Survival Rate Estimation in Patients with Colorectal Cancer by applying Fuzzy Product Limit Estimator
Abstract
Background: Survival rates are important to show the progress of the disease and the effect of treatments. The estimation of survival probabilities especially in presence of highly censored data is challenging. In this study, Fuzzy Product Limit Estimator (FPLE) is introduced to mitigate the challenge.
Methods: In a longitudinal study, data of 173 CRC patients were analyzed. To estimate survival probabilities, mean and median survival time, Fuzzy Product Limit Estimator (FPLE), a data-driven method, was applied to the data. It provides a smooth survival probability curve and the continuation of the survival curve is not a concern in the case while the largest observed time is censored.
Results: One-year survival rate for CRC patients was estimated to be 83% using FPLE and KM methods. The five-year survival rate was estimated to be 37% and 52% by the FPLE and KM methods, respectively. The largest observed time in data (71.96 months) was censored, so the survival rate after 71.96 months was not estimable by the KM method. But 10-year and 20-year survival rates were estimated by FPLE as 0.21 and 0.09. The mean (median) survival time was estimated 45.97 (65) and 82.69 (41.70) months by KM and FPLE methods, respectively.
Conclusion: In presence of highly censored survival data, the FPLE method provides acceptable estimates of CRC patients' survival rate. Also, the continuation of the survival curve was estimated after the largest observed time. The smaller estimates by the FPLE at 5-year could be considered as warning that the actual survival rate is lower than that reported by the KM method.
2. Keum NN, Giovannucci E. Global burden of colorectal cancer: emerging trends, risk factors and prevention strategies. Nat Rev Gastroenterol Hepatol. 2019;16(12):713–32.
3. Kalyan A, Kircher S, Shah H, Mulcahy M, Benson A. Updates on immunotherapy for colorectal cancer. J Gastrointest Oncol. 2018;9(1):160–9.
4. Cancer IA for R on. Globocan 2018: Cancer Fact Sheets—Colorectal Cancer. IARC http//gco iarc fr/today/data/factsheets/cancers/10_8_9-Colorectum-fact-sheet pdf. 2018;
5. Zendehdel K. Cancer Statis. Basic Clin Cancer Res. 2019;11(1):1–4.
6. Dolatkhah R, Dastgiri S, Somi M hossein, Jabbarpour Bonyadi M, Kermani IA, Farassati F. Colorectal cancer in Iran: Molecular epidemiology and screening strategies. J Clin Oncol. 2019;33(15_suppl):e12513–e12513.
7. Rafiemanesh H, Pakzad R, Abedi M, Kor Y, Moludi J, Towhidi F, et al. Original article : Colorectal cancer in Iran : Epidemiology and morphology trends. EXCLI J. 2016;15:738–44.
8. Khosravi Shadmani F, Ayubi E, Khazaei S, Sani M, Mansouri Hanis S, Khazaei S, et al. Geographic distribution of the incidence of colorectal cancer in Iran: a population-based study. Epidemiol Health. 2017;39:e2017020.
9. Nikbakht HA, Hassanipour S, Shojaie L, Vali M, Ghaffari-fam S, Ghelichi-ghojogh M, et al. Survival Rate of Colorectal Cancer in Eastern Mediterranean Region Countries: A Systematic Review and Meta-Analysis. Cancer Control. 2020;27(1):1–15.
10. Maajani K, Khodadost M, Fattahi A, Shahrestanaki E, Pirouzi A, Khalili F, et al. Survival rate of colorectal cancer in Iran: A systematic review and meta-analysis. Asian Pacific J Cancer Prev. 019;20(1):13–21.
11. Somi MH, Dolatkhah R, Sepahi S, Belalzadeh M, Sharbafi J, Abdollahi L, et al. Cancer incidence in the East Azerbaijan province of Iran in 2015-2016: Results of a population-based cancer registry. BMC Public Health. 2018;18(1):1–13.
12. Kaplan EL, Meier P. Nonparametric Estimation from Incomplete Observations. J Am Stat Assoc. 1958;53(282):457.
13. Kishore J, Goel M, Khanna P. Understanding survival analysis: Kaplan-Meier estimate. Int J Ayurveda Res. 2010;1(4):274.
14. Does your data violate Kaplan-Meier assumptions?
15. Breslow NE. Introduction to Kaplan and Meier (1958) Nonparametric estimation from incomplete observations. In: Breakthroughs in Statistics. Springer; 1992. p. 311–8.
16. Shafiq M, Shah S, Alamgir M. Modified Weighted Kaplan-Meier Estimator. Pakistan J Stat Oper Res. 2007;3(1):39.
17. Pokorny K, Sule D. Empirical fuzzy estimate of the survival curve. Int J Uncertainty, Fuzziness Knowlege-Based Syst. 2004;12(3):347–56.
18. Musavi S, Pokorny KL, Poorolajal J, Mahjub H. Fuzzy survival analysis of AIDS patients under ten years old in Hamadan-Iran. J Intell Fuzzy Syst. 2015;28(3):1385–92.
19. Laux SE. Techniques for. IEEE Transactions on Electron Devices. 1985. 2028–2037 p.
20. Shen Y, Fleming TR. Weighted mean survival test statistics: A class of distance tests for censored survival data. J R Stat Soc Ser B Stat Methodol. 1997;59(1):269–80.
21. Zhong M, Hess KR. Collection of Biostatistics Research Archive COBRA Preprint Series Mean Survival Time from Right Censored Data Mean Survival Time from Right Censored Data. 2009;99.
22. Mozafar Saadati H, Khodamoradi F, Salehiniya H. Associated Factors of Survival Rate and Screening for Colorectal Cancer in Iran: a Systematic Review. J Gastrointest Cancer. 2020;51(2):401–11.
| Files | ||
| Issue | Vol 9 No 1 (2023) | |
| Section | Original Article(s) | |
| DOI | https://doi.org/10.18502/jbe.v9i1.13973 | |
| Keywords | ||
| Colorectal cancer, Survival, Fuzzy logic, FPLE | ||
| Rights and permissions | |
|
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |
