Survival tree
Survival tree is a decision tree presentation of survival data (for example, progression-free survival or overall survival). Unlike Cox PH regression, the association of predictor variables with survival times does not have to be pre-specified. In the Survival tree, the association of predictor variables with survival times is obtained in a data-driven manner. Survival tree basically identifies the subgroups characterized by the predictor variables. The survival distribution within a given subgroup is homogeneous, but heterogeneous among the subgroups.
Heterogeneity in tree structure
In any decision tree analysis, trees are constructed based on underlying heterogeneity and therefore it is important to define the scope of heterogeneity. Survival trees are constructed primarily based on heterogeneity in survival distribution. [1] However, in some applications with marker dependent censoring (e.g., less education or better prognosis might lead to early censoring) ignorance of censoring distribution might lead to inconsistent survival tree.[2] In these cases, heterogeneity in censoring distribution should be considered as well. SurvCART algorithm[3]
Survival tree construction algorithms
There are a number of survival tree construction algorithms proposed in the literature. The SurvCART algorithm[3] is flexible to construct a survival tree based on heterogeneity both in time-to-event and censoring distribution. However, it is important to emphasize that the use of censoring heterogeneity in the construction of survival trees is optional. Other survival tree construction algorithms include CTREE algorithm,[4] MOB algorithm,[5] martingale residual-based,[6] relative-risk tree algorithm,[7] and the RECPAM algorithm.[8] The CTREE algorithm,[4] MOB algorithm [5] and SurvCART algorithm [3] are built under a unified conditional inference framework [4] that takes splitting decisions based on parameter instability tests. While CTREE algorithm is non-parametric, the SurvCART algorithm [3] and MOB [5] algorithms are parametric meaning the underlying survival and/or censoring distributions need to be pre-specified.
Software implementation
The SurvCART algorithm [3] for construction of survival tree is implemented through SurvCART() in R package "LongCART".[9] The CTREE [4] and MOB [5] algorithms are implemented in R packages "partykit" [10] and "party".[11] The relative risk tree and martingale based survival trees can be obtained using R package "rpart".[12]
References
- ↑ Segal, Mark Robert (1988). "Regression Trees for Censored Data". Biometrics. 44 (1): 35–47.
- ↑ Cui, Yifan; Zhu, Ruoqing; Zhou, Mai; Korok, Michael (2021). "Consistency of survival tree and forest models: Splitting bias and correction" (PDF). Statistica Sinica.
- ↑ 3.0 3.1 3.2 3.3 3.4 Kundu, Madan; Ghosh, Samiran (2021). "Survival trees based on heterogeneity in time-to-event and censoring distributions using parameter instability test". Statistical Analysis and Data Mining. 14 (5): 466–483.
- ↑ 4.0 4.1 4.2 4.3 Hothorn, Torsten; Hornik, Kurt; Zeileis, Achim (2006). "Unbiased recursive partitioning: A conditional inference framework". Journal of Computational and Graphical Statistics. 15 (3): 651–674.
- ↑ 5.0 5.1 5.2 5.3 Zeileis, Achim; Hothorn, Torsten; Hornik, Kurt (2008). "Model-based recursive partitioning". Journal of Computational and Graphical Statistics. 17 (2): 492–514.
- ↑ Therneau, Terry; Grambsch, Patricia; Fleming, Thomas (1990). "Martingale-based residuals for survival models". Biometrika. 77 (1): 147–160.
- ↑ LeBlanc, Michael; Crowley, John (1992). "Relative risk trees for censored survival data". Biometrics. 48 (2): 411–425.
- ↑ Antonio, Ciampi; Thiffault, Johanne; Sagman, Uri (1989). "Survival trees based on heterogeneity in time-to-event and censoring distributions using parameter instability test". Computer Methods and Programs in Biomedicine. 30 (4): 283–296.
- ↑ Kundu, Madan G. "LongCART: Recursive Partitioning for Longitudinal Data and Right Censored Data Using Baseline Covariates". CRAN. Retrieved December 26, 2021. Unknown parameter
|url-status=ignored (help) - ↑ Hothorn, Torsten; Seibold, Heidi; Zeileis, Achim. "partykit: A Toolkit for Recursive Partytioning". CRAN. Retrieved December 26, 2021. Unknown parameter
|url-status=ignored (help) - ↑ Hothorn, Torsten; Hornik, Kurt; Strobl, Carolin; Zeileis, Achim. "party: A Laboratory for Recursive Partytioning". CRAN. Retrieved December 26, 2021. Unknown parameter
|url-status=ignored (help) - ↑ Therneau, Terry J.; Atkinson, Elizabeth J. "rpart: Recursive Partitioning and Regression Trees". CRAN. Retrieved November 12, 2021. Unknown parameter
|url-status=ignored (help)
