Cross validation approaches for penalized Cox regression

Dai, Biyue; Breheny, Patrick

doi:10.48550/arxiv.1905.10432

Cited by 4 publications

(7 citation statements)

References 20 publications

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“…For example, glmnet uses cross-validated partial likelihood. In our implementation, however, we instead implement a cross-validated linear predictors criterion proposed in Dai and Breheny (2019). Specifically, for each of the J populations, we randomly assign subjects to one of K folds, K (j)1 , .…”

Section: Tuning Criterionmentioning

confidence: 99%

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Dimension reduction for integrative survival analysis

Molstad¹,

Patra²

2021

Preprint

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We propose a constrained maximum partial likelihood estimator for dimension reduction in integrative (e.g., pan-cancer) survival analysis with high-dimensional covariates. We assume that for each population in the study, the hazard function follows a distinct Cox proportional hazards model. To borrow information across populations, we assume that all of the hazard functions depend only on a small number of linear combinations of the predictors. We estimate these linear combinations using an algorithm based on "distance-to-set" penalties. This allows us to impose both low-rankness and sparsity. We derive asymptotic results which reveal that our estimator of the regression coefficients is more efficient than fitting a separate proportional hazards model for each population. Numerical experiments suggest that our method outperforms related competitors under various data generating models. We use our method to perform a pan-cancer survival analysis relating protein expression to survival across 18 distinct cancer types. Our approach identifies six linear combinations, depending on only 20 proteins, which explain survival across the cancer types. Finally, we validate our fitted model on four external datasets and show that our estimated coefficients can lead to better prediction than popular competitors.

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Section: Tuning Criterionmentioning

confidence: 99%

“…We found (10) worked better than cross-validated partial likelihood, particularly for applications where many subjects are censored. This is partly because cross-validated linear predictors do not require constructing a risk set separately for each fold: see Dai and Breheny (2019) for more on this approach.…”

Section: Tuning Criterionmentioning

confidence: 99%

Dimension reduction for integrative survival analysis

Molstad¹,

Patra²

2021

Preprint

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show abstract

“…While it is clear that the solution to ( 6) is the solution to (3), there are many redundancies in the n 2 variables θ i,j , which would impose a substantial burden on memory and storage. Instead, we use that θ i,j = −θ j,i and the fact that if δ i = 0 and δ j = 0, the value of θ i,j does not affect (6) to reduce the number of constraints. Thus, letting…”

Section: Formulation and Updating Equationsmentioning

confidence: 99%

“…Tuning parameters are often chosen by cross-validation, which requires the choice of a performance metric. In this section, we propose a new performance metric inspired by that of Dai and Breheny 6 , who studied various approaches for tuning parameter selection when fitting proportional hazards models. Let V 1 , .…”

Section: A New Tuning Parameter Selection Criterionmentioning

confidence: 99%

Scalable algorithms for semiparametric accelerated failure time models in high dimensions

Suder,

Molstad

2021

Preprint

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Semiparametric accelerated failure time (AFT) models are a useful alternative to Cox proportional hazards models, especially when the assumption of constant hazard ratios is untenable. However, rank-based criteria for fitting AFT models are often non-differentiable, which poses a computational challenge in high-dimensional settings. In this article, we propose a new alternating direction method of multipliers algorithm for fitting semiparametric AFT models by minimizing a penalized rank-based loss function. Our algorithm scales well in both the number of subjects and number of predictors; and can easily accommodate a wide range of popular penalties. To improve the selection of tuning parameters, we propose a new criterion which avoids some common problems in cross-validation with censored responses. Through extensive simulation studies, we show that our algorithm and software is much faster than existing methods (which can only be applied to special cases), and we show that estimators which minimize a penalized rank-based criterion often outperform alternative estimators which minimize penalized weighted least squares criteria. Application to nine cancer datasets further demonstrates that rank-based estimators of semiparametric AFT models are competitive with estimators assuming proportional hazards model in high-dimensional settings, whereas weighted least squares estimators are often not. A software package implementing the algorithm, along with a set of auxiliary functions, is available for download at github.com/ajmolstad/penAFT.

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“…Here (h, β) prev and (h, β) new are the previous and new estimated set of covariates, respectively. To validate that the selected covariates do not overfit the patient data, we use leave-one-out cross-validation (LOOCV) on the dataset and predict linear estimators [3] as ηi = h i • β −i and η = (η 1 , η2 , . .…”

Section: Survival Analysismentioning

confidence: 99%

Divide-and-Rule: Self-Supervised Learning for Survival Analysis in Colorectal Cancer

Abbet¹,

Zlobec²,

Bozorgtabar³

et al. 2020

Preprint

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With the long-term rapid increase in incidences of colorectal cancer (CRC), there is an urgent clinical need to improve risk stratification. The conventional pathology report is usually limited to only a few histopathological features. However, most of the tumor microenvironments used to describe patterns of aggressive tumor behavior are ignored. In this work, we aim to learn histopathological patterns within cancerous tissue regions that can be used to improve prognostic stratification for colorectal cancer. To do so, we propose a self-supervised learning method that jointly learns a representation of tissue regions as well as a metric of the clustering to obtain their underlying patterns. These histopathological patterns are then used to represent the interaction between complex tissues and predict clinical outcomes directly. We furthermore show that the proposed approach can benefit from linear predictors to avoid overfitting in patient outcomes predictions. To this end, we introduce a new well-characterized clinicopathological dataset, including a retrospective collective of 374 patients, with their survival time and treatment information. Histomorphological clusters obtained by our method are evaluated by training survival models. The experimental results demonstrate statistically significant patient stratification, and our approach outperformed the state-of-the-art deep clustering methods.

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Cross validation approaches for penalized Cox regression

Cited by 4 publications

References 20 publications

Dimension reduction for integrative survival analysis

Dimension reduction for integrative survival analysis

Scalable algorithms for semiparametric accelerated failure time models in high dimensions

Divide-and-Rule: Self-Supervised Learning for Survival Analysis in Colorectal Cancer

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