A mixed approach and a distribution-free multiple imputation technique for the estimation of a multivariate probit...

Area of Science:

• Statistics
• Biostatistics
• Psychiatric Epidemiology

Background:

• Multivariate probit models are crucial for analyzing correlated categorical outcomes.
• Missing data in these models pose significant estimation challenges.
• Existing methods may lack efficiency, particularly with high correlation structures.

Purpose of the Study:

• To propose a novel mixed generalized estimating/pseudo-score equations (GEPSE) approach for multivariate probit models with missing data.
• To introduce a generalized measure (pseudo-RT2) for assessing model fit in these settings.
• To evaluate the performance of the GEPSE method through simulation and real-world data analysis.

Main Methods:

• Developed a mixed GEPSE approach combined with distribution-free multiple imputation.
• Proposed a pseudo-RT2 statistic as a generalization of the squared trace correlation.
• Conducted simulation studies with varying correlation structures and missing data mechanisms.
• Applied the method to a psychiatric dataset on depressive in-patients.

Main Results:

• The GEPSE estimator demonstrated higher efficiency than GEE and was comparable to ML estimators, especially with high correlations.
• The pseudo-RT2 closely approximated the RT2 of the underlying linear model.
• Analysis of psychiatric data indicated that depression scores and stressful events predict major depression episodes post-discharge.
• Identified short-term correlation effects on depressive episodes not captured by the regression model.

Conclusions:

• The proposed GEPSE approach offers an efficient and robust method for analyzing multivariate probit models with missing data.
• The pseudo-RT2 serves as a valuable goodness-of-fit measure.
• The findings highlight key factors influencing depression recurrence and suggest the importance of modeling temporal correlation structures.