Ensuring valid inference for Cox hazard ratios after variable selection.

Area of Science:

• Epidemiology
• Biostatistics
• Causal Inference

Background:

• Selecting variables for confounding adjustment is crucial for estimating exposure effects in observational studies.
• Existing methods lack guaranteed performance across all sample sizes.
• Survival data presents unique challenges, as confounders may differ from censoring predictors.

Purpose of the Study:

• To develop a robust procedure for inferring conditional causal hazard ratios from observational survival data.
• To address the challenge of selecting appropriate confounding variables in the presence of high-dimensional covariates.
• To propose uniformly valid hypothesis tests for exposure effects under sparsity conditions.

Main Methods:

• A novel and simple procedure for confounding adjustment in survival analysis.
• Implementation using penalized Cox regression software.
• Development of uniformly valid tests for the null hypothesis of no exposure effect.

Main Results:

• The proposed methods provide valid causal hazard ratio estimations.
• Simulation results demonstrate the effectiveness of the approach, even with high-dimensional covariates.
• The procedure ensures valid inferences under standard sparsity conditions.

Conclusions:

• The novel procedure effectively addresses confounding in observational survival studies.
• The method is practical, implementable with standard software, and robust to high-dimensional data.
• This work advances causal inference techniques for survival data analysis.