Variance Inflation Due to Censoring in Survival Probability Estimates
Keywords:Survival, Right-censoring, Standard error, Kaplan-Meier
One of the most obvious features of time-to-event data is the occurrence of censoring. Rarely, if ever, studies are conducted until all participants experience the event of interest. Some participants survive beyond the end of follow-up time, some drop out from the studies for various non-study related reasons. During research planning it is paramount to consider the effect of censoring the follow-up times on the estimates. Herein, we look into the possibility of assessing
the loss of information, as measured by the variability of the survival probability estimates under right censoring. We provide the researchers with an easy to use formula to assess the magnitude of variance inflation due to censoring. Additionally, we conducted simulation studies assuming various survival distributions. We conclude that the provided variance inflation estimator can be an accurate practical tool for applied statisticians.
O. AALEN, O. BORGAN, H. GJESSING (2008). Survival and Event History Analysis: A Process Point of View. Springer-Verlag, New York.
M. G. AKRITAS (2000). The central limit theorem under censoring. Bernoulli, 6, no. 6, pp. 1109–1120.
P. K. ANDERSEN, O. BORGAN, R. D. GILL, N. KEIDING (2012). Statistical Models Based on Counting Processes. Springer-Verlag.
R. BROOKS (1982). On the loss of information through censoring. Biometrika, 69, no. 1, pp. 137–144.
A. BURTON, D. G. ALTMAN, P. ROYSTON, R. L. HOLDER (2006). The design of simulation studies in medical statistics. Statistics in Medicine, 25, no. 24, pp. 4279–4292.
A. B.CANTOR (2001). Projecting the standard error of the Kaplan–Meier estimator. Statistics in Medicine, 20, no. 14, pp. 2091–2097.
M.GREENWOOD (1926). A Report on the Natural Duration of Cancer. HMSO, London.
J. IRWIN (1949). The standard error of an estimate of expectation of life, with special reference to expectation of tumourless life in experiments with mice. Epidemiology & Infection, 47, no. 2, pp. 188–189.
E. L. KAPLAN, P. MEIER (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53, no. 282, pp. 457–481.
J. P. KLEIN (1991). Small sample moments of some estimators of the variance of the Kaplan-Meier and Nelson-Aalen estimators. Scandinavian Journal of Statistics, pp. 333–340.
J. P. KLEIN, M. L. MOESCHBERGER (2006). Survival Analysis: Techniques for Censored and Truncated Data. Springer-Verlag, New York.
K.-M. LEUNG, R. M. ELASHOFF, A. A. AFIFI (1997). Censoring issues in survival analysis. Annual Review of Public Health, 18, no. 1, pp. 83–104.
P. MEIER (1975). Estimation of a distribution function from incomplete observations. Journal of Applied Probability, 12, no. S1, pp. 67–87.
P. MEIER, T. KARRISON, R. CHAPPELL, H. XIE (2004). The price of Kaplan–Meier. Journal of the American Statistical Association, 99, no. 467, pp. 890–896.
S. NADARAJAH (2003). Reliability for lifetime distributions. Mathematical and Computer Modelling, 37, no. 7-8, pp. 683–688.
R. PETO, M. PIKE, P. ARMITAGE, N. E. BRESLOW, D. COX, S. HOWARD, N. MANTEL, K. MCPHERSON, J. PETO, P. SMITH (1977). Design and analysis of randomized clinical trials requiring prolonged observation of each patient. II. Analysis and examples. British Journal of Cancer, 35, no. 1, p. 1.
R CORE TEAM (2019). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
S. V. RAJKUMAR, S. JACOBUS, N. S. CALLANDER, R. FONSECA, D. H. VESOLE, M. E. WILLIAMS, R. ABONOUR, D. S. SIEGEL, M. KATZ, P. R. GREIPP (2010). Lenalidomide plus high-dose dexamethasone versus lenalidomide plus low-dose dexamethasone as initial therapy for newly diagnosed multiple myeloma: An open-label randomised controlled trial. The Lancet Oncology, 11, no. 1, pp. 29–37.
L. RICHELDI, M. KREUTER, M. SELMAN, B. CRESTANI, A.-M. KIRSTEN, W. A. WUYTS, Z. XU, K. BERNOIS, S. STOWASSER, M. QUARESMA (2018). Long-term treatment of patients with idiopathic pulmonary fibrosis with nintedanib: Results from
the tomorrow trial and its open-label extension. Thorax, 73, no. 6, pp. 581–583.
E. V. SLUD, D. P. BYAR, S. B. GREEN (1984). A comparison of reflected versus test-based confidence intervals for the median survival time, based on censored data. Biometrics, pp. 587–600.
W. STUTE (1995a). The central limit theorem under random censorship. The Annals of Statistics, 23, no. 2, pp. 422–439.
W. STUTE (1995b). The statistical analysis of Kaplan-Meier integrals. Lecture Notes- Monograph Series, 27, pp. 231–254.
W. STUTE (2003). Kaplan–Meier integrals. Handbook of Statistics, 23, pp. 87–104.
J. WANG (2016). Improved versions of Greenwood estimators under Koziol-Green model. Communications in Statistics-Theory and Methods, 45, no. 1, pp. 142–157.
G. YANG (1977). Life expectancy under random censorship. Stochastic Processes and their Applications, 6, no. 1, pp. 33–39.
P. H. ZHANG (1999). Exact bias and variance of the product limit estimator. Sankhy¯a: The Indian Journal of Statistics, Series B, pp. 413–421.
G. ZHAO (1996). The homogenetic estimate for the variance of survival rate. Statistics in Medicine, 15, no. 1, pp. 51–60.
G. ZHENG, J. L. GASTWIRTH (2001). On the Fisher information in randomly censored data. Statistics & Probability Letters, 52, no. 4, pp. 421–426.
How to Cite
Copyright (c) 2021 Statistica
This work is licensed under a Creative Commons Attribution 3.0 Unported License.