Logo PTI Logo FedCSIS

Proceedings of the 21st Conference on Computer Science and Intelligence Systems (FedCSIS)

Annals of Computer Science and Information Systems, Volume 47

Survival Estimation Under Censoring: A Four-Method Comparison With Actuarial Reserving Implications

, ,

DOI: http://dx.doi.org/10.15439/2026F9095

Citation: Lubomir Seif, ,

Full text

Abstract. Classical life tables assume fully observed lifespans and ignore censoring, which can bias survival and life expectancy estimates upward. In our last years work, we compared the classical life table with the Kaplan-Meier and actuarial estimators under a single 10 \% censoring scenario, using mortality data for the Czech Republic in 2021. The present paper extends that study in three directions. First, we introduce the Fleming-Harrington estimator as a fourth method and prove formally that it always lies above the Kaplan-Meier curve, completing a theoretical ordering of all four estimators. Second, we extend the simulation to four censoring levels (5 \%, 10 \%, 20 \%, 30 \%) and show how the bias in life expectancy grows with data incompleteness. Third, we quantify the financial consequences of survival estimation bias for actuarial reserving, considering both a whole-life annuity and a whole-life insurance product. Our results confirm that ignoring censoring leads to systematic overestimation of survival and, depending on the product type, to either underreserving or overreserving of liabilities.

References

  1. Slud, E. V. Actuarial Mathematics and Life-Table Statistics. University of Maryland, 2006. https://www.math.umd.edu/~slud/s470/BookChaps/ 01Book.pdf.
  2. Seif, L., Vít, O., and Štěpánek, L. “Bias in Classical Life Tables Under Censoring: A Comparative Study With Kaplan-Meier Estimation and Actuarial Estimation Using Real and Simulated Data.” Proceedings of the 2025 Federated Conference on Computer Science and Information Systems (FedCSIS), 2025. http://dx.doi.org/10.15439/2025F2264.
  3. HMD. Human Mortality Database. Max Planck Institute for Demographic Research (Germany), University of California, Berkeley (USA), and French Institute for Demographic Studies (France). www.mortality.org (data downloaded on 22.5.2025).
  4. Kaplan, E. L., and Meier, P. “Nonparametric estimation from incomplete observations.” Journal of the American Statistical Association 53.282 (1958): 457–481. https://doi.org/10.1080/01621459.1958.10501452.
  5. Clark, T. G., Bradburn, M. J., Love, S. B., and Altman, D. G. “Survival analysis part I: Basic concepts and first analyses.” British Journal of Cancer 89.2 (2003): 232–238. https://doi.org/10.1038/sj.bjc.6601118.
  6. Nelson, W. “Theory and applications of hazard plotting for censored failure data.” Technometrics 14.4 (1972): 945–966.
  7. Aalen, O. “Nonparametric inference for a family of counting processes.” The Annals of Statistics 6.4 (1978): 701–726.
  8. Štěpánek, L., Habarta, F., Malá, I., Marek, L. “Non-parametric comparison of survival functions with censored data: A computational analysis of greedy and Monte Carlo approaches.” Proceedings of the 19th Conference on Computer Science and Intelligence Systems (FedCSIS), 39 (2024): 725–730. http://dx.doi.org/10.15439/2024F223.
  9. Social Security Administration. Definitions of Life Table Functions. SSA, 2016. https://www.ssa.gov/oact/Downloadables/LifeTableDefinitions.pdf.
  10. Furman, E. Actuarial Mathematics. York University, 2020. https:// edfurman.info.yorku.ca/files/2020/09/MATH3280-2020-lec2.pdf.
  11. R Core Team (2024). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/.
  12. Therneau, T. (2024). A Package for Survival Analysis in R. R package version 3.6-4. https://CRAN.R-project.org/package=survival.
  13. Therneau, T. M., and Grambsch, P. M. (2000). Modeling Survival Data: Extending the Cox Model. Springer, New York.
  14. Wickham, H. ggplot2: Elegant Graphics for Data Analysis. SpringerVerlag New York, 2016.
  15. Wickham, H., François, R., Henry, L., Müller, K., and Vaughan, D. (2023). dplyr: A Grammar of Data Manipulation. R package version 1.1.4. https://CRAN.R-project.org/package=dplyr.
  16. Internal Revenue Service. (2024). Pension and annuity income (Publication No. 575). U.S. Department of the Treasury. irs.gov