OBJECTIVES: Cancer immunotherapies often show delayed onset of efficacy and long-term survival benefit compared with chemotherapy. This leads to survival data violating the proportional hazards assumption. Network meta-analysis (NMA) of such data should acknowledge this. Two suitable approaches are fractional polynomial (FP) models and piece-wise constant (PWC) models. FP models can be difficult to fit in practice, and there is a need for efficient model selection strategies.

METHODS: We re-formulated the FP and PWC NMA models using ANOVA like parameterization. With this approach, both models are expressed as generalized linear models with time-changing covariates. We then performed a case study using our in-house cancer immunotherapy programs. The evidence base involved 18 studies, some of which linked to the network via Matching Adjusted Indirect Comparison. First, we fitted fixed effects NMAs in a frequentist framework. Second, we fitted fixed and random effects versions of the best performing model in a Bayesian framework.

RESULTS: The frequentist fits were extremely fast and allowed exploration of FPs of different orders and PWCs with different cut-points very rapidly. The first step involved 6 FP and 8 PWC models, and fitting took less than a second. Second order FPs had lowest Akaike Information Criterion (AIC) but suffered from over-fitting. The PWC models with two cut-points were second in terms of AIC and performed best overall. We then fitted the best PWC model also in a Bayesian framework, where each model fit took several minutes to converge and to provide sufficient effective sample size.

CONCLUSIONS: NMA models with time-varying hazard ratios can be explored efficiently with a stepwise approach. A frequentist fixed effects framework and special parameterization enables rapid exploration of different models. The best model can then be assessed further in a Bayesian random effects framework to appropriately capture uncertainty and inform decision making.