Extrapolation of survival curves using standard parametric models and flexible parametric spline models: comparisons in large registry cohorts with advanced cancer

Background: It is often important to extrapolate survival estimates beyond the limited follow-up times of clinical trials. Extrapolated survival estimates can be highly sensitive to model choice; thus, appropriate model selection is crucial. Flexible parametric spline models have been suggested as an alternative to standard parametric models; however, their ability to extrapolate is not well understood.

Aim: To determine how well standard parametric and flexible parametric spline models predict survival when fitted to registry cohorts with artificially right-censored follow-up times.

Methods: Adults with advanced breast, colorectal, small cell lung, non–small cell lung, or pancreatic cancer with a potential follow-up time of 10 y were selected from the SEER 1973–2015 registry data set. Patients were classified into 15 cohorts by cancer and age group at diagnosis (18–59, 60–69, 70+ y). Follow-up times for each cohort were right censored at 20%, 35%, and 50% survival. Standard parametric models (exponential, Weibull, Gompertz, log-logistic, log-normal, generalized gamma) and spline models (proportional hazards, proportional odds, normal/probit) were fitted to the 10-y data set and the 3 right-censored data sets. Predicted 10-y restricted mean survival time and percentage surviving at 10 y were compared with the observed values.

Results: Across all data sets, the spline odds and spline normal models most frequently gave accurate predictions of 10-y survival outcomes. Visually, spline models tended to demonstrate better fit to the observed hazard functions than standard parametric models, both in the censored and 10-y data.

Conclusions: In these cohorts, where there was little uncertainty in the observed data, the spline models performed well when extrapolating beyond the observed data. Spline models should be routinely included in the set of models that are fitted when extrapolating cancer survival data.