OBJECTIVES: Fractional polynomials (FP) have been proposed for network meta-analysis (NMA) of survival data without relying on the proportional hazards assumption. However, there is limited guidance on modelling choices such as time intervals for data aggregation and model selection. This research aims to make recommendations for fitting FP models based on lessons learned from fitting a large number of FP models for a NICE guideline.

METHODS: Using a network of 10 studies on 9 treatments for advanced melanoma, we aggregated reconstructed Kaplan-Meier data for Progression Free Survival and Overall Survival in 9 different ways: 3 or 8 intervals, every 1, 2, 3, 4, 5, or 6 months, or every 1 month for 20 months followed by every 2 months. We then used the above aggregate data to fit first-order FP models with powers from the set -2, −1, −0.5, 0, 0.5, 1, 2, 3, estimated in WinBUGS. AIC and DIC statistics were used to compare model fit.

RESULTS: We were able to fit most FP models, however convergence was an issue for FP models with higher powers, and this was more problematic for data aggregated over wider time intervals. We found that NMA estimates gave a better visual fit to KM data when aggregating the data using the finest time interval (every 1 month). Run-time was increased with a finer aggregation, however this was not prohibitively long. When AIC and DIC indicated different powers as the most parsimonious, visual inspection suggested DIC selected the more appropriate model.

CONCLUSIONS: We recommend when fitting FP models that data is aggregated in fine time intervals. It is essential to check convergence, and lack of convergence indicates powers that give implausible survival curves. The DIC together with visual inspection can be used to select models for inference and economic models.