Censoring Unbiased Regression Trees and Ensembles

Steingrimsson, Jon A.; Diao, Liqun; Strawderman, Robert L.

doi:10.1080/01621459.2017.1407775

Cited by 43 publications

(56 citation statements)

References 32 publications

(82 reference statements)

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“…Motivated by above results, we propose a new bias-correction procedure that actively selects the best splitting variable at each internal node without the influence of the censoring distribution. This establishes a con-nection with existing methodology developments such as [20] and [37] who convert censored observations to fully observed ones through the inverse probability of censoring weighting. However, our proposed splitting rule is much more general in the sense that it compares the distributions of failure time from the two potential child nodes, rather than focusing on the mean differences.…”

Section: Introductionmentioning

confidence: 72%

“…as the subject-specific weight to fit regression random forests. One can also transform the censored observations into fully observed ones using, e.g., [34], and then fit a regression model with the complete data [29,36,37]. Similar ideas have also been used for imputing censored outcomes [42] when learning an optimal treatment strategy [14].…”

Section: Consistency Under Adaptive Splitting Rules29mentioning

confidence: 99%

“…To the best of our knowledge, the only consistency result to date is given by [22] who considered the setting where all predictors are categorical. Some other results are established based on augmented outcomes which transform the problem to a fully observed regression model [37].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Consistency of survival tree and forest models: splitting bias and correction

Cui¹,

Zhu²,

Zhou³

et al. 2022

STAT SINICA

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Random survival forests and survival trees are popular models in statistics and machine learning. However, there is a lack of general understanding regarding consistency, splitting rules and influence of the censoring mechanism. In this paper, we investigate the statistical properties of existing methods from several interesting perspectives. First, we show that traditional splitting rules with censored outcomes rely on a biased estimation of the within-node failure distribution. To exactly quantify this bias, we develop a concentration bound of the within-node estimation based on non i.i.d. samples and apply it to the entire forest. Second, we analyze the entanglement between the failure and censoring distributions caused by univariate splits, and show that without correcting the bias at an internal node, survival tree and forest models can still enjoy consistency under suitable conditions. In particular, we demonstrate this property under two cases: a finite-dimensional case where the splitting variables and cutting points

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Section: Introductionmentioning

confidence: 72%

Section: Consistency Under Adaptive Splitting Rules29mentioning

confidence: 99%

See 1 more Smart Citation

Consistency of survival tree and forest models: splitting bias and correction

Cui¹,

Zhu²,

Zhou³

et al. 2022

STAT SINICA

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show abstract

“…Recently, two papers introduced novel approaches to constructing ensemble methods for survival data. Steingrimsson et al (2018) proposed censoring unbiased regression survival trees and ensembles by extending the theory of censoring unbiased transformations applicable to loss functions for right-censored survival data. This new class of ensemble algorithms extends the random survival forest algorithm for use with an arbitrary loss function and allows the use of more general bootstrap procedures, such as the exchangeably weighted bootstrap (Weng, 1989).…”

Section: Other Ensemble Resampling Methodsmentioning

confidence: 99%

An ensemble method for interval-censored time-to-event data

2019

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Interval-censored data analysis is important in biomedical statistics for any type of time-to-event response where the time of response is not known exactly, but rather only known to occur between two assessment times. Many clinical trials and longitudinal studies generate interval-censored data; one common example occurs in medical studies that entail periodic follow-up. In this paper we propose a survival forest method for interval-censored data based on the conditional inference framework. We describe how this framework can be adapted to the situation of interval-censored data. We show that the tuning parameters have a non-negligible effect on the survival forest performance and guidance is provided on how to tune the parameters in a data-dependent way to improve the overall performance of the method. Using Monte Carlo simulations we find that the proposed survival forest is at least as effective as a survival tree method when the underlying model has a tree structure, performs similarly to an interval-censored Cox proportional hazards model fit when the true relationship is linear, and outperforms the survival tree method and Cox model when the true relationship is nonlinear. We illustrate the application of the method on a tooth emergence data set.

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“…For example, Davis and Anderson (1989) assumed that the survival time within any given node follows the exponential distribution; LeBlanc and Crowley (1992) adopted a proportional hazards model with an un-specified baseline hazard. More recently, the squared error loss commonly used in regression trees are extended to handle censored data (Molinaro et al, 2004;Steingrimsson et al, 2016Steingrimsson et al, , 2018. Other possible splitting criteria include a weighted sum of impurity of the censoring indicator and the squared error loss of the observed event time (Zhang, 1995), and the Harrell's C-statistic (Schmid et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

ROC‐guided survival trees and ensembles

2020

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Tree-based methods are popular nonparametric tools in studying time-to-event outcomes. In this article, we introduce a novel framework for survival trees and forests, where the trees partition the dynamic survivor population and can handle time-dependent covariates. Using the idea of randomized tests, we develop generalized time-dependent Receiver Operating Characteristic (ROC) curves to evaluate the performance of survival trees and establish the optimality of the target hazard function with respect to the ROC curve. The tree-building algorithm is guided by decision-theoretic criteria based on ROC, targeting specifically for prediction accuracy. We further extend the survival trees to random forests, where the ensemble is based on martingale estimating equations, in contrast with many existing survival forest algorithms that average the predicted survival or cumulative hazard functions.Simulations studies demonstrate strong performances of the proposed methods. We apply the methods to a study on AIDS for illustration.

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Censoring Unbiased Regression Trees and Ensembles

Cited by 43 publications

References 32 publications

Consistency of survival tree and forest models: splitting bias and correction

Consistency of survival tree and forest models: splitting bias and correction

An ensemble method for interval-censored time-to-event data

ROC‐guided survival trees and ensembles

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