Mitigating Selection Bias: A Bayesian Approach to Two-stage Causal Modeling With Instrumental Variables for Nonnormal Missing Data

This study proposes a two-stage causal modeling with instrumental variables to mitigate selection bias, provide correct standard error estimates, and address nonnormal and missing data issues simultaneously. Bayesian methods are used for model estimation. Robust methods with Student's t distributions are used to account for nonnormal data. Ignorable missing data are handled by multiple imputation techniques, while nonignorable missing data are handled by an added-on selection model structure. In addition to categorical treatment data, this study extends the work to continuous treatment variables. Monte Carlo simulation studies are conducted showing that the proposed Bayesian approach can well address common issues in existing methods. We provide a real data example on the early childhood relative age effect study to illustrate the application of the proposed method. The proposed method can be easily implemented using the R software package "ALMOND" (Analysis of Local Average Treatment Effect for missing or/and Nonnormal Data).