Gaussian Copula Models for Nonignorable Missing Data Using Auxiliary Marginal Quantiles

TL;DR

This paper introduces a Bayesian copula-based method for modeling and imputing nonignorable missing data using auxiliary marginal quantiles, enabling accurate inference even with complex dependencies and missingness mechanisms.

Contribution

It develops a novel approach combining Gaussian copulas with auxiliary quantiles for nonignorable missing data, proven to estimate dependencies consistently with an efficient MCMC algorithm.

Findings

Effective multivariate imputation for nonignorable missing data demonstrated in simulations.

Application to North Carolina student data reveals stronger associations between lead exposure and test scores.

Method outperforms traditional approaches like complete case analysis and MAR assumptions.

Abstract

We present an approach for modeling and imputation of nonignorable missing data. Our approach uses Bayesian data integration to combine (1) a Gaussian copula model for all study variables and missingness indicators, which allows arbitrary marginal distributions, nonignorable missingess, and other dependencies, and (2) auxiliary information in the form of marginal quantiles for some study variables. We prove that, remarkably, one only needs a small set of accurately-specified quantiles to estimate the copula correlation consistently. The remaining marginal distribution functions are inferred nonparametrically and jointly with the copula parameters using an efficient MCMC algorithm. We also characterize the (additive) nonignorable missingness mechanism implied by the copula model. Simulations confirm the effectiveness of this approach for multivariate imputation with nonignorable missing data. We apply the model to analyze associations between lead exposure and end-of-grade test scores for 170,000 North Carolina students. Lead exposure has nonignorable missingness: children with higher exposure are more likely to be measured. We elicit marginal quantiles for lead exposure using statistics provided by the Centers for Disease Control and Prevention. Multiple imputation inferences under our model support stronger, more adverse associations between lead exposure and educational outcomes relative to complete case and missing-at-random analyses.