OBJECTIVES: The use of extrapolation in cost-effectiveness analysis (CEA) is essential to estimate costs and benefits of treatments over a lifetime. Typically, parametric equations are used to extrapolate a ‘baseline’ comparator with relative treatment effects applied to obtain absolute values for all interventions. An assumption of proportional hazards (PH) is common in oncology, but may fail with cancer immunotherapies. METHODS: We conducted a systematic literature review and a fractional polynomial (FP) network meta-analysis (NMA) of second-line metastatic non-small cell lung cancer randomised controlled trials. We used a log-logistic distribution to model atezolizumab overall survival data and applied time varying hazard ratios (HR) from the FP NMA. While FPs can be estimated over an observed period, polynomials may not extrapolate well. Naïve extrapolation to a lifetime horizon could be difficult to justify without clinical evidence. We explored the effects on five comparators; nivolumab (3mg/kg), pembrolizumab (2mg/kg), atezolizumab (1,200mg), docetaxel and nintedanib plus docetaxel with three scenarios: increasing HRs without capping, capping HRs at 12 months and using the PH NMA HR estimate from 12 months onwards. RESULTS: A first order FP model with P1=0 (Weibull) was selected. The HRs for docetaxel and nintedanib plus docetaxel versus atezolizumab increased over the time scale of one week to 12 months; 0.81 to 1.57 and 0.79 to 1.44, respectively. Nivolumab and pembrolizumab did not show evidence to dismiss a PH model over time compared to atezolizumab. The mean overall survival for docetaxel was 1.24, 1.36 and 1.48 years for the increasing HR, capped at 12 months and using the PH NMA estimate (1.39) from 12 months, respectively. CONCLUSIONS: Incorporating time varying HRs into a CEA needs care and involves considerations beyond simple statistical measures of fit. This example demonstrates using PH HRs over extrapolated data may not be reasonable between immunotherapies and chemotherapies.