The cancer-specific survival has not included the deaths due to other causes. The cancer-specific rates also depend on the reliability of the assignment of the cause of death. Generally, cancer-specific death rates underestimate the mortality associated with a diagnosis of the specific cancer, because some patients died of other causes[26]. SEER is a set of geographically defined, population-based, central cancer registries in the United States, operated by local non-profit organizations under contract to the National Cancer Institute (NCI). Registry data are submitted electronically to the NCI on a biannual basis, and the NCI makes the data available for analysis. The SEER Program is considered the standard for quality among cancer registries around the world. Quality control has been an integral part of SEER since its inception. Every year, studies are conducted in SEER areas to evaluate the quality and completeness of the data being reported.
Gamel and Vogel [27] have compared the advantage of lognormal distribution over other distributions such as Weibull and log logit.
The 1973–1992 data were used so that the data were not out-dated. For a lognormal distribution of the survival time of those patients died of the specific cancer, there were only a very small proportion dying at the tail of follow-up (Figure 1), so it would not cause much change to the lognormal distribution, even with only 7 years of follow-up to 1999 at the tail. For those cancer sites with threshold years longer than 24 years, the 1973–1977 data were used so as to allow a long enough time for follow-up to 1999.
For 42 sites in the SEER database, the survival times of cancer patients who died of their disease followed different lognormal distributions. For 40 cancer sites, the ultimate cure rate can be roughly estimated from the cancer-specific survival rates at τ years. These are the required minimum number of follow-up years for the estimation of the cure rates. They are different for different cancer sites. For pancreatic cancer, with its typically short natural history, the cure rate can be estimated after only 2.6 years. For cancers with a longer natural history, longer follow-up periods are required; such as breast (36.2 years). These long periods are cancer-specific survival times and in reality patients may die from intercurrent non-cancer causes before τ years. For thyroid cancer, the estimated threshold year was 134.1 years. It seems that for some slow proliferating cancer types, the cure can never be estimated due to the limit of human lifetime.
We also find that the required minimum number of years of follow-up, τ, is independent of cure rate (correlation coefficient of determination, R2 = 0.10). Even for cancer sites where the cure rates were >50%, the required follow-up time τ could be less than 10 years. On the other hand, for other cancer sites, the cure rates could be < 50%, and the required follow-up time were >10 years. It shows that 5- or 10-year survival rates are inadequate to reflect the statistical cure rates.
If there are more patients dying due to other causes than dying due to the specific cancer, then the cause specific survival time distribution will not be lognormal. Hence it is not expected that all cancer-specific survival time distributions will follow lognormal distributions.
According to the bell-shaped property of a normal distribution, from 0 to τ year covers 97.75% of the lognormally distributed survival time of those cancer patients who died from their specific cancer. The cancer-specific survival rates estimated at τ years, generally, slightly overestimate the long-term cure rates compared to the Kaplan-Meier method, but the differences are reasonably small, by less than six percentage points as verified empirically. We still need to follow the patients to τ year to know the actual value of the estimated cure rates.
For both rapidly and slowly proliferating cancers, we have shown that the statistical cure rates can be estimated before a stable plateau is reached in the Kaplan-Meier survival curve. It may take decades to see a stable plateau, during this waiting time many patients might be lost to follow-up or die of intercurrent diseases.
Gamel and Vogel [28] used cause-specific survival and relative survival to determine actuarial survival in breast cancer patients from the SEER database. They found that there was only minimal deviation between the two survival methods.
Ries et al. [29] reported up to 20-year relative survival rates (RSR) from 9 registries of the SEER database. For cancers of pancreas, esophagus and stomach, the RSR were slightly decreased after five years since diagnosis. These are consistent with the threshold years of the present study varying from 2.6 years for pancreas, to 3.9 years for esophagus, and to 5.8 years for stomach. Dickman et al. [30] reported similar results with 10-year RSR for the Finnish Cancer Registry. Talback et al.[31] also showed the similar results on two RSR graphs up to 30 years for pancreas and stomach for the Swedish Cancer Registry.
The threshold year of statistical cure for ovarian cancer was 10.4 years. It was consistent with the results of Ries et al. and Dickman et al. up to 10 years. After 10 years, there was only a slight decrease in RSR as reported by Ries et al. Talback et al. showed the same results on a RSR graph for ovarian cancer. Their results were also consistent with the present study for the cancer sites of lung, colon and skin melanomas, which have threshold years of 9.0, 12.2 and 18.2 years respectively. These consistencies show that the results obtained from two SEER registries in the present study are similar to those from 9 registries and from the Finnish and Swedish Cancer Registries.
For prostate cancer, the threshold year for statistical cure was 24.6 years. The RSR graph started to level after 24 years since diagnosis in the article of Talback et al.
For breast cancer, the threshold year was 36.2 years, RSR leveling was not seen even 30 years after diagnosis in the article of Talback et al. Leveling of RSR in breast cancer was also not seen in two separate studies by Schairer et al. [32] and Brenner and Hakulinen [33]. Kerr et al. [34] reported that the ratio of observed to expected mortality remained significantly greater than unity for at least 25 years following diagnosis and treatment, indicating a failure to demonstrate cure of the disease in a statistical sense for a median of 32 years of follow-up.