Concordance indices with left-truncated and right-censored data

Area of Science:

• Biostatistics
• Survival Analysis
• Epidemiology

Background:

• Time-to-event analysis models event risk using predictors.
• The Concordance Index (C-Index) assesses model discrimination.
• Left-truncation is common in observational studies but poorly studied for C-Index estimation.

Purpose of the Study:

• To investigate the properties of conventional C-Index estimators with left-truncated data.
• To develop a novel, robust C-Index estimator for left-truncated and right-censored data.
• To evaluate the performance of the new estimator compared to conventional methods.

Main Methods:

• Demonstrated that conventional C-Index estimators are influenced by truncation time distributions.
• Developed a new C-Index estimator using inverse probability weighting (IPW).
• Generalized the IPW estimator for left-truncated and right-censored data and applied it to end-stage renal disease patient data.

Main Results:

• Conventional C-Index estimators' limiting values depend on truncation time distributions.
• The proposed IPW C-Index estimators are robust to truncation distributions.
• IPW estimators often show improved performance (bias, MSE, coverage) over conventional methods.

Conclusions:

• The developed IPW C-Index estimators provide a more reliable assessment of risk prediction models in the presence of left-truncation.
• These estimators offer a valuable tool for analyzing observational time-to-event data.
• The study highlights the importance of accounting for truncation in survival analysis.