Nonparametric bounds for the survivor function under general dependent truncation.

Area of Science:

• Biostatistics
• Epidemiology
• Survival Analysis

Background:

• Cohort studies with complex sampling schemes can experience truncation, where individuals are only included if their event time exceeds a certain threshold.
• Ignoring or mischaracterizing truncation can lead to biased estimates of the survival function.

Purpose of the Study:

• To derive completely nonparametric bounds for the survivor function under both truncation and censoring.
• To develop a hazard ratio function that connects the unobservable and observable regions under dependent truncation.
• To provide an approach that estimates the true marginal survivor function over its entire support, not just the observable region.

Main Methods:

• Derivation of nonparametric bounds for the survivor function, extending existing methods to account for truncation.
• Definition of a hazard ratio function to model the relationship between unobservable (event time < truncation time) and observable (event time > truncation time) regions.
• Evaluation of the proposed methods through simulations and clinical applications.

Main Results:

• The derived nonparametric bounds extend prior work by incorporating truncation.
• The hazard ratio function, when bounded with approximate truncation probabilities, yields narrower bounds than purely nonparametric methods.
• The proposed approach accurately targets the true marginal survivor function across its full support.

Conclusions:

• The developed methods provide accurate survival function estimation in the presence of truncation and censoring.
• The approach corrects for bias introduced by ignoring or misrepresenting truncation in cohort studies.
• The methods are applicable to both simulated data and real-world clinical scenarios.