Abstract
The semiparametric accelerated failure time (AFT) model is a log-linear model of failure times with an unspecified random error term. The rank-based estimator has been a popular estimation method for regression parameters in this model. An induced smoothing method has reduced computational complexity and instability in the original non-smooth rank-based estimator. This paper briefly reviews and compares the recently proposed computationally efficient variance estimation methods for the semiparametric AFT models in multivariate failure times settings. Comparisons are made via extensive simulation experiments. Based on our findings, we may recommend using ‘Diff-Boot’ and ‘Diff-Closed’ methods with a one-step iteration. These variance estimators are then illustrated with the well-known Diabetic retinopathy study data.
Similar content being viewed by others
References
Brown, B. M., & Wang, Y. G. (2005). Standard errors and covariance matrices for smoothed rank estimators. Biometrika, 92(1), 149–158.
Brown, B. M., & Wang, Y. G. (2007). Induced smoothing for rank regression with censored survival times. Statistics in Medicine, 26(4), 828–836.
Chiou, S. H., Kang, S., & Yan, J. (2014a). Fast accelerated failure time modeling for case-cohort data. Statistics and Computing, 24(4), 559–568.
Chiou, S. H., Kang, S., Kim, J., & Yan, J. (2014b). Marginal semiparametric multivariate accelerated failure time model with generalized estimating equations. Lifetime Data Analysis, 20(4), 599–618.
Chiou, S. H., Kang, S., & Yan, J. (2014c). Fitting accelerated failure time models in routine survival analysis with R Package aftgee. Journal of Statistical Software, 61(11), 1–23.
Chiou, S. H., Kang, S., & Yan, J. (2015a). Rank-based estimating equations with general weight for accelerated failure time models: An induced smoothing approach. Statistics in Medicine, 34(9), 1495–1510.
Chiou, S. H., Kang, S., & Yan, J. (2015b). Semiparametric accelerated failure time modeling for clustered failure times from stratified sampling. Journal of the American Statistical Association, 110(510), 621–629.
Cox, D. R. (1972). Regression models and life-tables (with discussion). Journal of the Royal Statistical Society, Series B: Methodological, 34(2), 187–220.
Diabetic Retinopathy Study Research Group. (1976). The 5-year prognosis for vision in diabetes. American Journal of Ophthalmology, 81(4), 383–396.
Fygenson, M., & Ritov, Y. (1994). Monotone estimating equations for censored data. The Annals of Statistics, 22(2), 732–746.
Gehan, E. A. (1965). A Generalized Wilcoxon test for comparing arbitrarily singly-censored samples. Biometrika, 52(1/2), 203–223.
Harrington, D. P., & Fleming, T. R. (1982). A class of rank test procedures for censored survival data. Biometrika, 69(3), 553–566.
Jin, Z., Lin, D. Y., Wei, L. J., & Ying, Z. (2003). Rank-based inference for the accelerated failure time model. Biometrika, 90(2), 341–353.
Jin, Z., Lin, D. Y., & Ying, Z. (2006). Rank regression analysis of multivariate failure time data based on marginal linear models. Scandinavian Journal of Statistics, 33(1), 1–23.
Jin, Z., Shao, Y., & Ying, Z. (2015). A Monte Carlo method for variance estimation for estimators based on induced smoothing. Biostatistics, 16(1), 179–188.
Jin, Z. (2016). Semiparametric accelerated failure time model for the analysis of right censored data. Communications for Statistical Applications and Methods, 23(6), 467–478.
Johnson, L. M., & Strawderman, R. L. (2009). Induced smoothing for the semiparametric accelerated failure time Model: asymptotics and extensions to clustered data. Biometrika, 96(3), 577–590.
Kalbfleisch, J. D., & Prentice, R. L. (2002). The statistical analysis of failure time data (2nd ed.). Hoboken: Wiley.
Mantel, N. (1966). Evaluation of survival data and two new rank order statistics arising in its consideration. Cancer Chemother Rep, 50(3), 163–170.
Nelsen, R. (2007). An introduction to copulas. Berlin: Springer Science & Business Media.
Prentice, R. L. (1978). Linear rank tests with right censored data. Biometrika, 65(1), 167–180.
R Core Team. (2020). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing.
Therneau, T. (2020). A Package for Survival Analysis in R. https://CRAN.R-project.org/package=survival.
Wang, Y. G., & Fu, L. (2011). ank regression for accelerated failure time model with clustered and censored data. Computational Statistics & Data Analysis, 55(7), 2334–2343.
Zeng, D., & Lin, D. Y. (2008). Efficient resampling methods for nonsmooth estimating functions. Biostatistics, 9(2), 355–363.
Acknowledgements
This work was partly supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2C1A0101313911) and the Graduate School of YONSEI University Research Scholarship Grants in 2020.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The first two authors (Kim and Ko) are co-first authors.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Kim, K., Ko, J. & Kang, S. Comparison of variance estimation methods in semiparametric accelerated failure time models for multivariate failure time data. Jpn J Stat Data Sci 4, 1179–1202 (2021). https://doi.org/10.1007/s42081-021-00126-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42081-021-00126-y