Variable selection for survival data with a class of adaptive elastic net techniques

Khan, Hasinur Rahaman; Shaw, J. Ewart H.

doi:10.1007/s11222-015-9555-8

Cited by 46 publications

(36 citation statements)

References 42 publications

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“…The procedure is referred to as

S I S + m e t h o d s

for example for the case of Enet, I call it

S I S + E n e t

. I implement six methods: two adaptive elastic net approaches designed for censored data known as AEnet and WEnet as proposed in Khan and Shaw (), simple elastic net (Enet) approach based on regularized SWLS method as defined in Equation (which is optimized with the cyclical coordinate descent algorithm as proposed by Friedman, Hastie and Tibshirani ()), another adaptive type elastic net for AFT models known as Enet‐AFT as proposed in Engler and Li (). Two other greedy variable selection approaches called tilted correlation screening (TCS), and PC‐simple are implemented with the weighted data under regularized SWLS method as discussed in Section .…”

Section: Discussionmentioning

confidence: 99%

“…Khan and Shaw () proposed another method that is weighted elastic net (WEnet) designed for censored data. This was proposed as an extension of the adaptive elastic net where for suitable weight w the ridge penalty term is expressed as

0true \sum_{j = 1}^{p} {false(w_{j} β_{j} false)}^{2}

, instead of

0true \sum_{j = 1}^{p} β_{j}^{2}

.…”

Section: Methodsmentioning

confidence: 99%

“…One of the ways to handle censored data is to employ Stute's weighted least squares (SWLS) method, where weights are introduced to account for censoring in the least square frameworks. A number of studies, where weighted least squares technique is used for AFT models, have been done recently by the researchers Huang, Ma, and Xie (), Khan and Shaw (, ), Khan (), etc. The SWLS method gives estimate

\hat{θ} = false(\overset{β_{0}}{true}, \overset{β}{true} false)

bold-italicθ = (β_{0}, β)

for the AFT model as

\hat{θ} = arg \underset{θ}{falseprefixmin} [0true \frac{1}{2} \sum_{i = 1}^{n} w_{i} {(() Y_{(i)} - β_{0} - X_{(i)}^{T} β)}^{2}] .

The quantity

w_{i}

's are the Kaplan–Meier weights that are defined by

0true w_{1} = \frac{δ_{(1)}}{n}, w_{i} = \frac{δ_{(i)}}{n - i + 1} \prod_{j = 1}^{i - 1} {(\frac{n - j}{n - j + 1})}^{δ_{(j)}},

where

i = 2, \dots, n

under the dataset

(T_{(i)}, δ_{(i)}, X_{(i)})

.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the performance of adaptive preprocessing technique in analyzing high‐dimensional censored data

Khan

2018

Biometrical J

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Preprocessing for high-dimensional censored datasets, such as the microarray data, is generally considered as an important technique to gain further stability by reducing potential noise from the data. When variable selection including inference is carried out with high-dimensional censored data the objective is to obtain a smaller subset of variables and then perform the inferential analysis using model estimates based on the selected subset of variables. This two stage inferential analysis is prone to circularity bias because of the noise that might still remain in the dataset. In this work, I propose an adaptive preprocessing technique that uses sure independence screening (SIS) idea to accomplish variable selection and reduces the circularity bias by some popularly known refined high-dimensional methods such as the elastic net, adaptive elastic net, weighted elastic net, elastic net-AFT, and two greedy variable selection methods known as TCS, PC-simple all implemented with the accelerated lifetime models. The proposed technique addresses several features including the issue of collinearity between important and some unimportant covariates, which is often the case in high-dimensional setting under variable selection framework, and different level of censoring. Simulation studies along with an empirical analysis with a real microarray data, mantle cell lymphoma, is carried out to demonstrate the performance of the adaptive pre-processing technique.

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“…The procedure is referred to as

S I S + m e t h o d s

for example for the case of Enet, I call it

S I S + E n e t

Section: Discussionmentioning

confidence: 99%

0true \sum_{j = 1}^{p} {false(w_{j} β_{j} false)}^{2}

, instead of

0true \sum_{j = 1}^{p} β_{j}^{2}

.…”

Section: Methodsmentioning

confidence: 99%

\hat{θ} = false(\overset{β_{0}}{true}, \overset{β}{true} false)

bold-italicθ = (β_{0}, β)

for the AFT model as

\hat{θ} = arg \underset{θ}{falseprefixmin} [0true \frac{1}{2} \sum_{i = 1}^{n} w_{i} {(() Y_{(i)} - β_{0} - X_{(i)}^{T} β)}^{2}] .

The quantity

w_{i}

's are the Kaplan–Meier weights that are defined by

0true w_{1} = \frac{δ_{(1)}}{n}, w_{i} = \frac{δ_{(i)}}{n - i + 1} \prod_{j = 1}^{i - 1} {(\frac{n - j}{n - j + 1})}^{δ_{(j)}},

where

i = 2, \dots, n

under the dataset

(T_{(i)}, δ_{(i)}, X_{(i)})

.…”

Section: Introductionmentioning

confidence: 99%

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On the performance of adaptive preprocessing technique in analyzing high‐dimensional censored data

Khan

2018

Biometrical J

Self Cite

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“…Finally, we also considered another high dimensional setting for the AFT model that is similar to that studied in Khan & Shaw (2016). Specifically, we set (n, p) = (100, 120) with the first 20 coefficients for β's are specified to be 4 whereas the remaining coefficients of β are chosen to be zero.…”

Section: Inmentioning

confidence: 99%

Pseudo value method for ultra high-dimensional semiparametric models with life-time data

Sit¹,

Xing²,

Xu³

et al. 2019

STAT SINICA

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We develop a new procedure called "pseudo value method" (PVM) that can handle ultra high-dimensional variable selection problems for semiparametric survival models. While there has only been the sure independence screening (SIS)-type strategy for ultra high-dimensional life-time data so far in literature, the new unified methodology covers a much broader class of survival models including general transformation models and the accelerated failure time (AFT) model. The proposed method is versatile because the conversion involved easily casts the current problem of interest into a regular linear regression framework.Through this translation, all the existing and powerful techniques developed for the linear regression problems can be leveraged to tackle the new challenge at almost no extra cost.Numerical performance of PVM has also demonstrated promising results: in addition to outperforming the (iterative) SIS for the Cox model, the new method can also accurately select the effective variables for probit, proportional odds and the AFT models, amongst which, to the best of our knowledge, has been studied under the ultra high-dimensional context on a case-by-case basis. Our unified Statistica Sinica: Newly accepted Paper (accepted version subject to English editing) method was also applied to analyse Diffuse large-B-cell lymphoma data, which discovered genes that may be overlooked yet be influential. This finding itself can potentially be of scientific importance.

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“…() derived some regularized versions including lasso and Huang and Ma () discussed bridge regression, and (Wang and Song, ) developed adaptive lasso for AFT models. Furthermore, Khan and Shaw () developed a class of adaptive elastic net techniques and synthesized techniques for variable selection in AFT models. However, they did not consider Bayesian settings in their research.…”

Section: Introductionmentioning

confidence: 97%

Bayesian data integration and variable selection for pan‐cancer survival prediction using protein expression data

et al. 2019

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Accurate prognostic prediction using molecular information is a challenging area of research, which is essential to develop precision medicine. In this paper, we develop translational models to identify major actionable proteins that are associated with clinical outcomes, like the survival time of patients. There are considerable statistical and computational challenges due to the large dimension of the problems. Furthermore, data are available for different tumor types; hence data integration for various tumors is desirable. Having censored survival outcomes escalates one more level of complexity in the inferential procedure. We develop Bayesian hierarchical survival models, which accommodate all the challenges mentioned here. We use the hierarchical Bayesian accelerated failure time model for survival regression. Furthermore, we assume sparse horseshoe prior distribution for the regression coefficients to identify the major proteomic drivers. We borrow strength across tumor groups by introducing a correlation structure among the prior distributions. The proposed methods have been used to analyze data from the recently curated “The Cancer Proteome Atlas” (TCPA), which contains reverse‐phase protein arrays–based high‐quality protein expression data as well as detailed clinical annotation, including survival times. Our simulation and the TCPA data analysis illustrate the efficacy of the proposed integrative model, which links different tumors with the correlated prior structures.

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Variable selection for survival data with a class of adaptive elastic net techniques

Cited by 46 publications

References 42 publications

On the performance of adaptive preprocessing technique in analyzing high‐dimensional censored data

On the performance of adaptive preprocessing technique in analyzing high‐dimensional censored data

Pseudo value method for ultra high-dimensional semiparametric models with life-time data

Bayesian data integration and variable selection for pan‐cancer survival prediction using protein expression data

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