Robust inverse probability weighted estimators for doubly truncated Cox regression with closed-form standard errors.

Area of Science:

• Biostatistics
• Survival Analysis
• Epidemiology

Background:

• Survival data analysis is complicated by double truncation, where only events within a specific interval are sampled.
• Current methods using inverse probability weighting and nonparametric maximum likelihood estimation (NPMLE) have limitations.
• Existing approaches lack robust methods for assessing key assumptions like quasi-independent truncation and positivity.

Purpose of the Study:

• To develop robust Cox regression estimators for doubly truncated data.
• To introduce methods for sensitivity analysis concerning sampling probabilities.
• To provide tools for assessing the quasi-independent truncation assumption.

Main Methods:

• Proposed robust Cox regression coefficient estimators with time-varying inverse probability weights.
• Development of a nonparametric test and graphical diagnostic for quasi-independent truncation.
• Derivation of closed-form standard errors for NPMLE and proposed estimators.
• Sensitivity analysis for potential non-positivity of sampling probabilities.

Main Results:

• The proposed estimators demonstrate robustness and improved performance in simulations.
• New diagnostic tools effectively verify the quasi-independent truncation assumption.
• Closed-form standard errors reduce computational burden and improve identifiability compared to bootstrapping.

Conclusions:

• The novel estimators effectively address limitations in analyzing doubly truncated survival data.
• The developed methods enhance the reliability and interpretability of survival analyses in epidemiological studies.
• The approach provides a more computationally efficient and statistically sound alternative for handling complex survival data.