Nonparametric analysis of doubly truncated and interval-censored data

Area of Science:

• Epidemiology
• Biostatistics
• Survival Analysis

Background:

• Epidemiological studies often encounter interval sampling, resulting in doubly truncated data.
• Failure events in DTIC data are recorded within intervals, complicating standard survival analysis.
• Existing methods for DTIC data may be inadequate under realistic sampling schemes.

Purpose of the Study:

• To evaluate the limitations of existing methods for doubly truncated and interval censored (DTIC) data.
• To propose a novel statistical approach for analyzing DTIC data under a realistic sampling scheme.
• To develop a nonparametric estimator for the joint distribution function of successive failure times.

Main Methods:

• Identified limitations of existing methods under a common diagnosis-based sampling scheme (Scheme 2).
• Defined a target population and sampling scheme (Scheme 3) to enable appropriate truncation variable definition.
• Utilized the expectation-maximization algorithm for nonparametric maximum likelihood estimation (NPMLE) of the cumulative distribution function.
• Employed inverse-probability-weighting for estimating the joint distribution function of successive durations.

Main Results:

• Demonstrated that existing methods can yield biased NPMLE for DTIC data under Scheme 2.
• Proposed a robust method for estimating cumulative and joint distribution functions with DTIC data.
• Simulation studies confirmed the proposed method's effectiveness with moderate sample sizes.

Conclusions:

• The developed method provides a more accurate approach for analyzing DTIC data compared to existing techniques.
• The findings are crucial for improving survival analysis in epidemiological research with interval-censored failure times.
• The proposed estimator offers a valuable tool for understanding disease progression and treatment efficacy.