Survival curve for cancer patients following treatment
Abstract
On the basis of experience with calculated survivorships of patients following treatment for cancer, a simple function, in terms of two physically meaningful parameters, has been evolved, which fits such survivorship data very well. These two parameters can be used to compare succinctly the mortality of two groups, different in respect of treatment, type of cancer, or other characteristics. The parameters are c (“cured”), which represents the proportion of the population which is subject only to “normal” death rates, and β, which is the death rate from the cancer, to which the rest of the population [not “cured,” (1–c)] is subject. Thus if one treatment is characterized by c 1 = 0.30, β 1 = 0.25, another by c 2 = 0.20, β 2 = 0.15, this could be interpreted as meaning that while the first treatment “cured” a larger proportion of the population than did the second treatment, it did not ameliorate the deaths attributable to cancer in the patients not cured as much as did the second treatment. If l T is the proportion of the total population surviving to time t, then the function is l T = cl 0+ (1 – c)l 0e −-βt where l 0 is the net survivorship corresponding to “normal” deaths, obtained from standard life tables. A graphic method and also a “least squares” method of estimating c and β are presented with an example, and the evaluated parameters are given for several series of treated cancer patients. Expectation of life and other functions of the life table also have been calculated from the evaluated parameters, for the same series.
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Clinicians have used five-year survival as a measure of cancer treatment effectiveness for over six decades.
“Five-year survival has been recognised by clinicians as an index of the effectiveness of the treatment of cancer for more than 60 years.”
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Nonparametric Estimation from Incomplete Observations
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- Authors
- Berkson, J., & Gage, R. P.
- Affiliations
- Mayo Clinic (US)
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1952-09
- Volume
- 47
- Issue
- 259
- Pages
- 501-515
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2092660489
- Cited by
- 889
- References
- 12
- Citations by year
- 2026: 36 · 2025: 33 · 2024: 35 · 2023: 38 · 2022: 36 · 2021: 55 · 2020: 42 · 2019: 42 · 2018: 35 · 2017: 46 · 2016: 39 · 2015: 33 · 2014: 25 · 2013: 41 · 2012: 32
- FWCI
- 2.49
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- Topics
- Health Sciences › Medicine › Oncology › Global Cancer Incidence and Screening
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Keywords
- cancer survivorship, survival curves, cancer mortality, parametric survival models, life tables, treatment comparison, least squares estimation
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