Mixed model and estimating equation approaches for zero inflation in clustered binary response data with application to a dating violence study

TL;DR

This paper develops likelihood-based and estimating equation methods to analyze zero-inflated clustered binary data, exemplified by adolescent dating violence survey data, addressing excessive zeros and cluster effects.

Contribution

It introduces mixed model and GEE approaches tailored for zero-inflated clustered binary responses, improving analysis accuracy in such complex data structures.

Findings

ML method performs well with correct model specification.

GEE approach offers robustness against misspecification.

Proper zero-inflation modeling significantly impacts results.

Abstract

The NEXT Generation Health study investigates the dating violence of adolescents using a survey questionnaire. Each student is asked to affirm or deny multiple instances of violence in his/her dating relationship. There is, however, evidence suggesting that students not in a relationship responded to the survey, resulting in excessive zeros in the responses. This paper proposes likelihood-based and estimating equation approaches to analyze the zero-inflated clustered binary response data. We adopt a mixed model method to account for the cluster effect, and the model parameters are estimated using a maximum-likelihood (ML) approach that requires a Gaussian-Hermite quadrature (GHQ) approximation for implementation. Since an incorrect assumption on the random effects distribution may bias the results, we construct generalized estimating equations (GEE) that do not require the correct specification of within-cluster correlation. In a series of simulation studies, we examine the performance of ML and GEE methods in terms of their bias, efficiency and robustness. We illustrate the importance of properly accounting for this zero inflation by reanalyzing the NEXT data where this issue has previously been ignored.