Simultaneous marginal survival estimators when doubly censored data is present.

Area of Science:

• Biostatistics
• Survival Analysis
• Nonparametric Statistics

Background:

• Doubly censored data, where observations are censored from both below (left) and above (right), presents unique challenges in survival analysis.
• Existing methods often struggle to simultaneously estimate marginal survival functions for the event time, left censoring time, and right censoring time.
• Accurate estimation is crucial for understanding time-to-event data in various fields, including medicine, reliability, and social sciences.

Purpose of the Study:

• To develop novel nonparametric simultaneous marginal estimators for the survival functions of event times (T), left censoring times (L), and right censoring times (R) under a doubly censoring scheme.
• To provide estimators that are computationally efficient, generalize existing methods like the empirical survival estimator and Kaplan-Meier estimator, and possess desirable statistical properties.

Main Methods:

• Proposed new nonparametric simultaneous marginal estimators (Ŝ(T), Ŝ(L), Ŝ(R)) for the survival functions.
• Employed an inverse-probability-of-censoring weighting approach.
• Validated the method using real-world data from a drug user cohort and a simulation study to assess performance across different censoring levels and sample sizes.

Main Results:

• The proposed estimators Ŝ(T), Ŝ(L), and Ŝ(R) are computationally efficient and generalize the empirical survival estimator.
• Ŝ(T) reduces to the Kaplan-Meier estimator when left-censored data is absent and is equivalent to a self-consistent estimator.
• The estimator Ŝ(T) demonstrates uniform strong consistency and asymptotic normality.

Conclusions:

• The developed nonparametric method provides a robust approach for estimating marginal survival functions in the presence of doubly censored data.
• The estimators are versatile, extending to scenarios with only right-censored data and offering reliable performance in practical applications.
• The study successfully illustrated the method's utility with real-world data on time to AIDS diagnosis among drug users.