A survival tree for interval-censored failure time data

Jia Chen; Renato De Leone; Jia Chen; Renato De Leone

doi:10.3934/math.2022996

AIMS Mathematics

2022, Volume 7, Issue 10: 18099-18126. doi: 10.3934/math.2022996

Previous Article Next Article

Research article Special Issues

A survival tree for interval-censored failure time data

Jia Chen ^1,2,
Renato De Leone ^{1
,
,}

1.
School of Science and Technology, University of Camerino, Camerino 62032, Italy
2.
School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China

Received: 25 April 2022 Revised: 25 July 2022 Accepted: 02 August 2022 Published: 09 August 2022
MSC : 62-08, 62N03

Interval-censored failure time data as a general type of survival data often arises in medicine and other applied fields. Survival tree is a flexible predictive method for survival data because no specific assumptions are required.

Generalized Log-Rank Test have good power with parameters for interval-censored failure time data. We construct a special test statistic of Generalized Log-Rank Tests, and propose a new survival tree with hyper-parameter by combining the test statistic with Conditional Inference Framework for interval-censored failure time data. The effect of tuning hyper-parameter are discussed and hyper-parameter tuning allows the tree method to be more general and flexible. Thus the tree method either improve upon or remain competitive with existing tree method for interval-censored failure time data-ICtree, which is a special case of ours. An extensive simulation is executed to assess the predictive performance of our tree methods. Finally, the tree methods are applied to a tooth emergence data.
- survival tree,
- interval-censored,
- conditional inference framework,
- hyper-parameter tuning,
- generalized log-rank tests
Citation: Jia Chen, Renato De Leone. A survival tree for interval-censored failure time data[J]. AIMS Mathematics, 2022, 7(10): 18099-18126. doi: 10.3934/math.2022996

Related Papers:

Abstract

Interval-censored failure time data as a general type of survival data often arises in medicine and other applied fields. Survival tree is a flexible predictive method for survival data because no specific assumptions are required.

Generalized Log-Rank Test have good power with parameters for interval-censored failure time data. We construct a special test statistic of Generalized Log-Rank Tests, and propose a new survival tree with hyper-parameter by combining the test statistic with Conditional Inference Framework for interval-censored failure time data. The effect of tuning hyper-parameter are discussed and hyper-parameter tuning allows the tree method to be more general and flexible. Thus the tree method either improve upon or remain competitive with existing tree method for interval-censored failure time data-ICtree, which is a special case of ours. An extensive simulation is executed to assess the predictive performance of our tree methods. Finally, the tree methods are applied to a tooth emergence data.

References

[1]	D. Chen, J. Sun, K. E. Peace, Interval-censored time-to-event data: Methods and Applications, 1 Eds., Florida: Chapman and Hall/CRC, 2013. https://doi.org/10.13140/2.1.3493.2169
[2]	D. R. Cox, Regression models and life-tables, J. R. Sta. Soc. B, 34 (1972), 187–220. http://dx.doi.org/10.1111/j.2517-6161.1972.tb00899.x doi: 10.1111/j.2517-6161.1972.tb00899.x
[3]	D. M. Finkelstein, A proportional hazards model for interval-censored failure time data, Biometrics, 42 (1986), 845–854. http://dx.doi.org/10.2307/2530698 doi: 10.2307/2530698
[4]	J. Sun, The statistical analysis of interval-censored failure time data, 1 Eds., New York: Springer Press, 2006. http://dx.doi.org/10.1007/0-387-37119-2
[5]	L. Breiman, J. H. Friedman, R. A. Olshen, C. J. Stone, Classification and regression trees, Biometrics, 40 (1984), 358. http://dx.doi.org/10.2307/2530946 doi: 10.2307/2530946
[6]	I. Bou-Hamad, D. Larocque, H. Ben-Ameur, A review of survival trees, Stat. Surv., 5 (2011), 44–71. http://dx.doi.org/10.1214/09-SS047 doi: 10.1214/09-SS047
[7]	L. Gordon, R. A. Olshen, Tree-structured Survival Analysis, Cancer Treat. Rep. 69 (1985), 1065–1069. https://pubmed.ncbi.nlm.nih.gov/4042086/
[8]	M. R. Segal, Regression trees for censored data, Biometrics, 44 (1988), 35–47. http://www.jstor.org/stable/2531894
[9]	A. Ciampi, S. A. Hogg, S. McKinney, J. Thiffault, RECPAM: A computer program for recursive partition and amalgamation for censored survival data and other situations frequently occurring in biostatistics.Ⅰ. Methods and program features, Comput. Meth. Prog. Bio., 26 (1988), 239–256. http://dx.doi.org/10.1016/0169-2607(88)90004-1 doi: 10.1016/0169-2607(88)90004-1
[10]	A. Ciampi, S. A. Hogg, S. McKinney, J. Thiffault, RECPAM: A computer program for recursive partition and amalgamation for censored survival data and other situations frequently occurring in biostatistics.Ⅱ. Applications to data on small cell carcinoma of the lung (SCCL), Comput. Meth. Prog. Bio., 30 (1989), 283–296. http://dx.doi.org/10.1016/0169-2607(89)90099-0 doi: 10.1016/0169-2607(89)90099-0
[11]	G. V. Kass, An exploratory technique for investigating large quantities of categorical data, Appl. Stat., 29 (1980), 119–127. http://dx.doi.org/10.2307/2986296 doi: 10.2307/2986296
[12]	T. Hothorn, K. Hornik, A. Zeileis, Unbiased recursive partitioning: A conditional inference framework, J. Comput. Graph. Stat., 15 (2006), 651–674. https://doi.org/10.1198/106186006X133933 doi: 10.1198/106186006X133933
[13]	H. Strasser, C. Weber, On the asymptotic theory of permutation statistics, Math. Methods Stat., 8 (1999), 220–250. http://epub.wu.ac.at/102/1/document.pdf
[14]	W. Fu, J. S. Simonoff, Survival trees for left-truncated and right-censored data with application to time-varying covariate data, Biostatistics, 18 (2017), 352–369. http://dx.doi.org/10.1093/biostatistics/kxw047 doi: 10.1093/biostatistics/kxw047
[15]	L. Breiman, Random forests, Mach. Learn., 45 (2001), 5–32. http://dx.doi.org/10.1023/A:1010933404324 doi: 10.1023/A:1010933404324
[16]	H. Ishwaran, U. B. Kogalur, E. H. Blackstone, M. S. Lauer, Random survival forests, Ann. Appl. Stat., 2 (2008), 841–860. http://dx.doi.org/10.1214/08-AOAS169 doi: 10.1214/08-AOAS169
[17]	J. A. Steingrimsson, L. Diao, R. L. Strawderman, Censoring unbiased regression trees and ensembles, J. Am. Stat. Assoc., 114 (2019), 370–383. http://dx.doi.org/10.1080/01621459.2017.140777 doi: 10.1080/01621459.2017.140777
[18]	Y. M. Yin, S. J. Anderson, Tree-structured modeling for interval-censored survival data, Joint Statistical Meetings, (2002), 3877–3882. https://www.researchgate.net/publication/265027875
[19]	W. Fu, J. S. Simonoff, Survival trees for interval-censored survival data, Stat. Med., 36 (2017), 4831–4842. http://dx.doi.org/10.1002/sim.7450 doi: 10.1002/sim.7450
[20]	W. Pan, Rank invariant tests with left truncated and interval censored data, J. Stat. Comput. Sim., 61 (1998), 163–174. http://dx.doi.org/10.1080/00949659808811907 doi: 10.1080/00949659808811907
[21]	H. Y. Cho, N. P. Jewell, M. R. Kosorok, Interval censored recursive forests, J. Comput. Graph. Stat., (2021), in press. https://doi.org/10.1080/10618600.2021.1987253
[22]	J. G. Sun, Q. Zhao, X. Q. Zhao, Generalized log-rank tests for interval-censored failure time data, Scand. J. Stats., 32 (2005), 49–57. http://dx.doi.org/https://doi.org/10.1002/bimj.200710419 doi: 10.1002/bimj.200710419
[23]	J. Vanobbergen, L. Martens, E. Lesaffre, D. Declerck, The Signal-Tandmobiel project a longitudinal intervention health promotion study in Flanders (Belgium): baseline and first year results, Eur. J. Paediatr. Dent., 2 (2000), 87–96. http://hdl.handle.net/1854/LU-127864
[24]	C. Anderson-Bergman, An efficient implementation of the EMICM algorithm for the interval censored NPMLE, J. Comput. Graph. Stat., 26 (2017), 463–467. http://dx.doi.org/10.1080/10618600.2016.1208616 doi: 10.1080/10618600.2016.1208616
[25]	C. Anderson-Bergman, icenReg: Regression models for interval censored data. Version 2.0.15., (2020). https://cran.r-project.org/web/packages/icenReg/index.html.
[26]	Y. Benoist, P. Foulon, F. Labourie, On Convergence of convex minorant algorithms for distribution estimation with interval-censored data, J. Comput. Graph. Stat., 1 (1992), 129–140. http://dx.doi.org/10.1080/10618600.1992.10477009 doi: 10.1080/10618600.1992.10477009
[27]	G. Gomez, R. O. Pique, A new class of rank tests for interval-censored data, Harvard University Biostatistics Working Paper Series, (2008), unpublished work. http://biostats.bepress.com/harvardbiostat/paper93
[28]	P. Wei, A comparison of some two-sample tests with interval censored data, J. Nonparametr. Stat., 12 (1999), 133–146. https://doi.org/10.1080/10485259908832801 doi: 10.1080/10485259908832801
[29]	D. Krstajic, L. J. Buturovic, D. E. Leahy, S. Thomas, Cross-validation pitfalls when selecting and assessing regression and classification models, J. Cheminformatics, 6 (2014), 1–15. http://www.jcheminf.com/content/6/1/10
[30]	T. R. Tsai, S. H. Wu, Y. Shen, Model selection methods for reliability assessment based on interval-censored field failure samples, Int. J. Reliab. Qual. Sa., 27 (2020), 1–19. http://dx.doi.org/10.1142/S0218539320500187 doi: 10.1142/S0218539320500187
[31]	E. Graf, C. Schmoor, W. Sauerbrei, M. Schumacher, Assessment and comparison of prognostic classification schemes for survival data, Stat. Med., 18 (1999), 2529–2545. https://doi.org/10.1002/(SICI)1097-0258(19990915/30)18:17/18<2529::AID-SIM274>3.0.CO; 2-5 doi: 10.1002/(SICI)1097-0258(19990915/30)18:17/18<2529::AID-SIM274>3.0.CO;2-5
[32]	S. Tsouprou, Measures of discrimination and predictive accuracy for interval censored survival data, MA. D. thesis, University Leiden, 2015. https://www.universiteitleiden.nl/binaries/content/assets/science/mi/scripties/mastertsouprou.pdf
[33]	T. Hothorn, B. Lausen, A. Benner, M. Radespiel-Tro${\rm{\ddot g}}$er, Bagging survival trees, Stat.Med., 23 (2004), 77–91. https://doi.org/10.1002/sim.1593 doi: 10.1002/sim.1593
[34]	A. Komárek, bayesSurv: Bayesian survival regression with flexible error and random effects distributions, R package version3.3, 2020. https://cran.r-project.org/web/packages/bayesSurv/index.html
[35]	E. Lesaffre, A. Komárek, D. Declerck, An overview of methods for interval-censored data with an emphasis on applications in dentistry, Stat. Methods Med. Res., 14 (2005), 539–552. https://doi.org/10.1191/0962280205sm417oa doi: 10.1191/0962280205sm417oa
[36]	W. C. Yao, H. Frydman, J. S. Simonoff, An ensemble method for interval-censored time-to-event data, Biostatistics, 22 (2021), 198–213. http://dx.doi.org/10.1093/biostatistics/kxz025 doi: 10.1093/biostatistics/kxz025

Reader Comments

Your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)