Estimating expected survival probabilities for relative survival analysis – Exploring the impact of including cancer patient mortality in the calculations

Abstract

Relative survival is a widely used measure of cancer patient survival, defined as the observed survival of the cancer patients divided by the expected survival of a comparable group from the general population, free from the cancer under study. In practise, expected survival is usually calculated from general population life tables. Such estimates are known to be biased since they also include mortality from the cancer patients, but the bias is ignored since mortality among individuals with a specific cancer is thought to constitute only a small proportion of total mortality. Using the computerised population registers that exist in Sweden we had the unique opportunity to calculate expected survival both including and excluding individuals with cancer, and thereby estimate the size of the bias arising from using general population estimates. We also evaluated a simple method to adjust expected survival probabilities estimated from general population statistics as an aid to researchers who do not have access to computerised registers of the entire national population.

Our results show that the bias is sufficiently small to be ignorable for most applications, notably for cancers with high or low mortality and for younger age groups (<60 years). However, the bias in relative survival estimates can be greater than 1 percent unit for older age groups for common cancers and even larger for all sites combined. For example, the bias in 10-year relative survival for men aged 75+ diagnosed with prostate cancer was 2.6 percent units, which we think is of sufficient magnitude to warrant adjustment.

Introduction

Relative survival is the preferred measure of cancer patient survival used by population-based cancer registries. It is, for example, used for comparing the survival among cancer patients in different countries or regions1, 2, 3 as it enables comparisons of cancer patient survival while accounting for differences in general-population (non-cancer) mortality. The relative survival ratio is defined as the observed survival of the cancer patients divided by the expected survival of a comparable group from the general population, free from the cancer under study.⁴ In their seminal 1961 paper, Ederer et al. ⁴ (p. 103) define ‘the expected survival rate is that of a group similar to the patient group in such characteristics as age, sex, and race, but free of the specific disease under study’ [their italics].

However, the expected survival probabilities are usually calculated from general population life tables and since these tables reflect the mortality from all causes of death it is theoretically necessary to adjust the probabilities for cancer patient mortality. This is nonetheless rarely, if ever done, as the mortality from a specific form of cancer often is regarded as a negligible part of the total mortality and that general-population life table estimates provide a satisfactory proxy for a disease-free reference population. This seems plausible when the prevalence of the specific cancer is low (e.g. for younger patients and less common forms of cancer) but it could be questioned for older age groups, common forms of cancer, and for all sites combined.

Ederer et al. addressed this issue in 1961,⁴ citing five studies performed during the 1950s, and concluded that ‘since we are usually concerned with analysing survival of patients with specific forms of cancer, it appears that we do not need to make an adjustment in estimating expected survival from population life tables’,⁴ (p. 104). Oksanen addressed this issue in her 1998 doctoral thesis⁵ but to our knowledge this issue has not otherwise been systematically evaluated. Oksanen, who modelled the relative survival and relative mortality for patients with prostate cancer, concluded that even though prostate cancer is the most common cancer in men the effect of excluding prevalent cases from the whole population in order to form a proper disease-free population had only a minor effect on the mortality figures.

Sweden maintains an electronic register of the entire population (currently around 9.4 million) along with registers of all incident cases of cancer and deaths. We therefore had the possibility to calculate expected survival (and relative survival) both including and excluding individuals with cancer from the population base, and thereby estimate the size of the bias arising from using general population estimates. We also evaluated a simple method to adjust expected survival probabilities estimated from general population statistics as an aid to researchers who do not have access to computerised registers of the entire national population.