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

Gi-Soo Kim1, Youngjo Lee1, Hongsoo Kim2,3,4

  • 1Department of Statistics, Seoul National University, Seoul, South Korea.

Statistical Methods in Medical Research
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Summary

This study introduces a novel method to address endogeneity in multilevel regression models, improving coefficient estimation accuracy for clustered data. The approach effectively handles correlated effects and missing data without external instruments.

Keywords:
Cluster-specific nonignorable missingnesscorrelated effectsendogeneityinstrumental variable

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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.