Dataset Information

Quasi-linear Cox proportional hazards model with cross- L₁ penalty.

ABSTRACT:

Background

To accurately predict the response to treatment, we need a stable and effective risk score that can be calculated from patient characteristics. When we evaluate such risks from time-to-event data with right-censoring, Cox's proportional hazards model is the most popular for estimating the linear risk score. However, the intrinsic heterogeneity of patients may prevent us from obtaining a valid score. It is therefore insufficient to consider the regression problem with a single linear predictor.

Methods

we propose the model with a quasi-linear predictor that combines several linear predictors. This provides a natural extension of Cox model that leads to a mixture hazards model. We investigate the property of the maximum likelihood estimator for the proposed model. Moreover, we propose two strategies for getting the interpretable estimates. The first is to restrict the model structure in advance, based on unsupervised learning or prior information, and the second is to obtain as parsimonious an expression as possible in the parameter estimation strategy with cross- L₁ penalty. The performance of the proposed method are evaluated by simulation and application studies.

Results

We showed that the maximum likelihood estimator has consistency and asymptotic normality, and the cross- L₁-regularized estimator has root-n consistency. Simulation studies show these properties empirically, and application studies show that the proposed model improves predictive ability relative to Cox model.

Conclusions

It is essential to capture the intrinsic heterogeneity of patients for getting more stable and effective risk score. The proposed hazard model can capture such heterogeneity and achieve better performance than the ordinary linear Cox proportional hazards model.

SUBMITTER: Omae K

PROVIDER: S-EPMC7336640 | biostudies-literature | 2020 Jul

REPOSITORIES: biostudies-literature

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Publications

Quasi-linear Cox proportional hazards model with cross- L<sub>1</sub> penalty.

Omae Katsuhiro K Eguchi Shinto S

BMC medical research methodology 20200706 1

<h4>Background</h4>To accurately predict the response to treatment, we need a stable and effective risk score that can be calculated from patient characteristics. When we evaluate such risks from time-to-event data with right-censoring, Cox's proportional hazards model is the most popular for estimating the linear risk score. However, the intrinsic heterogeneity of patients may prevent us from obtaining a valid score. It is therefore insufficient to consider the regression problem with a single ...[more]

PMID: 32631280

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Project description:BackgroundAnalysing distributed medical data is challenging because of data sensitivity and various regulations to access and combine data. Some privacy-preserving methods are known for analyzing horizontally-partitioned data, where different organisations have similar data on disjoint sets of people. Technically more challenging is the case of vertically-partitioned data, dealing with data on overlapping sets of people. We use an emerging technology based on cryptographic techniques called secure multi-party computation (MPC), and apply it to perform privacy-preserving survival analysis on vertically-distributed data by means of the Cox proportional hazards (CPH) model. Both MPC and CPH are explained.MethodsWe use a Newton-Raphson solver to securely train the CPH model with MPC, jointly with all data holders, without revealing any sensitive data. In order to securely compute the log-partial likelihood in each iteration, we run into several technical challenges to preserve the efficiency and security of our solution. To tackle these technical challenges, we generalize a cryptographic protocol for securely computing the inverse of the Hessian matrix and develop a new method for securely computing exponentiations. A theoretical complexity estimate is given to get insight into the computational and communication effort that is needed.ResultsOur secure solution is implemented in a setting with three different machines, each presenting a different data holder, which can communicate through the internet. The MPyC platform is used for implementing this privacy-preserving solution to obtain the CPH model. We test the accuracy and computation time of our methods on three standard benchmark survival datasets. We identify future work to make our solution more efficient.ConclusionsOur secure solution is comparable with the standard, non-secure solver in terms of accuracy and convergence speed. The computation time is considerably larger, although the theoretical complexity is still cubic in the number of covariates and quadratic in the number of subjects. We conclude that this is a promising way of performing parametric survival analysis on vertically-distributed medical data, while realising high level of security and privacy.

Project description:BackgroundThe successful identification of breast cancer (BRCA) prognostic biomarkers is essential for the strategic interference of BRCA patients. Recently, various methods have been proposed for exploring a small prognostic gene set that can distinguish the high-risk group from the low-risk group.MethodsRegularized Cox proportional hazards (RCPH) models were proposed to discover prognostic biomarkers of BRCA from gene expression data. Firstly, the maximum connected network with 1142 genes by mapping 956 differentially expressed genes (DEGs) and 677 previously BRCA-related genes into the gene regulatory network (GRN) was constructed. Then, the 72 union genes of the four feature gene sets identified by Lasso-RCPH, Enet-RCPH, [Formula: see text]-RCPH and SCAD-RCPH models were recognized as the robust prognostic biomarkers. These biomarkers were validated by literature checks, BRCA-specific GRN and functional enrichment analysis. Finally, an index of prognostic risk score (PRS) for BRCA was established based on univariate and multivariate Cox regression analysis. Survival analysis was performed to investigate the PRS on 1080 BRCA patients from the internal validation. Particularly, the nomogram was constructed to express the relationship between PRS and other clinical information on the discovery dataset. The PRS was also verified on 1848 BRCA patients of ten external validation datasets or collected cohorts.ResultsThe nomogram highlighted that the importance of PRS in guiding significance for the prognosis of BRCA patients. In addition, the PRS of 301 normal samples and 306 tumor samples from five independent datasets showed that it is significantly higher in tumors than in normal tissues ([Formula: see text]). The protein expression profiles of the three genes, i.e., ADRB1, SAV1 and TSPAN14, involved in the PRS model demonstrated that the latter two genes are more strongly stained in tumor specimens. More importantly, external validation illustrated that the high-risk group has worse survival than the low-risk group ([Formula: see text]) in both internal and external validations.ConclusionsThe proposed pipelines of detecting and validating prognostic biomarker genes for BRCA are effective and efficient. Moreover, the proposed PRS is very promising as an important indicator for judging the prognosis of BRCA patients.

Dataset Information

Quasi-linear Cox proportional hazards model with cross- L₁ penalty.

Background

Methods

Results

Conclusions

Publications

Quasi-linear Cox proportional hazards model with cross- L<sub>1</sub> penalty.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets

Dataset Information

Quasi-linear Cox proportional hazards model with cross- L1 penalty.

Background

Methods

Results

Conclusions

Publications

Quasi-linear Cox proportional hazards model with cross- L<sub>1</sub> penalty.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets

Quasi-linear Cox proportional hazards model with cross- L₁ penalty.