Diagnostic measures for the Cox regression model with missing covariates

Zhu, Hongtu; Ibrahim, Joseph G.; Chen, Ming Hui

doi:10.1093/biomet/asv047

Cited by 9 publications

(5 citation statements)

References 39 publications

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“…Several researchers have considered handling missing covariates in other contexts than linear or generalized linear models. Zhu et al extended the case‐deletion and residual analysis approaches in their earlier work to a Cox regression modeling scenario. A recent paper by Cotos et al considered model checks for nonparametric regression with a variety of sophisticated methods for single imputation.…”

Section: Introductionmentioning

confidence: 99%

Model validation and influence diagnostics for regression models with missing covariates

Bernhardt

2018

Statistics in Medicine

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Missing covariate values are prevalent in regression applications. While an array of methods have been developed for estimating parameters in regression models with missing covariate data for a variety of response types, minimal focus has been given to validation of the response model and influence diagnostics. Previous research has mainly focused on estimating residuals for observations with missing covariates using expected values, after which specialized techniques are needed to conduct proper inference. We suggest a multiple imputation strategy that allows for the use of standard methods for residual analyses on the imputed data sets or a stacked data set. We demonstrate the suggested multiple imputation method by analyzing the Sleep in Mammals data in the context of a linear regression model and the New York Social Indicators Status data with a logistic regression model.

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Section: Introductionmentioning

confidence: 99%

Model validation and influence diagnostics for regression models with missing covariates

Bernhardt

2018

Statistics in Medicine

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“…In cases where two moderately influential observations have substantial joint influence, or where two individually influential observations have little joint influence, however, their proposed diagnostic cannot identify them. Zhu et al (2015) investigated case-deletion measures, conditional martingale residuals, and score residuals for the Cox model with missing covariate values. They proposed the Q-distance to examine the effects of deleting individual observations on the estimates of finite-dimensional and infinitedimensional parameters.…”

Section: Overall Influencementioning

confidence: 99%

“…A large value of detection probability is an indicator of being influential. The forms and derivation of the Q-distance and the detection probability are complicated; the interested reader should see Zhu et al (2015) for full details. …”

Section: Overall Influencementioning

confidence: 99%

Diagnostics for the Cox model

Xue

Schifano

2017

CSAM

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The most popular regression model for the analysis of time-to-event data is the Cox proportional hazards model. While the model specifies a parametric relationship between the hazard function and the predictor variables, there is no specification regarding the form of the baseline hazard function. A critical assumption of the Cox model, however, is the proportional hazards assumption: when the predictor variables do not vary over time, the hazard ratio comparing any two observations is constant with respect to time. Therefore, to perform credible estimation and inference, one must first assess whether the proportional hazards assumption is reasonable. As with other regression techniques, it is also essential to examine whether appropriate functional forms of the predictor variables have been used, and whether there are any outlying or influential observations. This article reviews diagnostic methods for assessing goodness-of-fit for the Cox proportional hazards model. We illustrate these methods with a case-study using available R functions, and provide complete R code for a simulated example as a supplement.

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“…Pinto et al 18 propose a new outlier detection method in the PH model based on the c‐index. Zhu et al 24 investigate diagnostic measures for identifying influential observations with missing covariates. However, these methods are based on either the leave‐one‐out or leave‐two‐out techniques and thus are not able to detect multiple outliers.…”

Section: Introductionmentioning

confidence: 99%

Penalized weighted proportional hazards model for robust variable selection and outlier detection

Luo

Gao

Halabi

2022

Statistics in Medicine

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Identifying exceptional responders or nonresponders is an area of increased research interest in precision medicine as these patients may have different biological or molecular features and therefore may respond differently to therapies.Our motivation stems from a real example from a clinical trial where we are interested in characterizing exceptional prostate cancer responders. We investigate the outlier detection and robust regression problem in the sparse proportional hazards model for censored survival outcomes. The main idea is to model the irregularity of each observation by assigning an individual weight to the hazard function. By applying a LASSO-type penalty on both the model parameters and the log transformation of the weight vector, our proposed method is able to perform variable selection and outlier detection simultaneously. The optimization problem can be transformed to a typical penalized maximum partial likelihood problem and thus it is easy to implement. We further extend the proposed method to deal with the potential outlier masking problem caused by censored outcomes. The performance of the proposed estimator is demonstrated with extensive simulation studies and real data analyses in low-dimensional and high-dimensional settings.

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Diagnostic measures for the Cox regression model with missing covariates

Cited by 9 publications

References 39 publications

Model validation and influence diagnostics for regression models with missing covariates

Model validation and influence diagnostics for regression models with missing covariates

Diagnostics for the Cox model

Penalized weighted proportional hazards model for robust variable selection and outlier detection

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