Survival forests under test: Impact of the proportional hazards assumption on prognostic and predictive forests for amyotrophic lateral sclerosis survival

Korepanova, Natalia; Seibold, Heidi; Steffen, Verena; Hothorn, Torsten

doi:10.1177/0962280219862586

Cited by 16 publications

(34 citation statements)

References 46 publications

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“…This yields not only a conditional parameter function for the transformation parameters ϑ(x) but additionally a personalized treatment effect β(x). Recently, there has been increasing interest in using random forest algorithms for estimating such personalized treatment effects (Foster, Taylor, and Ruberg 2011; Seibold, Zeileis, andHothorn 2016, 2018;Wager and Athey 2018) and transformation trees and forests can readily couple this with the flexibility of transformation models: Korepanova et al (2020) provide empirical results in the context of transformation survival forests.…”

Section: Discussionmentioning

confidence: 99%

Predictive Distribution Modeling Using Transformation Forests

Hothorn

Zeileis

2021

Journal of Computational and Graphical Statistics

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Regression models for supervised learning problems with a continuous response are commonly understood as models for the conditional mean of the response given predictors. This notion is simple and therefore appealing for interpretation and visualization. Information about the whole underlying conditional distribution is, however, not available from these models. A more general understanding of regression models as models for conditional distributions allows much broader inference, for example, the computation of prediction intervals or probabilistic predictions for exceeding certain thresholds. Several random forest-type algorithms aim at estimating conditional distributions, most prominently quantile regression forests. We propose a novel approach based on a parametric family of distributions characterized by their transformation function. A dedicated novel "transformation tree" algorithm able to detect distributional changes is developed. Based on these transformation trees, we introduce "transformation forests" as an adaptive local likelihood estimator of conditional distribution functions. The resulting predictive distributions are fully parametric yet very general and allow inference procedures, such as likelihood-based variable importances, to be applied in a straightforward way. Supplemental files for this article are available online.

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Section: Discussionmentioning

confidence: 99%

Predictive Distribution Modeling Using Transformation Forests

Hothorn

Zeileis

2021

Journal of Computational and Graphical Statistics

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“…The core functionality provided by mlt was instrumental in developing statistical learning procedures based on transformation models. Transformation trees and corresponding transformation forests were introduced by Hothorn and Zeileis (2017) and implemented in package trtf; an application to conditional distributions for body mass indices was described by Hothorn (2018) and novel survival forests have been evaluated by Korepanova, Seibold, Steffen, and Hothorn (2019). Two different gradient boosting schemes allowing complex models to be built in the transformation modelling framework were proposed by Hothorn (2020d) and are implemented in package tbm.…”

Section: Discussionmentioning

confidence: 99%

Most Likely Transformations: The mlt Package

Hothorn¹

2020

J. Stat. Soft.

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The mlt package implements maximum likelihood estimation in the class of conditional transformation models. Based on a suitable explicit parameterization of the unconditional or conditional transformation function using infrastructure from package basefun, we show how one can define, estimate, and compare a cascade of increasingly complex transformation models in the maximum likelihood framework. Models for the unconditional or conditional distribution function of any univariate response variable are set-up and estimated in the same computational framework simply by choosing an appropriate transformation function and parameterization thereof. As it is computationally cheap to evaluate the distribution function, models can be estimated by maximization of the exact likelihood, especially in the presence of random censoring or truncation. The relatively dense high-level implementation in the R system for statistical computing allows generalization of many established implementations of linear transformation models, such as the Cox model or other parametric models for the analysis of survival or ordered categorical data, to the more complex situations illustrated in this paper. Journal of Statistical Software5 transformation model P(Y ≤ y) = Φ(h(y)) = Φ(a(y) ϑ) by maximization of the exact likelihood as follows. After loading package mlt we specify the duration variable we are interested in R> library("mlt") R> var_d <-numeric_var("duration", support = c(1.0, 5.0), + add = c(-1, 1), bounds = c(0, Inf)) This abstract representation refers to a positive and conceptually continuous variable duration. We then set-up a basis function a for this variable in the interval [1, 5] (which can be evaluated in the interval [0, 6] as defined by the add argument), in our case a monotone increasing Bernstein polynomial of order eight (details can be found in Section 2.1) R> B_d <-Bernstein_basis(var = var_d, order = 8, ui = "increasing") The (in our case unconditional) transformation model is now fully defined by the parameterization h(y) = a(y) ϑ and F Z = Φ which is specified using the ctm() function as R> ctm_d <-ctm(response = B_d, todistr = "Normal") Because, in this simple case, the transformation function transforms Y ∼ F Y to Z ∼ F Z = Φ, the latter distribution is specified using the todistr argument. An equidistant grid of 200 duration times in the interval support + add = [0, 6] is generated by R> str(nd_d <-mkgrid(ctm_d, 200)) List of 1 $ duration: num [1:200] 0 0.0302 0.0603 0.0905 0.1206 ...

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“…Although this work is restricted to normally distributed endpoints and linear models, the original MOB and hence the predMOB as well are applicable to any kind of data that can be analyzed using a fully parameterized model, for example, binary endpoints. Even the application to time‐to‐event endpoints is feasible using parametric failure time models such as the Weibull model or a more flexible alternative using Bernstein polynomials as originally proposed by Hothorn et al…”

Section: Discussionmentioning

confidence: 99%

Exploratory identification of predictive biomarkers in randomized trials with normal endpoints

Krzykalla

Benner

Kopp‐Schneider

2019

Statistics in Medicine

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One of the main endeavours in present‐day medicine, especially in oncological research, is to provide evidence for individual treatment decisions (“stratified medicine”). In the pursuit of optimal treatment decision rules, the identification of predictive biomarkers that modify the treatment effect is essential. Proposed methods have often been based on recursive partitioning since a wide variety of interaction patterns can be captured automatically and the results are easily interpretable. Furthermore, these methods are readily extendable to high‐dimensional settings by means of ensemble learning. In this article, we present predMOB, an adaptation of the model‐based recursive partitioning (MOB) for subgroup analysis approach specifically tailored to the identification of predictive factors. In a simulation study, predMOB outperforms the original MOB with respect to the number of false detections and shows to be more robust in moderately complex settings. Furthermore, we compare the results of predMOB for the application to a public data base of amyotrophic lateral sclerosis patients to those obtained from the original MOB and are able to elucidate the nature of the biomarkers' effects.

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Survival forests under test: Impact of the proportional hazards assumption on prognostic and predictive forests for amyotrophic lateral sclerosis survival

Cited by 16 publications

References 46 publications

Predictive Distribution Modeling Using Transformation Forests

Predictive Distribution Modeling Using Transformation Forests

Most Likely Transformations: The mlt Package

Exploratory identification of predictive biomarkers in randomized trials with normal endpoints

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