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13-11-2023

Bias reduction for semi-competing risks frailty model with rare events: application to a chronic kidney disease cohort study in South Korea

Authors: Jayoun Kim, Boram Jeong, Il Do Ha, Kook-Hwan Oh, Ji Yong Jung, Jong Cheol Jeong, Donghwan Lee

Published in: Lifetime Data Analysis

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Abstract

In a semi-competing risks model in which a terminal event censors a non-terminal event but not vice versa, the conventional method can predict clinical outcomes by maximizing likelihood estimation. However, this method can produce unreliable or biased estimators when the number of events in the datasets is small. Specifically, parameter estimates may converge to infinity, or their standard errors can be very large. Moreover, terminal and non-terminal event times may be correlated, which can account for the frailty term. Here, we adapt the penalized likelihood with Firth’s correction method for gamma frailty models with semi-competing risks data to reduce the bias caused by rare events. The proposed method is evaluated in terms of relative bias, mean squared error, standard error, and standard deviation compared to the conventional methods through simulation studies. The results of the proposed method are stable and robust even when data contain only a few events with the misspecification of the baseline hazard function. We also illustrate a real example with a multi-centre, patient-based cohort study to identify risk factors for chronic kidney disease progression or adverse clinical outcomes. This study will provide a better understanding of semi-competing risk data in which the number of specific diseases or events of interest is rare.

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Appendix
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Literature
go back to reference Ambler G, Seaman S, Omar R (2012) An evaluation of penalised survival methods for developing prognostic models with rare events. Stat Med 31(11–12):1150–1161 MathSciNetCrossRef Ambler G, Seaman S, Omar R (2012) An evaluation of penalised survival methods for developing prognostic models with rare events. Stat Med 31(11–12):1150–1161 MathSciNetCrossRef
go back to reference Ha ID, Xiang L, Peng M, Jeong J-H, Lee Y (2020) Frailty modelling approaches for semi-competing risks data. Lifetime Data Anal 26(1):109–133 MathSciNetCrossRefMATH Ha ID, Xiang L, Peng M, Jeong J-H, Lee Y (2020) Frailty modelling approaches for semi-competing risks data. Lifetime Data Anal 26(1):109–133 MathSciNetCrossRefMATH
go back to reference Kang E, Han M, Kim H, Park SK, Lee J, Hyun YY, Kim Y-S, Chung W, Kim HJ, Oh YK et al (2017) Baseline general characteristics of the korean chronic kidney disease: report from the korean cohort study for outcomes in patients with chronic kidney disease (know-ckd). J Korean Med Sci 32(2):221–230 CrossRef Kang E, Han M, Kim H, Park SK, Lee J, Hyun YY, Kim Y-S, Chung W, Kim HJ, Oh YK et al (2017) Baseline general characteristics of the korean chronic kidney disease: report from the korean cohort study for outcomes in patients with chronic kidney disease (know-ckd). J Korean Med Sci 32(2):221–230 CrossRef
go back to reference Kohl M, Plischke M, Leffondré K, Heinze G (2015) Pshreg: a sas macro for proportional and nonproportional subdistribution hazards regression. Comput Methods Programs Biomed 118(2):218–233 CrossRef Kohl M, Plischke M, Leffondré K, Heinze G (2015) Pshreg: a sas macro for proportional and nonproportional subdistribution hazards regression. Comput Methods Programs Biomed 118(2):218–233 CrossRef
go back to reference Lee Y, Nelder JA (1996) Hierarchical generalized linear models. J R Stat Soc Ser B (Methodol) 58(4):619–656 MathSciNetMATH Lee Y, Nelder JA (1996) Hierarchical generalized linear models. J R Stat Soc Ser B (Methodol) 58(4):619–656 MathSciNetMATH
go back to reference Lee Y, Nelder JA, Pawitan Y (2018) Generalized linear models with random effects: unified analysis via H-likelihood. Chapman and Hall/CRC, Florida CrossRefMATH Lee Y, Nelder JA, Pawitan Y (2018) Generalized linear models with random effects: unified analysis via H-likelihood. Chapman and Hall/CRC, Florida CrossRefMATH
go back to reference Oh K-H, Park SK, Park HC, Chin HJ, Chae DW, Choi KH, Han SH, Yoo TH, Lee K, Kim Y-S et al (2014) Know-ckd (korean cohort study for outcome in patients with chronic kidney disease): design and methods. BMC Nephrol 15(1):1–9 CrossRef Oh K-H, Park SK, Park HC, Chin HJ, Chae DW, Choi KH, Han SH, Yoo TH, Lee K, Kim Y-S et al (2014) Know-ckd (korean cohort study for outcome in patients with chronic kidney disease): design and methods. BMC Nephrol 15(1):1–9 CrossRef
go back to reference O’Mahony C, Jichi F, Pavlou M, Monserrat L, Anastasakis A, Rapezzi C (2014) A novel clinical risk prediction model for sudden cardiac death in hypertrophic cardiomyopathy (hcm risk-scd). Eur Heart J 35(30):2010–2020 CrossRef O’Mahony C, Jichi F, Pavlou M, Monserrat L, Anastasakis A, Rapezzi C (2014) A novel clinical risk prediction model for sudden cardiac death in hypertrophic cardiomyopathy (hcm risk-scd). Eur Heart J 35(30):2010–2020 CrossRef
go back to reference Omar RZ, Morton LS, Halliday DA, Danns EM, Beirne MT, Blot WJ, Taylor KM (2001) Outlet strut fracture of björk-shiley convexo concave heart valves: the uk cohort study heart. Heart 865(1):57–62 Omar RZ, Morton LS, Halliday DA, Danns EM, Beirne MT, Blot WJ, Taylor KM (2001) Outlet strut fracture of björk-shiley convexo concave heart valves: the uk cohort study heart. Heart 865(1):57–62
go back to reference Putter H, Fiocco M, Geskus RB (2007) Tutorial in biostatistics: competing risks and multi-state models. Stat Med 26(11):2389–2430 MathSciNetCrossRef Putter H, Fiocco M, Geskus RB (2007) Tutorial in biostatistics: competing risks and multi-state models. Stat Med 26(11):2389–2430 MathSciNetCrossRef
go back to reference Xu J, Kalbfleisch JD, Tai B (2010) Statistical analysis of illness-death processes and semicompeting risks data. Biometrics 66(3):716–725 MathSciNetCrossRefMATH Xu J, Kalbfleisch JD, Tai B (2010) Statistical analysis of illness-death processes and semicompeting risks data. Biometrics 66(3):716–725 MathSciNetCrossRefMATH
Metadata
Title
Bias reduction for semi-competing risks frailty model with rare events: application to a chronic kidney disease cohort study in South Korea
Authors
Jayoun Kim
Boram Jeong
Il Do Ha
Kook-Hwan Oh
Ji Yong Jung
Jong Cheol Jeong
Donghwan Lee
Publication date
13-11-2023
Publisher
Springer US
Published in
Lifetime Data Analysis
Print ISSN: 1380-7870
Electronic ISSN: 1572-9249
DOI
https://doi.org/10.1007/s10985-023-09612-9