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Selection of effects in Cox frailty models by regularization methods.

ABSTRACT: In all sorts of regression problems, it has become more and more important to deal with high-dimensional data with lots of potentially influential covariates. A possible solution is to apply estimation methods that aim at the detection of the relevant effect structure by using penalization methods. In this article, the effect structure in the Cox frailty model, which is the most widely used model that accounts for heterogeneity in survival data, is investigated. Since in survival models one has to account for possible variation of the effect strength over time the selection of the relevant features has to distinguish between several cases, covariates can have time-varying effects, time-constant effects, or be irrelevant. A penalization approach is proposed that is able to distinguish between these types of effects to obtain a sparse representation that includes the relevant effects in a proper form. It is shown in simulations that the method works well. The method is applied to model the time until pregnancy, illustrating that the complexity of the influence structure can be strongly reduced by using the proposed penalty approach.

SUBMITTER: Groll A

PROVIDER: S-EPMC6261611 | biostudies-literature | 2017 Sep

REPOSITORIES: biostudies-literature

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Selection of effects in Cox frailty models by regularization methods.

Groll Andreas A Hastie Trevor T Tutz Gerhard G

Biometrics 20170113 3

In all sorts of regression problems, it has become more and more important to deal with high-dimensional data with lots of potentially influential covariates. A possible solution is to apply estimation methods that aim at the detection of the relevant effect structure by using penalization methods. In this article, the effect structure in the Cox frailty model, which is the most widely used model that accounts for heterogeneity in survival data, is investigated. Since in survival models one has ...[more]

PMID: 28085181

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Project description:BackgroundPrevious cancer prognostic prediction models often consider only the most important transcriptomic expressions, and their power is limited. It is unknown whether prediction power can be further improved when additional transcriptomic information is incorporated.MethodsTo integrate transcriptomes, four models are compared based on 32 types of cancer in the Cancer Genome Atlas, including the general Cox model with only clinical covariates, the Cox model with a lasso penalty (coxlasso), the Cox model with an elastic net penalty (coxenet), and the mixed-effects Cox model (coxlmm). Furthermore, we partition the survival variance into the relative contribution of clinical and transcriptomic components within the framework of coxlmm. Finally, the influence of different numbers of genes was evaluated in the context of coxlmm.ResultsCompared with the clinical covariates-only Cox model, the average prediction gain was 2.4% for coxlasso, 4.2% for coxenet, and 7.2% for coxlmm across 16 low-censored cancers; a significant elevation of prediction power was observed for SARC, SKCM, LGG, PAAD, and HNSC. Similar findings were observed for all 32 cancers with the average prediction gain of 2.7, 3.8, and 5.8% for coxlasso, coxenet, and coxlmm. Coxlmm always had comparable or better prediction performance relative to coxlasso and coxenet with an average of 2.8% prediction improvement across the 16 low-censored cancers. In addition, it is shown that the predictive accuracy of coxlmm generally increases with the number of genes included. The survival variance partition analysis demonstrates that the transcriptomic contribution was higher for some cancers (e.g., LGG, CESC, PAAD, SKCM, and SARC) and lower for others (e.g., BRCA, COAD, KIRC, and STAD).ConclusionThis study demonstrates that the integration of transcriptomic information can substantially improve prognostic prediction accuracy, but the prediction performance is cancer-specific and varies across cancer types. It further reveals that gene expression exhibits distinct contributions to survival variation across cancers.

Project description:Non-targeted metabolomics constitutes a part of the systems biology and aims at determining numerous metabolites in complex biological samples. Datasets obtained in the non-targeted metabolomics studies are high-dimensional due to sensitivity of mass spectrometry-based detection methods as well as complexity of biological matrices. Therefore, a proper selection of variables which contribute into group classification is a crucial step, especially in metabolomics studies which are focused on searching for disease biomarker candidates. In the present study, three different statistical approaches were tested using two metabolomics datasets (RH and PH study). The orthogonal projections to latent structures-discriminant analysis (OPLS-DA) without and with multiple testing correction as well as the least absolute shrinkage and selection operator (LASSO) with bootstrapping, were tested and compared. For the RH study, OPLS-DA model built without multiple testing correction selected 46 and 218 variables based on the VIP criteria using Pareto and UV scaling, respectively. For the PH study, 217 and 320 variables were selected based on the VIP criteria using Pareto and UV scaling, respectively. In the RH study, OPLS-DA model built after correcting for multiple testing, selected 4 and 19 variables as in terms of Pareto and UV scaling, respectively. For the PH study, 14 and 18 variables were selected based on the VIP criteria in terms of Pareto and UV scaling, respectively. In the RH and PH study, the LASSO selected 14 and 4 variables with reproducibility between 99.3 and 100%, respectively. In the light of PLS-based models, the larger the search space the higher the probability of developing models that fit the training data well with simultaneous poor predictive performance on the validation set. The LASSO offers potential improvements over standard linear regression due to the presence of the constrain, which promotes sparse solutions. This paper is the first one to date utilizing the LASSO penalized logistic regression in untargeted metabolomics studies.

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Selection of effects in Cox frailty models by regularization methods.

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Selection of effects in Cox frailty models by regularization methods.

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