Nonparametric and semiparametric estimation with sequentially truncated survival data

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Observational studies often face truncation, where event times are only observed within a specific range.
• Simple truncation estimators are inadequate for complex scenarios like sequential truncation, where event time order matters.
• Accurate event time distribution estimation is crucial for understanding disease progression and treatment effects.

Purpose of the Study:

• To develop novel nonparametric and semiparametric estimators for event time distributions under sequential truncation.
• To address the inconsistency of existing estimators in complex truncation settings.
• To provide a practical implementation for these advanced statistical methods.

Main Methods:

• Proposed nonparametric and semiparametric maximum likelihood estimators.
• Investigated two distinct sequential truncation models.
• Demonstrated the equivalence between inverse probability weighted and product limit estimators under a specific model.
• Studied large sample properties and derived asymptotic variance estimators.

Main Results:

• Developed consistent estimators for event time distributions under sequential truncation.
• Established theoretical properties, including asymptotic variances, for the proposed methods.
• Validated the performance of the new estimators through simulation studies.
• Successfully applied the methods to a real-world Alzheimer's disease cohort study.

Conclusions:

• The proposed maximum likelihood estimators provide reliable methods for analyzing event time data with sequential truncation.
• The developed R package, seqTrun, facilitates the application of these advanced statistical techniques.
• This work enhances the ability to analyze complex observational data, with implications for disease research and public health.