Modified Kaplan-Meier Estimator Based on Competing Risks for Heavy Censoring Data
DOI:
https://doi.org/10.6000/1929-6029.2013.02.04.6Keywords:
Competing risks, Kaplan-Meier estimator, Heavy Censoring, Net and Crude probabilitiesAbstract
Most follow-up studies are conducted to determine the survival rates of subjects affected by a specific risk. These subjects are also exposed to other risks. Every subject in a medical follow-up is exposed not only to the risk of dying, but also to the risk of being censored. In case of heavy censoring, the Kaplan-Meier estimates are biased and overestimate the survival distribution. A new methodology based on competing risks is proposed to estimate the survival function by using net and crude probabilities. These estimates reduce the bias and overestimation of the survival distribution noted in Kaplan-Meier estimators. In this study, the method of modified Kaplan-Meier (MKM) is compared with the Kaplan-Meier (KM), Huang’s method and also the two other methods namely Weighted Kaplan-Meier (WKM) and Modified Weighted Kaplan-Meier (MWKM). Either of the weighted methods depends heavily on the event times and censoring distributions. Due to this fact, the weighted methods can have misleading results when the censoring patterns are different in the individual samples. The results showed that the MKM estimator considers not only the problem of heavy censoring but also the problem of weighted methods and competing risks in complicated data. In this study “Stanford Heart Transplant Data” was used to investigate the effectiveness of the proposed methods.
References
Andersen PK. Statistical models based on counting processes. Springer 1993. http://dx.doi.org/10.1007/978-1-4612-4348-9 DOI: https://doi.org/10.1007/978-1-4612-4348-9
Young KD, Menegazzi JJ, Lewis RJ. Statistical methodology. Acad Emerg Med 1999; 6(3): 244-49. http://dx.doi.org/10.1111/j.1553-2712.1999.tb00165.x DOI: https://doi.org/10.1111/j.1553-2712.1999.tb00165.x
Klein JP, Moeschberger ML. Survival analysis: techniques for censored and truncated data. Springer 2003. DOI: https://doi.org/10.1007/b97377
Klein JP, Zhang MJ. Survival analysis, software. Wiley Online Library 2005. DOI: https://doi.org/10.1002/0470011815.b2a11073
Murray S. Using Weighted Kaplan‐Meier Statistics in Nonparametric Comparisons of Paired Censored Survival Outcomes. Biometrics 2001; 57(2): 361-68. http://dx.doi.org/10.1111/j.0006-341X.2001.00361.x DOI: https://doi.org/10.1111/j.0006-341X.2001.00361.x
Hosmer Jr, DW, Lemeshow S, May S. Applied survival analysis: regression modeling of time to event data. Wiley-Interscience 2011; Vol. 618.
Jan B, et al. Weighted Kaplan Meier estimation of survival function in heavy censoring. Pak J Statistics-All Series 2005; 21(1): 55.
Jan B. Improved Inferences in the context of Survival/Failure Time, Ph. D Thesis University of Peshawar 2004.
Shafiq M, Shah S, Alamgir M. Modified Weighted Kaplan-Meier Estimator. Pak J Statist Operat Res 2007; 3(1). DOI: https://doi.org/10.18187/pjsor.v3i1.75
Huang M. A weighted estimation method for survival function. Appl Math Sci 2008; 2(16): 753-62.
Kaplan EL, Meier P. Nonparametric estimation from incomplete observations. J Am Statist Assoc 1958; 53(282): 457-81. http://dx.doi.org/10.1080/01621459.1958.10501452 DOI: https://doi.org/10.1080/01621459.1958.10501452
Kaplan E, Meier P. Nonparametric Estimation from Incomplete Observations, in Breakthroughs in Statistics. Springer 1992; pp. 319-337. http://dx.doi.org/10.1007/978-1-4612-4380-9_25 DOI: https://doi.org/10.1007/978-1-4612-4380-9_25
Chiang CL. A stochastic study of the life table and its applications. III. The follow-up study with the consideration of competing risks. Biometrics 1961; 17(1): 57-78. http://dx.doi.org/10.2307/2527496 DOI: https://doi.org/10.2307/2527496
Chiang CL. Competing risks and conditional probabilities. Biometrics 1970; 767-776. http://dx.doi.org/10.2307/2528722 DOI: https://doi.org/10.2307/2528722
Chiang CL. Competing risks in mortality analysis. Annual Rev Public Health 1991; 12(1): 281-307. http://dx.doi.org/10.1146/annurev.pu.12.050191.001433 DOI: https://doi.org/10.1146/annurev.pu.12.050191.001433
Bowers NL, et al., Actuarial mathematics. Society of Actuaries Itasca, Ill 1986; Vol. 2.
Jordan C. Life Contingencies. Society of Actuaries 1975.
Kalbfleisch JD, Prentice RL. The statistical analysis of failure time data. John Wiley & Sons 2011; Vol. 360.
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Copyright (c) 2013 Ali Zare, Mahmood Mahmoodi
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