Adaptive kernel estimation of the baseline function in the Cox model with high-dimensional covariates

Guilloux, Agathe; Lemler, Sarah; Taupin, Marie-Luce

doi:10.1016/j.jmva.2016.03.002

Cited by 7 publications

(4 citation statements)

References 29 publications

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“…We follow the two-step procedure of Guilloux et al (2016): first, we estimate β from the penalized Cox partial likelihood, and then we estimate α 0 (t) from the kernel estimator introduced by Ramlau-Hansen (1983), in which we have plugged the Lasso estimate of β.…”

Section: The Cox Modelmentioning

confidence: 99%

“…For that purpose, we estimate the baseline risk α 0 (t), with the kernel estimator introduced by Ramlau-Hansen (1983). As for the Cox model, we estimate α 0 (t) with the two-steps procedure of Guilloux et al (2016) and this estimator is defined by:…”

Section: Cox-nnetmentioning

confidence: 99%

“…Biganzoli et al (1998) have studied this neural network only in low-dimension. In this paper, our objective is to study and adapt this model to the high-dimensional cases, and compare its performances to two other methods: the two-step procedure with the classical estimation of the parameters of the Cox model with a Lasso penalty to estimate the regression parameter and a kernel estimator of the baseline function (as in Guilloux et al (2016)) and the Cox-nnet neural network (Ching et al, 2018) based on the partial likelihood of the Cox model. Section 2 recalls the different notations used in survival analysis and presents the different models.…”

Section: Introductionmentioning

confidence: 99%

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Neural networks to predict survival from RNA-seq data in oncology

Sautreuil¹,

Lemler²,

Cournède³

2021

Preprint

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Survival analysis consists of studying the elapsed time until an event of interest, such as the death or recovery of a patient in medical studies. This work explores the potential of neural networks in survival analysis from clinical and RNA-seq data. If the neural network approach is not recent in survival analysis, methods were classically considered for low-dimensional input data. But with the emergence of high-throughput sequencing data, the number of covariates of interest has become very large, with new statistical issues to consider. We present and test a few recent neural network approaches for survival analysis adapted to high-dimensional inputs.

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Section: The Cox Modelmentioning

confidence: 99%

Section: Cox-nnetmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Neural networks to predict survival from RNA-seq data in oncology

Sautreuil¹,

Lemler²,

Cournède³

2021

Preprint

Self Cite

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“…Another point of origin for future research might be to consider the case of highdimensional covariates as was done recently in [GLT16a] and [GLT16b].…”

Section: Conclusion and Outlook To Future Researchmentioning

confidence: 99%

Non-parametric Poisson regression from independent and weakly dependent observations by model selection

Kroll

2019

Journal of Statistical Planning and Inference

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We consider the non-parametric Poisson regression problem where the integer valued response Y is the realization of a Poisson random variable with parameter λ(X). The aim is to estimate the functional parameter λ from independent or weakly dependent observations (X1, Y1), . . . , (Xn, Yn) in a random design framework.First we determine upper risk bounds for projection estimators on finite dimensional subspaces under mild conditions. In the case of Sobolev ellipsoids the obtained rates of convergence turn out to be optimal.The main part of the paper is devoted to the construction of adaptive projection estimators of λ via model selection. We proceed in two steps: first, we assume that an upper bound for λ ∞ is known. Under this assumption, we construct an adaptive estimator whose dimension parameter is defined as the minimizer of a penalized contrast criterion. Second, we replace the known upper bound on λ ∞ by an appropriate plug-in estimator of λ ∞. The resulting adaptive estimator is shown to attain the minimax optimal rate up to an additional logarithmic factor both in the independent and the weakly dependent setup. Appropriate concentration inequalities for Poisson point processes turn out to be an important ingredient of the proofs.We illustrate our theoretical findings by a short simulation study and conclude by indicating directions of future research.

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