Doubly robust survival trees

Steingrimsson, Jon A.; Diao, Liqun; Molinaro, Annette M.; Strawderman, Robert L.

doi:10.1002/sim.6949

Cited by 40 publications

(69 citation statements)

References 26 publications

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“…It is implemented using the rpart package in R. Default tuning parameters in rpart are used apart from that the minimum number of observations in a terminal node is set to 30. To ensure that the positivity assumption holds empirically, a "Method 2" truncation as described in Steingrimsson et al (2016) is used within each terminal node. "Method 2" truncation within a terminal node modifies the data by setting the failure time indicator for the largest 10% of observations falling in each terminal node to one.…”

Section: Algorithms Estimating P (T ≥ T|w )mentioning

confidence: 99%

“…IPCW estimators are inefficient as they fail to utilize information in censored observations. Using semiparametric efficiency theory for missing data, Steingrimsson et al (2016) developed a "doubly robust" estimator for the full data risk that is both more efficient and more robust to the modeling choices made than the IPCW loss. Steingrimsson et al (2017) proposed a class of censoring unbiased loss (CUL) functions that includes both the IPCW and the "doubly robust" losses as a special case.…”

Section: Introductionmentioning

confidence: 99%

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Deep learning for survival outcomes

Steingrimsson

Morrison

2020

Statistics in Medicine

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This manuscripts develops a new class of deep learning algorithms for outcomes that are potentially censored. To account for censoring, the unobservable loss function used in the absence of censoring is replaced by a censoring unbiased transformation. The resulting class of algorithms can be used to estimate both survival probabilities and restricted mean survival. We show how the deep learning algorithms can be implemented using software for uncensored data using a form of response transformation. Simulations and analysis of the Netherlands 70 Gene Signature Data show strong performance of the proposed algorithms.

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Section: Algorithms Estimating P (T ≥ T|w )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Deep learning for survival outcomes

Steingrimsson

Morrison

2020

Statistics in Medicine

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“…The MSE is defined as

100 0^{- 1} \sum_{i = 1}^{1000} {false(\overset{α}{true} false(X_{i} false) - α false(X_{i} false) false)}^{2}

, where X i , i =1,…,1000 are the covariates from the test set. Proportion of correct trees: For a continuous covariate the probability of getting exactly the correct split point is zero. Following the work of Steingrimsson et al, we define a tree to be correct if it splits on all variables the correct number of times independently of the ordering or the selection of splitting point. Number of noise variables: The average number of times the tree splits on the noise variables ( X (1) − X (5) for the homogeneous treatment effect setting and X (2) − X (5) for the heterogeneous treatment effect setting). Pairwise prediction similarity: Let I T ( i , j ) and I M ( i , j ) be indicators whether participants i and j have the same prediction when run down the true tree and the fitted tree, respectively. Pairwise prediction similarity is defined as

1 - \sum_{i = 1}^{1000} \sum_{j > i}^{1000} \frac{| I_{T} (i, j) - I_{M} (i, j) |}{(\frac{0}{1000})} .

Hence, pairwise prediction similarity measures the ability of the algorithms to separate participants into different risk groups. Time: Average time in seconds it takes to build the models.…”

Section: Simulationsmentioning

confidence: 99%

Subgroup identification using covariate‐adjusted interaction trees

Steingrimsson

Yang

2019

Statistics in Medicine

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We consider the problem of identifying subgroups of participants in a clinical trial that have enhanced treatment effect. Recursive partitioning methods that recursively partition the covariate space based on some measure of between groups treatment effect difference are popular for such subgroup identification.The most commonly used recursive partitioning method, the classification and regression tree algorithm, first creates a large tree by recursively partitioning the covariate space using some splitting criteria and then selects the final tree from all the subtrees of the large tree. In the context of subgroup identification, calculation of the splitting criteria and the evaluation measure used for final tree selection rely on comparing differences in means between the treatment and control arm. When covariates are prognostic for the outcome, covariate adjusted estimators have the ability to improve efficiency compared to using differences in averages between the treatment and control group. This manuscript develops two covariate adjusted estimators that can be used to both make splitting decisions and for final tree selection. The performance of the resulting covariate adjusted recursive partitioning algorithm is evaluated using simulations and by analyzing a clinical trial that evaluates if motivational interviews improve treatment engagement for substance abusers. KEYWORDSclassification and regression trees, model standardization, randomized controlled trials 3974

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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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Doubly robust survival trees

Cited by 40 publications

References 26 publications

Deep learning for survival outcomes

Deep learning for survival outcomes

Subgroup identification using covariate‐adjusted interaction trees

ROC‐guided survival trees and ensembles

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