Cluster-specific nonignorably missing, endogenous, and continuous regressors in multilevel model for binary outcome.

Area of Science:

• Biostatistics
• Econometrics
• Epidemiology

Background:

• Endogeneity in multilevel models causes biased estimators.
• Existing instrumental variable methods have limitations, requiring unverifiable conditions or restrictive assumptions.
• Addressing endogeneity is crucial for valid analysis of observational clustered data.

Purpose of the Study:

• To propose a new method for handling endogeneity in logistic mixed-effects models with binary outcomes.
• To develop an estimator that does not require external instrumental variables.
• To accommodate non-linear relationships between endogenous variables and cluster-level random effects.

Main Methods:

• Utilizes the within-cluster variation of the endogenous variable.
• Applies to logistic mixed-effects models with binary outcomes and normally distributed endogenous variables.
• Does not impose linearity on the random effect and handles nonignorable missing data.

Main Results:

• The proposed estimator is consistent and asymptotically normal.
• Demonstrates the ability to analyze multilevel data with correlated effects by exploiting clustered structures.
• Successfully applied to a healthcare study using San Diego inpatient data.

Conclusions:

• The novel method effectively addresses endogeneity in multilevel logistic regression without external instruments.
• The approach offers a robust solution for correlated effects and nonignorable missing data in clustered observational studies.
• Exploiting clustered data structures is key to valid multilevel data analysis.