OBJECTIVES : Fractional polynomials (FP) provide flexible parametric modeling approaches for meta-analyzing time-to-event data. Our objective was to present a model selection heuristic that improves transparency of model selection and incorporates clinical plausibility of model extrapolations. An FP-based network meta-analysis (NMA) in first-line advanced melanoma served as an example.

METHODS : We fit Weibull- and Gompertz-based FP NMA models to overall survival data, with treatment effects on scale parameters (d₀), representing proportional hazards. To each model, we added: 1) treatment effects on the shape (i.e. time-related) parameter (d₁); 2) a second shape parameter (shape2; powers chosen from {-1, -0.5, 0, 0.5, 1}); and 3) treatment effects on shape2 (d₂). These increasingly complex models were grouped into model families having the same shape parameter powers. The model selection heuristic involved ranking models according to four criteria: 1) deviance information criterion (DIC); 2) visual inspection of observed versus modeled output; 3) clinical plausibility of extrapolation periods; and 4) additional model complexity penalties. Model extrapolation periods were displayed visually by demarking the minimum follow-up time along the network path between comparators of interest.

RESULTS : The top ranked model families for DIC included two Weibull-based FP model families (shape2 powers 0.5 and 0) and one Gompertz-based FP model (shape2 power -0.5). All top-ranked models matched well with observed data; however, the most complex models (having d₀, d₁, and d₂) showed clinically implausible within-drug-class heterogeneity in the extrapolated periods. This heterogeneity was not evident in the less complex models (d₀, d₁) of the same model families. The model best fitting all criteria was the Weibull-based FP with shape2 power 0.5 which incorporated treatment effects d₀ and d₁ and involved a treatment-independent shape2 parameter.

CONCLUSIONS : This model selection heuristic upholds the principle of parsimony in FP model selection, and emphasizes the importance of transparency and critical evaluation of model extrapolations.