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.

Temporal changes in loss of life expectancy due to cancer in Australia: a flexible parametric approach

“…Recently, we have published population-based estimates of a newer measure, the loss of life expectancy (LOLE) [5,6], which addresses the question ''On average, how much does my life expectancy change now that I have been diagnosed with cancer?'' LOLE (measured in years) was calculated using flexible parametric models [5,7] to estimate and extrapolate a cohort's observed and expected survival, and represents the difference between the expectation of life in the general population and the expectation of life among cancer patients.…”

“…LOLE (measured in years) was calculated using flexible parametric models [5,7] to estimate and extrapolate a cohort's observed and expected survival, and represents the difference between the expectation of life in the general population and the expectation of life among cancer patients. By the use of a relative survival approach, the LOLE is not dependent on accurate cause of death information and additionally provides estimates of the loss in expectation of life for an entire cohort diagnosed with a specific cancer compared to the general population, irrespective of whether they died from that cancer.…”

Understanding the impact of socioeconomic differences in breast cancer survival in England and Wales: Avoidable deaths and potential gain in expectation of life

“…We use a model-based approach, and make projections of the relative survival, rather than projecting the all-cause survival until it reaches zero. This has been shown to be a more effective way of reliably estimating the survival experience for a cohort of cancer patients [10]. We have made the assumption that beyond 15 years of follow-up, the effect of deprivation will be proportional and be the same across all age-groups.…”

“…Details of the sensitivity analysis are given in the Appendix. We use the approach described by Andersson et al [10] in order to estimate the loss in expectation of life from a flexible parametric excess mortality model. In order to estimate the number of avoidable deaths and the loss in expectation of life we incorporated the background population mortality for the patients using general population mortality files stratified by age, deprivation group and calendar year [16].…”

“…This measure is highly dependent upon follow-up time, but is often reported at a time single point, usually at 5-years after diagnosis. A second measure that has also recently been re-introduced is the difference in the number of life years in one group compared to another [9,10].…”