Regression dilution in the proportional hazards model

Area of Science:

• Biostatistics
• Survival Analysis
• Epidemiology

Background:

• Covariate measurement error introduces regression dilution bias in survival data.
• The naive approach using observed covariates in proportional hazards models leads to biased parameter estimates.

Purpose of the Study:

• To investigate regression dilution bias in survival data under the proportional hazards model.
• To derive a bias-corrected estimation method for survival analysis with measurement error.

Main Methods:

• Utilized the proportional hazards model for survival data analysis.
• Derived a theoretical relationship between naive and true parameters under normal error assumptions.
• Developed a bias adjustment factor dependent on censorship and variability ratios.

Main Results:

• The bias in naive estimates is independent of the baseline hazard function for normally distributed errors.
• An adjustment factor (1 + lambda) effectively removes bias with high censorship.
• Bias correction becomes more complex and dependent on the true risk relationship with increasing censorship.

Conclusions:

• Regression dilution bias is a significant issue in survival analysis with covariate measurement error.
• The proposed adjustment method offers a practical solution, particularly in scenarios with substantial censorship.
• Accurate estimation requires accounting for both measurement error and censoring levels.