Résumé : We provide supporting details for the search for a 3 þ 1 sterile neutrino using data collected over10.7 years at the IceCube Neutrino Observatory. The analysis uses atmospheric muon-flavored neutrinosfrom 0.5 to 100 TeV that traverse Earth to reach the IceCube detector and finds a best-fit point at sin2ð2θ24Þ ¼0.16 and Δm2 41 ¼ 3.5 eV2 with a goodness-of-fit p value of 12% and consistency with the null hypothesis ofno oscillations to sterile neutrinos with a p value of 3.1%. Several improvements were made over pastanalyses, which are reviewed in this article, including upgrades to the reconstruction and the study of sourcesof systematic uncertainty. We provide details of the fit quality and discuss stability tests that split the data forseparate samples, comparing results. We find that the fits are consistent between split datasets.