Comparing Survival Extrapolation within All-Cause and Relative Survival Frameworks by Standard Parametric Models and Flexible Parametric Spline Models Using the Swedish Cancer Registry

Abstract

Background In health technology assessment, restricted mean survival time and life expectancy are commonly evaluated. Parametric models are typically used for extrapolation. Spline models using a relative survival framework have been shown to estimate life expectancy of cancer patients more reliably; however, more research is needed to assess spline models using an all-cause survival framework and standard parametric models using a relative survival framework. Aim To assess survival extrapolation using standard parametric models and spline models within relative survival and all-cause survival frameworks. Methods From the Swedish Cancer Registry, we identified patients diagnosed with 5 types of cancer (colon, breast, melanoma, prostate, and chronic myeloid leukemia) between 1981 and 1990 with follow-up until 2020. Patients were categorized into 15 cancer cohorts by cancer and age group (18–59, 60–69, and 70–99 y). We right-censored the follow-up at 2, 3, 5, and 10 y and fitted the parametric models within an all-cause and a relative survival framework to extrapolate to 10 y and lifetime in comparison with the observed Kaplan-Meier survival estimates. All cohorts were modeled with 6 standard parametric models (exponential, Weibull, Gompertz, log-logistic, log-normal, and generalized gamma) and 3 spline models (on hazard, odds, and normal scales). Results For predicting 10-y survival, spline models generally performed better than standard parametric models. However, using an all-cause or a relative survival framework did not show any distinct difference. For lifetime survival, extrapolating from a relative survival framework agreed better with the observed survival, particularly using spline models. Conclusions For extrapolation to 10 y, we recommend spline models. For extrapolation to lifetime, we suggest extrapolating in a relative survival framework, especially using spline models. Highlights For survival extrapolation to 10 y, spline models generally performed better than standard parametric models did. However, using an all-cause or a relative survival framework showed no distinct difference under the same parametric model. Survival extrapolation to lifetime within a relative survival framework agreed well with the observed data, especially using spline models. Extrapolating parametric models within an all-cause survival framework may overestimate survival proportions at lifetime; models for the relative survival approach may underestimate instead.