Modeling Binary Data with Time-Dependent Covariates: A Two-Stage Logistic Regression Approach

Music City Center 

A two-stage logistic regression framework tailored for analyzing longitudinal binary data with time-dependent covariates. The model incorporates Bayesian priors and random effects to address feedback loops, correlations from repeated measurements, and the complexities of evolving covariates in hierarchical contexts. By partitioning covariates into time-dependent and time-independent components, the framework effectively handles unequally spaced observations and missing-at-random data. Generalized Method of Moments is used to identify valid instruments, distinguishing between valid and invalid moment conditions. Parameter estimation is conducted via Markov Chain Monte Carlo (MCMC) techniques, ensuring consistent and asymptotically normal estimates. The approach is validated by simulation studies and applied to medical data, highlighting its utility in capturing dynamic predictor-outcome relationships. This model is relevant for fields like medical research, public health, and behavioral sciences, where dynamic processes play a critical role. The proposed framework is capable of managing highly correlated data and reducing biases typically seen in traditional methods.

Longitudinal Binary Data

Two-stage Logistic Regression

Time-Dependent Covariates

Bayesian Priors

Random Effects Models

Hierarchical Models 

Biometrics Section