Nonparametric estimation of time-to-event distribution based on recall data in observational studies

Area of Science:

• Biostatistics
• Epidemiology
• Survival Analysis

Background:

• Estimating time-to-event distributions is crucial in observational studies.
• Traditional methods like Turnbull's estimator may be biased with informative recall.
• Accurate estimation is needed for understanding event occurrences over time.

Purpose of the Study:

• To develop a new nonparametric maximum likelihood estimator for time-to-event data with informative censoring due to recall.
• To provide a computationally simple approximation of the proposed estimator.
• To evaluate the performance of the new estimators compared to existing methods.

Main Methods:

• Developed a novel nonparametric maximum likelihood estimator tailored for interval-censored data with informative recall.
• Proposed a computationally efficient approximation of the new estimator.
• Validated estimator consistency under mild conditions and performed Monte Carlo simulations.

Main Results:

• The proposed estimators demonstrated reduced bias and variance compared to the Turnbull estimator.
• The new method exhibited a smaller mean squared error than existing approaches for both current status and recall data.
• Simulations confirmed the statistical properties of the developed estimators.

Conclusions:

• The novel estimator effectively addresses informative censoring in time-to-event analysis from recall data.
• The proposed method offers improved accuracy and efficiency over traditional techniques.
• This approach is valuable for analyzing epidemiological data, such as menarcheal data from adolescent females.