Analysis of semi-parametric regression models with non-ignorable non-response

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Missing data in statistical models is a common challenge.
• Non-ignorable non-response, where missingness depends on unobserved data, complicates standard inference.
• Accurate estimation of regression parameters (beta zero) is crucial for understanding relationships between variables.

Purpose of the Study:

• To propose new inverse probability of censoring weighted (IPCW) estimators for beta zero.
• To address non-ignorable missing data in regression analysis.
• To develop estimators that are consistent and asymptotically normal (CAN).

Main Methods:

• Development of a new class of IPCW estimators.
• Parametric modeling of non-response probabilities.
• No requirement for full likelihood specification or numerical integration.
• Specialization of general representations for efficient scores and influence functions.

Main Results:

• The proposed IPCW estimators are consistent and asymptotically normal (CAN).
• The optimal estimator achieves the semi-parametric variance bound.
• A general algorithm is provided to determine the existence of CAN estimators for beta zero.
• The methods are applicable to semi-parametric models with non-ignorable non-response.

Conclusions:

• The new IPCW estimators offer a robust solution for estimating regression parameters with non-ignorable missing data.
• These methods provide efficient and asymptotically normal estimates without complex computations.
• The study clarifies conditions for the existence of CAN estimators in challenging missing data scenarios.