High‐dimensional robust inference for Cox regression models using desparsified Lasso

Kong, Shengchun; Yu, Zhuqing; Zhang, Xianyang; Cheng, Guang

doi:10.1111/sjos.12543

Cited by 6 publications

(16 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Oracle inequalities for the penalized MPLE have been obtained in Gaïffas and Guilloux (2012); Huang et al (2013); Kong and Nan (2014). A more recent line of research studies hypothesis testing and confidence interval construction for high-dimensional Cox regression using the debiasing approach (Fang et al, 2017;Yu et al, 2018;Kong et al, 2021).…”

Section: Prior Work and Our Contributionmentioning

confidence: 99%

A Modern Theory for High-dimensional Cox Regression Models

Zhang¹,

Zhou²,

Ye³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

The proportional hazards model has been extensively used in many fields such as biomedicine to estimate and perform statistical significance testing on the effects of covariates influencing the survival time of patients. The classical theory of maximum partial-likelihood estimation (MPLE) is used by most software packages to produce inference, e.g., the coxph function in R and the PHREG procedure in SAS. In this paper, we investigate the asymptotic behavior of the MPLE in the regime in which the number of parameters p is of the same order as the number of samples n. The main results are (i) existence of the MPLE undergoes a sharp 'phase transition'; (ii) the classical MPLE theory leads to invalid inference in the high-dimensional regime. We show that the asymptotic behavior of the MPLE is governed by a new asymptotic theory. These findings are further corroborated through numerical studies. The main technical tool in our proofs is the Convex Gaussian Min-max Theorem (CGMT), which has not been previously used in the analysis of partial likelihood. Our results thus extend the scope of CGMT and shed new light on the use of CGMT for examining the existence of MPLE and non-separable objective functions.

show abstract

Section: Prior Work and Our Contributionmentioning

confidence: 99%

A Modern Theory for High-dimensional Cox Regression Models

Zhang¹,

Zhou²,

Ye³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…We propose a de-biased lasso approach for Cox models stratified by transplant centers, which solves a series of quadratic programming problems to estimate the inverse information matrix, and corrects the biases from the lasso estimator for valid statistical inference. Our asymptotic results enable us to draw inference on any linear combinations of model parameters, including the low-dimensional targets in Fang et al (2017) and Kong et al (2021) as special cases and fundamentally deviating from the stepwise regression adopted by . When the number of covariates is relatively large compared to the sample size, our approach yields less biased estimates and more properly covered confidence intervals than MSPLE as well as the methods of Fang et al (2017); Kong et al (2021); Yu et al (2021) adapted to the stratified setting.…”

Section: Introductionmentioning

confidence: 99%

“…Our asymptotic results enable us to draw inference on any linear combinations of model parameters, including the low-dimensional targets in Fang et al (2017) and Kong et al (2021) as special cases and fundamentally deviating from the stepwise regression adopted by . When the number of covariates is relatively large compared to the sample size, our approach yields less biased estimates and more properly covered confidence intervals than MSPLE as well as the methods of Fang et al (2017); Kong et al (2021); Yu et al (2021) adapted to the stratified setting. Therefore, it is well-suited for analyzing the SRTR data, especially among the oldest recipient group that has the smallest sample size.…”

Section: Introductionmentioning

confidence: 99%

“…There is literature on inference for unstratified Cox proportional hazards models under the related asymptotic framework. For example, Fang et al (2017) proposed decorrelated score tests for a low-dimensional component in the regression parameters, and Kong et al (2021), Yu et al (2021) and Xia et al (2022) proposed to correct asymptotic biases of the lasso estimator following the framework of van de Geer et al (2014), Zhang and Zhang (2014) and Javanmard and Montanari (2014) that were originated from high-dimensional linear or generalized linear models. For Cox models, all of these methods, except Xia et al (2022) which considered the "large n, diverging p" scenario, assumed sparsity on the inverse information matrix.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

De-biased lasso for stratified Cox models with application to the national kidney transplant data

Xia¹,

Nan²,

Li³

2022

Preprint

View full text Add to dashboard Cite

The Scientific Registry of Transplant Recipients (SRTR) system has become a rich resource for understanding the complex mechanisms of graft failure after kidney transplant, a crucial step for allocating organs effectively and implementing appropriate care. As transplant centers that treated patients might strongly confound graft failures, Cox models stratified by centers can eliminate their confounding effects. Also, since recipient age is a proven non-modifiable risk factor, a common practice is to fit models separately by recipient age groups. The moderate sample sizes, relative to the number of covariates, in some age groups may lead to biased maximum stratified partial likelihood estimates and unreliable confidence intervals even when samples still outnumber covariates. To draw reliable inference on a comprehensive list of risk factors measured from both donors and recipients in SRTR, we propose a de-biased lasso approach via quadratic programming for fitting stratified Cox models. We establish asymptotic properties and verify via simulations that our method produces consistent estimates and confidence intervals with nominal coverage probabilities. Accounting for nearly 100 confounders in SRTR, the de-biased method detects that the graft failure hazard nonlinearly increases with donor's age among all recipient age groups, and that organs from older donors more adversely impact the younger recipients. Our method also delineates the associations between graft failure and many risk factors such as recipients' primary diagnoses (e.g. polycystic disease, glomerular disease, and diabetes) and donor-recipient mismatches for human leukocyte antigen loci across recipient age groups. These results may inform the refinement of donor-recipient matching criteria for stakeholders.

show abstract

“…Our work presents several advantages. First, compared to high dimensional Cox models (Zhao and Li, 2012;Fang et al, 2017;Kong et al, 2021), the employed HDCQR stems from the accelerated failure time model (Wei, 1992) and offers straightforward interpretations (Hong et al, 2019). Second, utilizing the global conditional quantile regression, it uses various segments of the conditional survival distribution to improve the robustness of variable selection and capture global sparsity.…”

mentioning

confidence: 99%

Inference for High Dimensional Censored Quantile Regression

Fei

Zheng

Hong

et al. 2021

Preprint

View full text Add to dashboard Cite

With the availability of high dimensional genetic biomarkers, it is of interest to identify heterogeneous effects of these predictors on patients' survival, along with proper statistical inference. Censored quantile regression has emerged as a powerful tool for detecting heterogeneous effects of covariates on survival outcomes. To our knowledge, there is little work available to draw inference on the effects of high dimensional predictors for censored quantile regression. This paper proposes a novel procedure to draw inference on all predictors within the framework of global censored quantile regression, which investigates covariate-response associations over an interval of quantile levels, instead of a few discrete values. The proposed estimator combines a sequence of low dimensional model estimates that are based on multi-sample splittings and variable selection. We show that, under some regularity conditions, the estimator is consistent and asymptotically follows a Gaussian process indexed by the quantile level. Simulation studies indicate that our procedure can properly quantify the uncertainty of the estimates in high dimensional settings. We apply our method to analyze the heterogeneous effects of SNPs residing in lung cancer pathways on patients' survival, using the Boston Lung Cancer Survival Cohort, a cancer epidemiology study on the molecular mechanism of lung cancer.

show abstract

High‐dimensional robust inference for Cox regression models using desparsified Lasso

Cited by 6 publications

References 22 publications

A Modern Theory for High-dimensional Cox Regression Models

A Modern Theory for High-dimensional Cox Regression Models

De-biased lasso for stratified Cox models with application to the national kidney transplant data

Inference for High Dimensional Censored Quantile Regression

Contact Info

Product

Resources

About