As part of its single technology appraisal process, the National Institute for Health and Care Excellence (NICE) invited the company that manufactures ponatinib (Inclusig®; Incyte Corporation) to submit evidence for the clinical and cost effectiveness for previously treated chronic myeloid leukaemia (CML) and Philadelphia-chromosome-positive acute lymphoblastic leukaemia (Ph+ ALL). This paper focusses on the three phases of CML: the chronic phase (CP), the accelerated phase (AP) and the blast crisis phase (BP). The School of Health and Related Research Technology Appraisal Group at the University of Sheffield was commissioned to act as the independent Evidence Review Group (ERG). This article presents the critical review of the company's submission by the ERG and the outcome of the NICE guidance. Clinical evidence for ponatinib was derived from a phase II, industry-sponsored, single-arm, open-label, multicentre, non-comparative study. Despite the limited evidence and potential for biases, this study demonstrated that ponatinib was likely to be an effective treatment (in terms of major cytogenetic response and major haematological response) with an acceptable safety profile for patients with CML. Given the absence of any head-to-head studies comparing ponatinib with other relevant comparators, the company undertook a matching-adjusted indirect comparison (MAIC) of ponatinib with bosutinib. The approach was only used for patients with CP-CML because comprehensive data were not available for the AP- or BP-CML groups to allow the matching technique to be used. Despite the uncertainty about the MAIC approach, ponatinib was considered likely to offer advantages over bosutinib in the third-line setting, particularly for complete cytogenetic response. The company developed two health economic models to assess the cost effectiveness of ponatinib for the treatment of patients in CP-CML or in advanced CML (AP- or BP-CML, which were modelled separately). The company did not adequately explore the uncertainty in the survivor functions. As a result, the ERG believed the uncertainty in the decision problem was underestimated. Exploratory analyses undertaken by the ERG produced the following results for ponatinib. In CP-CML, from £18,246 to £27,667 per quality-adjusted life-year (QALY) gained compared with best supportive care (BSC), from £19,680 to £37,381 per QALY gained compared with bosutinib and from £18,279 per QALY gained to dominated compared with allogeneic stem cell transplant (allo-SCT). In AP-CML, the cost per QALY gained for ponatinib ranged from £7123 to £17,625 compared with BSC, and from dominating to £61,896 per QALY gained compared with allo-SCT. In BP-CML, the cost effectiveness of ponatinib ranged from £5033 per QALY gained to dominated compared with allo-SCT, although it was likely to be at the more favourable end of this range, and dominant in all scenarios compared with BSC. The NICE appraisal committee concluded that ponatinib is a cost-effective use of NHS resources in the considered population, subject to the company providing the agreed discount in the Patient Access Scheme.