# br LE of the general

LE of the general population in the period 2009-2011 was compared with those of patients born at any time and diagnosed in 1985-2011. Cancer patients’ LE was calculated in four steps. In step one, RS of cancer patients was estimated by the period method [13] for coherence with the population life table. RS estimates using the period approach were estimated for the period 2009-2011 using the survival experience of patients diagnosed in 1985-2011. The period estimate combined the survival of 25 different three-year cohorts of diagnosis. One-year RS was estimated from patients diagnosed in 2009-2011, 2-year RS from patients diagnosed in 2008-2010 and surviving at least one year, and so on up to the specific 25-year RS estimated from patients diagnosed in 1985-1987 and surviving at least 24 years after diagnosis. Interval-specific RSs were estimated using the Ederer-2 approach [14] for each sex, cancer type, and by seven age classes, in years (40-49, 50-54, 55-59, 60-64, 65-69, 70-74, and 75-84 years). The first (40-49 years) and last (75-84 years) age 2NBDG were wider, the former because of the lower number of cases and the latter because of the requirement for sufficient numbers of long-term survivors to properly estimate LE. In addition, for thyroid cancer and Hodgkin lymphoma, the analyses started from the age of 15 years (by 5-year age classes). Finally, for testis cancer, the first age class included patients aged 15-24 years. The number of cases of the selected cancers according to age class entering into each survival period life

table at the first interval after diagnosis is reported in the Supplementary material (Supplementary material Table 1). The interval-specific RS of cancer patients was then derived from the age at diagnosis and the time since diagnosis. In step two, cancer-specific annual death hazard up to age 119 years, not observable using the current 23-year-long dataset, was estimated for each age class using the moving average method. Ten-year moving average was used to reach age 119 years for each cohort of diagnosis. Step three consisted of adding patients’ excess mortality risk due to cancer to the general population’s mortality risk to obtain their overall risk for all causes, and cancer patients’ LE was calculated with the same method used for the general population [1]. In this calculation, cohorts of patients were considered as centred at the mid-point of the age class at diagnosis (ages 17, 22, …, 45, 52, …, 80 years). Standard errors of cancer patients’ LE estimates were calculated using the delta method. Details of these first three steps are described by Capocaccia et al. [10]. The final step consisted of applying a smoothing algorithm to stabilise the cancer patients’ LE values obtained after the previous steps. To this end, a third degree polynomial model was fitted to these LE values (up to a maximum age of 90 years) for each sex and cancer, with age and time since diagnosis as the independent variables and the log of the differences between the general population (pop) and cancer patients’ (cp) LE as the dependent variable:

where age is the age at diagnosis, t is the time since diagnosis, and t1, t2, and t3 are indicator variables for the first three years following diagnosis, in which mortality risk is often very high and rapidly changing. The purpose of this model is to assure continuity of the LE function with time after diagnosis and its consistency across age classes. The model provides a very good fit of the data with a determination coefficient always > 0.8 and in most cases > 0.9.

The LE by age and time since diagnosis for the two sexes combined was obtained by weighting the sex-specific estimates with the corresponding number of cases alive at the considered time. Finally, years of life lost (YLL) was calculated as the difference between LEpop and LEcp estimated using the polynomial model, which represents the LE gap of survivors of the considered cancers with respect to sex- and age-matched cancer-free population. All analyses were conducted using Stata Statistical Software: Release 13 (StataCorp, College Station, TX, USA).

Results

Figs. 1 and 2 show all cancers combined and three common cancer sites, the LE patterns by attained age of the female and male patients, according to the age at diagnosis, compared with the general population.

Fig. 1: Life expectancy of the general population (black) and of each age class at diagnosis by age for all cancers; colon, rectum, and anus; lung; and breast, Italy, females

Fig. 2: Life expectancy of the general population (black) and of each age class at diagnosis by age for all cancers; colon, rectum, and anus; lung; and prostate, Italy, males

The complete set of figures including the LE estimates, by cancer, sex, age at diagnosis, and attained age are available online (Supplementary material Figs. A and B).