Estimating the loss in expectation of life due to cancer using flexible parametric survival models

Abstract

A useful summary measure for survival data is the expectation of life, which is calculated by obtaining the area under a survival curve. The loss in expectation of life due to a certain type of cancer is the difference between the expectation of life in the general population and the expectation of life among the cancer patients. This measure is used little in practice as its estimation generally requires extrapolation of both the expected and observed survival. A parametric distribution can be used for extrapolation of the observed survival, but it is difficult to find a distribution that captures the underlying shape of the survival function after the end of follow-up. In this paper, we base our extrapolation on relative survival, because it is more stable and reliable. Relative survival is defined as the observed survival divided by the expected survival, and the mortality analogue is excess mortality. Approaches have been suggested for extrapolation of relative survival within life-table data, by assuming that the excess mortality has reached zero (statistical cure) or has stabilized to a constant. We propose the use of flexible parametric survival models for relative survival, which enables estimating the loss in expectation of life on individual level data by making these assumptions or by extrapolating the estimated linear trend at the end of follow-up. We have evaluated the extrapolation from this model using data on four types of cancer, and the results agree well with observed data.