In this paper, we
introduce three different data transformation approaches such as synthetic data
transformation ([1]; [2]; [3]), Kaplan-Meier weights ([4]; [5] ; [6]) and k-nearest neighbour (kNN)
imputation method ([7]) which are commonly used in censored data applications. The
aforementioned approaches are particularly useful when one deals with censored
data. The key idea expressed here is to find the smoothing spline estimates for
the parametric and nonparametric components of a semiparametric regression
model with right-censored data. The estimation is then carried out based on the
modified (or transformed) data set obtained via these transformation
techniques. In order to compare the outcomes of three approaches in
semi-parametric regression setting, we carried out a simulation study.
According to the results of the simulation, it can be said that the Kaplan-Meier
weights have been very successful in dealing with censored observations.
[1] J. Buckley, I. James, Linear Regression with Censored Data, Biometrika, 66(3), 429-436, 1979[2] H. Koul, V. Susarla, J. Van Ryzin, Regression Analysis with Randomly Right-Censored Data, The Annals of Statistics, 1276-1285, 1981.[3] S. Leurgans, Linear Models, Random Censoring and Synthetic Data, Biometrika, 74, 301-309, 1987.[4] E.L. Kaplan, P. Meier, Nonparametric Estimation from Incomplete Observations, Journal of the American Statistical Association, 53(282), 457-481, 1958.[5] R.G. Miller, Least Squares Regression with Censored Data, Biometrika, 63, 449-464, 1976.[6] W. Stute, Consistent Estimation under Random Censorship when Covariables are Present, Journal of Multivariate Analysis, 45, 89-103, 1993.[7] G.E.A.P.A. Batista and M.C. Monard, K-Nearest Neighbour as an Imputation Method: Experimental Results, Technical Report, ICMC-USP, ISSN-0103-2569, 2002.[8] W. Stute, The Central Limit Theorem under Random Censorship. The Annals of Statistics, 2, 422-439, 1995.[9] W. Stute, Nonlinear Censored Regression, Statistica Sinica, 9, 1089-1102, 1999.[10] O. Troyanskaya, M. Cantor, Sherlock, G., P. Brown, T. Hastie, R. Tibshirani, D. Botstein, R.B. Altman, Missing value estimation methods for DNA microarrays, Bioinformatics, 17(6), 520-525, 2001.[11] P.J. Green, B.W. Silverman, Nonparametric Regression and Generalized Linear Model, Chapman & Hall, 1994.[12] C.M. Hurvich, S. Simonoff, S. and C.L. Tsai, Smoothing Parameter Selection in Nonparametric Regression using an Improved Akaike Information Criterion. Journal of Royal Statistical Society B, 60(2), 271-293, 1998.[13] D. Aydın, E. Yılmaz, Modified Spline Regression Based on Randomly Right-Censored Data: A Comparison Study, Communication in Statistics-Simulation and Computation, 47(9), 2587-2611, 2018.[14] M. Talamakrouni, A.E. Gouch, I. Van Keilegom, Guided Censored Regression, Scandinavian Journal of Statistics-Theory and Applications, 42(1), 214-233, 2015.
[1] J. Buckley, I. James, Linear Regression with Censored Data, Biometrika, 66(3), 429-436, 1979[2] H. Koul, V. Susarla, J. Van Ryzin, Regression Analysis with Randomly Right-Censored Data, The Annals of Statistics, 1276-1285, 1981.[3] S. Leurgans, Linear Models, Random Censoring and Synthetic Data, Biometrika, 74, 301-309, 1987.[4] E.L. Kaplan, P. Meier, Nonparametric Estimation from Incomplete Observations, Journal of the American Statistical Association, 53(282), 457-481, 1958.[5] R.G. Miller, Least Squares Regression with Censored Data, Biometrika, 63, 449-464, 1976.[6] W. Stute, Consistent Estimation under Random Censorship when Covariables are Present, Journal of Multivariate Analysis, 45, 89-103, 1993.[7] G.E.A.P.A. Batista and M.C. Monard, K-Nearest Neighbour as an Imputation Method: Experimental Results, Technical Report, ICMC-USP, ISSN-0103-2569, 2002.[8] W. Stute, The Central Limit Theorem under Random Censorship. The Annals of Statistics, 2, 422-439, 1995.[9] W. Stute, Nonlinear Censored Regression, Statistica Sinica, 9, 1089-1102, 1999.[10] O. Troyanskaya, M. Cantor, Sherlock, G., P. Brown, T. Hastie, R. Tibshirani, D. Botstein, R.B. Altman, Missing value estimation methods for DNA microarrays, Bioinformatics, 17(6), 520-525, 2001.[11] P.J. Green, B.W. Silverman, Nonparametric Regression and Generalized Linear Model, Chapman & Hall, 1994.[12] C.M. Hurvich, S. Simonoff, S. and C.L. Tsai, Smoothing Parameter Selection in Nonparametric Regression using an Improved Akaike Information Criterion. Journal of Royal Statistical Society B, 60(2), 271-293, 1998.[13] D. Aydın, E. Yılmaz, Modified Spline Regression Based on Randomly Right-Censored Data: A Comparison Study, Communication in Statistics-Simulation and Computation, 47(9), 2587-2611, 2018.[14] M. Talamakrouni, A.E. Gouch, I. Van Keilegom, Guided Censored Regression, Scandinavian Journal of Statistics-Theory and Applications, 42(1), 214-233, 2015.
Aydın D, Yılmaz E. SEMIPARAMETRIC REGRESSION ESTIMATES BASED ON SOME TRANSFORMATION TECHNIQUES FOR RIGHT-CENSORED DATA. Estuscience - Se. December 2019;20:1-12. doi:10.18038/estubtda.632694