Generalized Gamma in Economic Models: A Persistent Issue With Time-to-Event Regression Analysis and the Proposed Solution

OBJECTIVES: Generalised gamma (GG) is one of six probability distributions recommended by the National Institute for Health and Care Excellence (NICE) Decision Support Unit (DSU) for survival analysis. A persistent issue was investigated, where some survival models fitted using the GG distribution would produce deterministic results that functioned appropriately, however, the mean survival would be overestimated in the probabilistic sensitivity analysis (PSA). The objective of this analysis was to identify the cause of this overestimation.

METHODS: The reconstructed individual participant data (IPD) were used to provide example survival analysis inputs. The GG parametric survival models were fitted using the R package ‘flexsurv’. Extrapolation and PSA were performed in both Microsoft Excel and R to control for any differences between the two.

RESULTS: The formulae used in Excel and R for extrapolation were found to be identical. The cause of the overestimation was identified as PSA samples where extrapolated survival was constant at 100% due to high parameter variance and covariance (particularly of the shape parameter 'Q') in the GG model. This is statistically and clinically implausible. The potential for survival overestimation in the PSA is not observable unless the survival analysis coefficients are applied probabilistically. The erroneous PSA samples only occurred when the GG distribution was used. This issue was observed in both Excel and R, and in raw and reconstructed IPD.

CONCLUSIONS: When reporting a GG model, it is recommended to check for: high variance and covariance in the survival model parameters; PSA samples with 100% survival; incongruence between mean survival in the PSA and deterministic estimates. If these elements are present, the GG model is inappropriate due to the inadvertent inclusion of statistically and clinically implausible survival probabilities in the PSA and the high levels of overall uncertainty this represents.