The present invention relates to a method for discontinuing a treatment with a TKI by determining the number and/or frequency of innate CD8(+) T-cells in subject and concluding that the treatment with a TKI should be discontinued when the number and/or frequency of innate CD8 T-cells is higher than the predetermined reference value. rnInventors evaluated whether innate CD8(+) T-cells are an early target of CML therapy success. Among peripheral blood effector CD8(+) T-cells, inventors shown that both number and/or frequency and functional signatures of innate CD8(+) T-cells are enhanced as early as 3 months of therapy. Strikingly, they observe that patients with high innate CD8(+) T-cell number and/or frequency at 3 months and/or diagnosis achieve a DMR earlier than patients with low innate CD8(+) T-cell number. Furthermore, a higher number and/or frequency of high innate CD8(+) T-cell patients achieved a stable DMR for over 2 years. Collectively, these findings highlight innate CD8(+) T-cells as a potential marker for both CML therapy success and therapy discontinuation eligibility.rn