Cure fraction: The proportion of cancer patients expected to have no excess mortality compared with general population.
5-year cure probability: The probability of being cured at five years since cancer diagnosis.
Time to cure: The minimum time at which the probability of being cured was above 95%.
Median survival of uncured: The median survival time of the uncured cancer cases.
All results were estimated from flexible cure models using the SEER-9 database, covering 9.4% of the population in the United States. The cure patterns reported in this study should be interpreted at the population-level. Clinical cure of cancer is currently impossible to establish with complete certainty in an individual patient.
When the all-cause mortality of a cohort of cancer patients is reduced to the level of the general population at some time during follow-up, the cohort of patients still alive are considered being cured at population-level. This can be determined when the excess mortality become negligible or the conditional relative survival is close to 100%.
We used four measures to quantify the population-level cure profiles, corresponding to the major four questions concerned by patients and clinicians after cancers being diagnosed:
(a) Population-level cure fraction: The proportion of patients expected to reach the same death rates of general population of the same sex, race and age. This measure was used to answer question 1: What percentage of patients can be cured at population-level?
(b) 5-Year population-level cure fraction: The conditional probability of being cured at 5 years of follow-up. This measure was used to answer question 2: Can patients with a survival of more than 5 years be considered as cured at population-level?
(c) Time to population-level cure: Time point at which the conditional probability of cure reaches the threshold of 95%. Namely, the number of years necessary to eliminate, or at least to make negligible (<5%), the excess mortality due to cancer. If 95% was not reached within max follow-up time, no solution will be reported. This measure was used to answer question 3: How long will it take for 95% of the patients to be cured at population-level?
(d) Median survival time of population-level uncured cases: Median survival time of fatal cases, reached when 50% of uncured patients had died. This measure was used to answer question 4: How long can patients live with uncured cancer?
Cancer patients remain in complete remission for 5 years or more are sometimes considered as clinical cured. Although this can happen for some patients, clinical cure from cancer is currently impossible to establish with complete certainty in an individual patient. Nevertheless, population-level cure is a concept which were measurable in patient cohorts. Unlike clinical cure, which focuses on cancer occurrence, population-level cure uses excess mortality as the evaluation indicator.
Cure model assumes that a proportion, π, of the patients will be cured (do not experience excess mortality), while the remainder, 1 - π, are "uncured". Su (t) is the cancer-specific survival function for the "uncured", and is estimated by the model along with the cure proportion. A parametric distribution for Su (t) has to be chosen, and a Weibull distribution is often used.
By the use of splines flexible cure model can more easily capture the shape of the underlying distribution. The flexible parametric survival model is fitted on the log cumulative excess hazard scale, using restricted cubic splines to estimate the baseline cumulative excess hazard. When cure is reached the excess hazard rate is zero, and the cumulative excess hazard will be constant after this time. By forcing the log cumulative excess hazard in the flexible parametric survival model to not only be linear but also to have zero slope after the last knot, we would be able to estimate the cure proportion. This is done by calculating the spline variables "backwards", treating the knots in reversed order, and then restricting the linear spline variable to be zero.
Prof. Wanqing Chen, MD PhD.
National Cancer Center/National Clinical Research Center for Cancer/Cancer Hospital, Chinese Academy of Medical Sciences and Peking Union Medical College
No.17 Pan-jia-yuan South Lane, Chaoyang District, Beijing 100021, China.
E-mail: chenwq@cicams.ac.cn
or
Dr. Changfa Xia, MPH PhD.
National Cancer Center/National Clinical Research Center for Cancer/Cancer Hospital, Chinese Academy of Medical Sciences and Peking Union Medical College
No.17 Pan-jia-yuan South Lane, Chaoyang District, Beijing 100021, China.
E-mail: xiacfa@163.com