Robust estimation of models for longitudinal data with dropouts and outliers

Area of Science:

• Biostatistics
• Longitudinal Data Analysis
• Rheumatology

Background:

• Longitudinal studies, particularly in rheumatoid arthritis research, frequently encounter missing data and outliers.
• Classical generalized estimating equation (GEE) approaches are invalidated by missing data and outliers, compromising analysis integrity.
• Accurate analysis of Health Assessment Questionnaire (HAQ) scores over time requires methods robust to these data imperfections.

Purpose of the Study:

• To develop a robust estimating equation approach for analyzing longitudinal data with missing responses and outliers.
• To extend a doubly robust method to handle missing at random responses.
• To incorporate an outlier robust method to correct bias induced by outliers in longitudinal data.

Main Methods:

• Developed a novel robust estimating equation approach combining doubly robust methods for missing data and outlier robust methods.
• Extended doubly robust methodology to accommodate missing at random responses.
• Utilized an outlier robust method involving covariate matrix centralization to mitigate outlier-induced bias.

Main Results:

• The proposed estimator demonstrated robustness against both model misspecification for missing data and the presence of outliers.
• Consistency and asymptotic normality of the proposed estimator were established under standard regularity conditions.
• Simulation studies and real data analysis confirmed the robustness properties of the developed method.

Conclusions:

• The proposed robust estimating equation method provides a reliable tool for analyzing longitudinal data with missing values and outliers.
• This approach enhances the validity of analyses in rheumatoid arthritis cohort studies using the Health Assessment Questionnaire.
• The method offers a significant improvement over classical GEE when dealing with imperfect longitudinal data.