Surface Plots for Cancer Survival
While previous chapters focused only on the event of death, this chapter investigates the dynamics over age and time for the duration between being diagnosed with a specific cancer and death. We use five year survival as our indicator of survival in general, disease-specific survival and relative survival for selected cancer sites such as breast cancer, colorectal cancer, lung cancer or pancreatic cancer. The major impact of the stage of the tumor at the time of diagnosis for survival is illustrated using stage 1 and stage 4 of colorectal cancer as an example.
10.1 Introduction and Overview: The Impact of Cancer on Mortality in the United States
The converging trajectories of these two major causes of death can be also presented from the perspective of cause-elimination life tables (results not shown here; see, for instance Preston et al. (2001) or Kintner (2004) for the methodology): If circulatory diseases had been non-existent, life expectancy at birth would have been 11 years higher in the 1960s. This gap decreased to about 4 years during the most recent years (3.62 for women, 4.16 for men), whereas the impact of eradicating cancer remained relatively stationary over time for malignant neoplasms.
10.2 Dynamics of Cancer Survival by Cancer Site
People are usually not healthy and then die suddenly of a chronic, non-communicable disease such as cancer. In a very simplified manner, we can regard this as a two-step process: (1) People are healthy and then are diagnosed with a certain chronic disease x. (2) People who are diagnosed with disease x die of x or of another disease. The SEER data allow us to investigate developments for both steps. We can look at incidence data for the first step and see how incidence has changed over time by age. This might allow us to make inferences about the successes and failures of cancer prevention. We focus, however, on the second step: Analyzing survival from the moment of diagnosis to death. Thus, our focus is rather on the successes and failures of cancer treatment.
For each cancer site and sex we estimate by single calendar year and single age how many persons are still alive 60 months after diagnosis. Thus, the first approach measures the survival chances in general of someone who was diagnosed with a specific cancer.
Obviously, the first operationalization is highly dependent on age: someone aged 95 years has much lower survival chances in general than someone aged 45 years with the same diagnosis. The interest is often not on survival/mortality in general but on mortality due to the diagnosed disease. We therefore estimated also the probability that someone will not die of the diagnosed cancer within 5 years. This second operationalization is sometimes called “corrected survival rate”, “net survival” or “disease-specific survival” (Parkin and Hakulinen 1991, p. 167). We use the last term.
While the first two approaches describe the risk of dying of any cause (1) or of the diagnosed cancer (2), the third approach compares the survival chances of the diagnosed individuals with the general population. The ratio of observed survival to expected survival is called “relative survival” and can be traced back to Berkson and Gage (1952). Relative survival 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” (Talbäck and Dickman 2011, p. 2626). The observed survival rate for relative survival corresponds to our first approach, i.e., the probability of surviving from all causes of death. The most common methods to estimate relative survival (e.g., Ederer I, Ederer II, Hakulinen) differ with regard to the estimation of expected survival, though (Cho et al. 2011). As shown by Rutherford et al. (2012, p. 20), “[t]aking age into account […] removes most of the differences between the methods.” Since we analyze by single ages and single calendar years, the choice of method to estimate expected survival is less of a problem. We estimated expected survival with life table data from the Human Mortality Database (2017): Expected five year survival for 55 year old women in the year 2000 was the probability to survive age 55 in the year 2000 multiplied by the probability to survive age 56 in the year 2001, …multiplied by the probability to survive age 59 in the year 2004. Using the general population instead of the general population free from cancer violates the definition of relative survival. It has been done and justified, however, since the inception of the method (please see Appendix Note 2 of Berkson and Gage (1952) or Ederer et al. (1961)). Also recent papers such as Talbäck and Dickman (2011, p. 2626 and Table 2) argue “that the bias is sufficiently small to be ignorable for most applications.” Not accounting for the inclusion of cancer patient mortality becomes a problem only for the oldest subjects and follow-up times of 10 years or more. We would also argue that our estimates for five-year survival are sufficiently close to the official estimates. For example, SEER estimates relative survival of women diagnosed with breast cancer aged 50–64 years to be 90.1% during the period 2007–2013.2 Our results for the most recent 3 years of our analysis varied between 90.05% and 91.08%.
The panel on the left denotes the probability to survive for another 5 years after being diagnosed with breast cancer, regardless of the actual cause of death. The figure exhibits an obvious age gradient: Values of 30% or less at ages above 90 are the consequence that the women are not only at an elevated risk of dying from breast cancer. Other causes, most notably circulatory diseases, further reduce the chances to survive for five more years. Consequently, the upward trend of the contour lines can not be interpreted as progress made against the lethality of breast cancer. Still it provides the answer to the question “How likely is it that I survive for another five years?” for someone who got diagnosed with breast cancer.
While the left panel takes all “exit” possibilities into account, the panel in the middle looks only at death from breast cancer. As a consequence, one minus the depicted value equals the probability to die from breast cancer within 5 years after diagnosis. The rather vertical lines from about age 40 to about age 80 indicate that the chance of surviving breast cancer for at least 5 years has increased over time. For instance, the probability for 60-year-old women who got diagnosed with breast cancer in 1980 to survive 5 years was 80%; the equivalent value in 2000 was higher than 90%. To express it even more positively: The risk of dying was cut in half within less than 20 years (1980: 1 − 0. 8 = 20%; ∼ 1995: 1 − 0. 9 = 10%)!
The panel on the right of Fig. 10.3 shows “relative survival”, i.e., it illustrates the relative survival disadvantage of those diagnosed with breast cancer in relation to the general population. A level of one would indicate that there was no difference in the chance to survive for five more years between someone with a cancer diagnosis and the general population. Unfortunately—but also not surprisingly—women with breast cancer have lower survival chances than the general population. We can detect, however, progress over time. The excess risk is less than 10% in recent years for women with breast cancer in comparison to the general population (contour line of 0.9) whereas it was about 30% just 25 years earlier. It is important to point out that the increasing values of the vertical lines suggest a clear period effect: Progress against breast cancer was faster than progress in survival in general, regardless of the age when the woman was diagnosed.
It is theoretically possible to observe relative survival estimates that are higher than one. For instance, it could be the outcome of a selection effect: Persons that take advantage of screening programs and other early preventive measures are possibly leading rather healthy lifestyles. If those persons are diagnosed with a cancer that is virtually non-lethal, their survival advantage of their health behavior might be stronger than the additional mortality risk of the malignant neoplasm. Hence, it can not be concluded that getting diagnosed with a certain cancer could actually improve survival chances. We would argue, though, that the small area at ages 90–95 in 2000 is not the outcome of such a selection effect. Instead, we assume that it is the outcome of random data fluctuations due to small numbers of persons getting diagnosed. For example, 46 women at age 93 were diagnosed with breast cancer in 2000.
“in situ”—a noninvasive neoplasm
“localized”—an invasive neoplasm confined entirely to the organ of origin
“regional”—a neoplasm that can not only be found in the organ of origin
“distant”—a neoplasm that has spread to parts of the body remote from the primary tumor site.
and death: Relative survival is about ten to 20% lower than in the general population when being diagnosed at an early stage (upper three panels in each figure). This excess mortality is pale beside cancer that has already metastasized when being diagnosed (lower three panels in each figure): Only 10% as many people survive the next 10 years as in the general population.
Since it is a percentage/proportion, we wonder why the term “rate” has become so commonly used.
Further details can be found in the field description of variable “SEER Historic Stage A” in the SEER research data record description.
- Camarda, C. G. (2015). Smoothing and forecasting Poisson counts with P-splines. http://CRAN.R-project.org/package=MortalitySmooth, R package version 2.3.4.
- CDC/NCHS. (2015). Mortality in the United States, 2014. NCHS Data Brief, Number 229, Dec 2015. Available online as Supplementary Material at: https://www.cdc.gov/nchs/data/databriefs/db229_table.pdf#1.
- Cho, H., Howlader, N., Mariotto, A. B., & Cronin, K. A. (2011). Estimating relative survival for cancer patients from the SEER program using expected rates based on Ederer I versus Ederer II method. Tech. Rep. 2011-01, National Cancer Institute.Google Scholar
- Ederer, F., Axtell, L. M., & Cutler, S. J. (1961). The relative survival rate: A statistical methodology (Chap. 6, pp. 101–121). National Cancer Institute Monograph, National Cancer Institute.Google Scholar
- Kintner, H. J. (2004). The life table. In J. B. Siegel & D. A. Swanson (Eds.), The methods and materials of demography (2nd ed., Chap. 13, pp. 301–340). San Diego: Elsevier.Google Scholar
- Moore, T. B., & Hurvitz, C. G. (2009). Cancers in childhood. In D. A. Casciato & M. C. Territo (Eds.), Manual of clinical oncology (Chap. 18, p. 397). Philadelphia: Lippincott Williams & Wilkins.Google Scholar
- National Cancer Institute. (2017). NCI dictionary of cancer terms. Available Online at https://www.cancer.gov/publications/dictionaries/cancer-terms.Google Scholar
- Parkin, D., & Hakulinen, T. (1991). Analysis of survival. In O. Jensen, D. Parkin, R. MacLennan, C. Muir, & R. Skeet (Eds.), Cancer registration: Principles and methods (Chap. 12, pp. 159–176). No. 95 in IARC Scientific Publication, International Agency for Research on Cancer (IARC).Google Scholar
- Preston, S. H., Heuveline, P., & Guillot, M. (2001). Demography. Measuring and modeling population processes. Oxford, UK: Blackwell Publishers.Google Scholar
- University of California, Berkeley (USA), and Max Planck Institute for Demographic Research, Rostock, (Germany). (2017). Human mortality database. Available at http://www.mortality.org.
Open Access This chapter is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, a link is provided to the Creative Commons license, and any changes made are indicated.
The images or other third party material in this book are included in the work’s Creative Commons license, unless indicated otherwise in the credit line; if such material is not included in the work’s Creative Commons license and the respective action is not permitted by statutory regulation, users will need to obtain permission from the license holder to duplicate, adapt or reproduce the material.