A diagnostic for Cox regression with discrete failure-time models

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Maximum likelihood parameter estimates are crucial for regression diagnostics and robust covariance estimation.
• Existing analytical approximations for delete-one statistics work for many likelihoods but not general conditional or Cox partial likelihoods.
• A previous augmentation approach offered an alternative for these complex likelihoods.

Purpose of the Study:

• To extend the analytic augmentation approach for computing delete-one statistics.
• To explicitly address discrete failure-time models where individuals can appear in multiple risk sets.
• To incorporate time-dependent covariates within this framework.

Main Methods:

• Extending an analytic approximation method based on an augmented design matrix.
• Applying the method to discrete failure-time models with multiple event times per subject.
• Handling time-dependent covariates within the augmented model.

Main Results:

• The extended augmentation approach provides accurate analytical approximations for delete-one statistics in discrete failure-time models.
• This method effectively handles individuals contributing information over multiple time points.
• The approach accommodates time-dependent covariates without additional computational cost.

Conclusions:

• The proposed augmentation method offers an efficient and accurate way to compute delete-one statistics for complex survival models.
• This technique improves statistical diagnostics and robust estimation in discrete failure-time analyses.
• The extension is computationally advantageous, requiring no extra resources while enhancing results.