Sieve Maximum Likelihood Estimation of Partially Linear Transformation Models With Interval-Censored Data

Area of Science:

• Statistics
• Survival Analysis
• Biostatistics

Background:

• Partially linear models are crucial for survival analysis, but methods for interval-censored data are limited.
• Interval-censored data, common in periodical follow-ups, offer less precise information than right-censored data.
• Existing inference methods primarily focus on right-censored data, neglecting interval-censored scenarios.

Purpose of the Study:

• To propose a flexible class of partially linear transformation models for interval-censored outcomes.
• To investigate both parametric and nonparametric covariate effects in the presence of interval censoring.
• To develop robust statistical methods for analyzing complex failure time data.

Main Methods:

• Utilized sieve maximum likelihood estimation with monotone splines and B-splines.
• Developed an expectation-maximization algorithm with three-stage data augmentation.
• Established theoretical consistency and asymptotic distribution of estimators using empirical process techniques.

Main Results:

• The proposed method demonstrates satisfactory performance in finite sample simulations.
• Theoretical analysis confirms the consistency of estimators and asymptotic distribution of parametric components.
• Identified a significant dynamic and nonlinear effect of the TR360 variable on hypobaric decompression sickness risk.

Conclusions:

• The developed partially linear transformation models effectively handle interval-censored failure time data.
• The methodology provides a valuable tool for analyzing complex covariate effects in survival analysis.
• The findings highlight the importance of considering nonlinear covariate effects in studies like hypobaric decompression sickness.