Nuisance parameter elimination for proportional likelihood ratio models with nonignorable missingness and random...

Area of Science:

• Statistics
• Biostatistics
• Statistical Modeling

Background:

• Missing data and truncated data present significant challenges in statistical analysis.
• Existing methods may yield biased estimates when data are nonignorable missing or truncated.

Purpose of the Study:

• To demonstrate the model-invariant properties of the proportional likelihood ratio model for nonignorable missing data and randomly double-truncated data.
• To develop an alternative, consistent estimator for target parameters using a pseudo-likelihood approach.
• To introduce a score-type test for regression coefficients.

Main Methods:

• Investigated model-invariant properties of the proportional likelihood ratio model.
• Constructed a pseudo-likelihood estimator to eliminate nuisance parameters.
• Developed a U-statistic based estimating equation.
• Designed a score-type test for hypothesis testing.

Main Results:

• The proportional likelihood ratio model provides consistent estimation of population parameters from biased samples under specific missingness and truncation mechanisms.
• The alternative estimator demonstrates good small-sample efficiency, comparable to nonparametric likelihood estimators.
• The proposed methods perform well in simulations for nonignorable missing data scenarios.

Conclusions:

• The proportional likelihood ratio model offers a robust approach for parameter estimation with complex data structures.
• The developed estimator and test provide valuable tools for statistical inference in the presence of missing and truncated data.