Estimating life expectancy and related probabilities in screen-detected breast cancer patients with restricted follow-up information

Abstract

Issues such as life expectancy after diagnosis, the number of life years gained by early diagnosis through screening, the probability of dying from breast cancer or of dying from other causes during the lead time period or thereafter can be derived from information on complete survival after diagnosis. A method is presented to estimate complete survival and relevant outcomes after diagnosis of screen-detected cancer when the follow-up period is substantially shorter than the maximum follow-up possible. Survival after diagnosis until death from breast cancer is modelled as the sum of the lead time (LT) and the post-lead time (PLT), where both time periods follow exponential distributions and are assumed to be independent. The survival period after diagnosis until death from causes other than breast cancer (X) is assumed to follow a Gompertz distribution. The survival period after diagnosis until death from any cause (Z) is modelled as the minimum of LT+PLT and X. Maximum likelihood methods were then used to estimate all parameters of Z. This procedure for obtaining maximum likelihood estimates of Z does not need the cause of death (breast cancer or other), which is an advantage over most other methods. Especially in older patients, it may be difficult or even impossible to ascertain the true cause of death. The model was applied to data from the long-term breast cancer screening programme in Nijmegen, the Netherlands. Complete survival was estimated on the basis of survival data on 528 screen-detected breast cancer patients, diagnosed in 1975-1997 and with a mean follow-up of 8.9 years. Estimated life expectancy ranged between 22.3 and 9.0 years for patients diagnosed at the age of 50 and 79 years, respectively, that is, 6.1 and 0.7 life years gained by screening. Through early diagnosis and treatment, screen-detected patients diagnosed at the age of 50 years may have reduced their lifetime risk of dying from breast cancer from 79 per cent to 56 per cent; at the age of 79 the reduction of risk is reduced from 23 per cent to 13 per cent.