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Updated: May 8, 2026

An R-Based Landscape Validation of a Competing Risk Model

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Pseudo-partial likelihood estimators for the Cox regression model with missing covariates.

Xiaodong Luo¹, Wei Yann Tsai, Qiang Xu

¹Department of Psychiatry , Mount Sinai School of Medicine , New York, New York 10029 , U.S.A. Xiaodong.Luo@mssm.edu.

|August 16, 2013

Summary

This study introduces pseudo-partial likelihood estimators for Cox regression models with missing covariate data. These new estimators offer improved performance and efficiency, especially when data observation probabilities are low.

Keywords:

Augmented estimator Biased sampling data Embedding missing data Left-truncation Martingale structure Right censoring U-statistic

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Establishing a Competing Risk Regression Nomogram Model for Survival Data

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Published on: October 23, 2020

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Last Updated: May 8, 2026

An R-Based Landscape Validation of a Competing Risk Model

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Published on: October 23, 2020

Area of Science:

Biostatistics
Survival Analysis
Statistical Modeling

Background:

Missing covariate data presents a significant challenge in survival analysis, particularly within the Cox regression framework.
Existing methods like inverse-probability weighting can be inefficient or unstable when observation probabilities are low.

Purpose of the Study:

To develop a novel class of weighted estimating functions for the Cox regression model to address missing covariate data.
To introduce and evaluate the performance of pseudo-partial likelihood estimators in the presence of missing covariates.

Main Methods:

Embedding missing covariate data into a left-truncated and right-censored survival model.
Formulating new weighted estimating functions based on the Cox regression model.
Developing pseudo-partial likelihood estimators and assessing their theoretical properties (consistency, asymptotic normality).

Main Results:

The proposed pseudo-partial likelihood estimators are demonstrated to be consistent and asymptotically normal.
Simulation studies show superior performance of the new estimators compared to inverse-probability weighted estimators, particularly under low observation probabilities.
The new estimators enhance the efficiency of estimating missing covariate effects.

Conclusions:

The pseudo-partial likelihood approach provides a robust and efficient method for handling missing covariates in Cox regression models.
This methodology offers significant advantages over traditional inverse-probability weighting, especially in challenging data scenarios.
The findings are validated through simulation and a practical data example.