Robustness of individual and marginal model-based estimates: A sensitivity analysis of flexible parametric models

Flexible parametric survival models (FPMs) are commonly used in epidemiology. These are preferred as a wide range of hazard shapes can be captured using splines to model the log-cumulative hazard function and can include time-dependent effects for more flexibility. An important issue is the number of knots used for splines. The reliability of estimates are assessed using English data for 10 cancer types and the use of online interactive graphs to enable a more comprehensive sensitivity analysis at the control of the user is demonstrated.

Sixty FPMs were fitted to each cancer type with varying degrees of freedom to model the baseline excess hazard and the main and time-dependent effect of age. For each model, we obtained age-specific, age-group and internally age-standardised relative survival estimates. The Akaike Information Criterion and Bayesian Information Criterion were also calculated and comparative estimates were obtained using the Ederer II and Pohar Perme methods. Web-based interactive graphs were developed to present results.

Age-standardised estimates were very insensitive to the exact number of knots for the splines. Age-group survival is also stable with negligible differences between models. Age-specific estimates are less stable especially for the youngest and oldest patients, of whom there are very few, but for most scenarios perform well.

Although estimates do not depend heavily on the number of knots, too few knots should be avoided, as they can result in a poor fit. Interactive graphs engage researchers in assessing model sensitivity to a wide range of scenarios and their use is highly encouraged.