on similarity, homogeneity, and consistency. The aim of this paper is to propose a practicable approach to addressing the underlying assumptions of MTCs. Using data from clinical studies of antidepressants included in a health technology assessment (HTA), we present a stepwise approach to dealing with challenges related to checking the above assumptions and to judging the robustness of the results of an MTC. At each step, studies that were dissimilar or contributed to substantial heterogeneity or inconsistency were excluded from the primary analysis. In a comparison of the MTC estimates from the consistent network with the MTC estimates from the homogeneous network including inconsistencies, few were affected by notable changes; that is, a change in effect size (factor 2), direction of effect or statistical significance. Considering the small proportion of studies excluded from the network due to inconsistency, as well as the number of notable changes, the MTC results were deemed sufficiently robust. In the absence of standard methods, our approach to checking assumptions in MTCs may inform other researchers in need of practical options, particularly in HTA.