Marginal modeling in community randomized trials with rare events: Utilization of the negative binomial regression...

Area of Science:

• Biostatistics
• Epidemiology
• Public Health Research

Background:

• Cluster randomized trials (CRTs) are used to evaluate interventions in large populations, such as the HEALing Communities Study focused on reducing opioid overdose fatalities.
• Traditional methods like generalized estimating equations or quasi-likelihood models are used for count outcomes in CRTs, often reporting the intra-cluster correlation coefficient (ICC).
• When communities are large and events are rare, alternative modeling strategies are needed to accurately capture data variability and intervention effects.

Purpose of the Study:

• To demonstrate that negative binomial regression models the same marginal parameters as over-dispersed binomial models for rare count data in large communities.
• To derive formulas connecting the negative binomial overdispersion parameter (k) with the ICC, coefficient of variation (CV), and R coefficient.
• To analyze real-world data from the HEALing Communities Study to compare models and illustrate reporting of overdispersion metrics.

Main Methods:

• Contrasting negative binomial and over-dispersed binomial regression models regarding their setup, parameter estimation, and overdispersion formulation.
• Developing mathematical relationships between the negative binomial overdispersion parameter (k) and other measures of dispersion (ICC, CV, R coefficient).
• Applying these models to pre-intervention data from the HEALing Communities Study to showcase practical implementation and comparative analysis.

Main Results:

• Negative binomial regression models the same marginal parameters as over-dispersed binomial models, though estimates may differ due to distinct overdispersion handling.
• The negative binomial overdispersion parameter (k) is shown to be approximately related to the ICC, CV, and R coefficient, enabling the reporting of all four metrics.
• Analysis of HEALing Communities Study data illustrates the application and comparison of these regression approaches for count data.

Conclusions:

• Negative binomial regression is a valid and practical alternative for analyzing rare count outcomes in large community randomized trials.
• This method facilitates the comprehensive reporting of overdispersion parameters, including ICC, CV, and R coefficient, alongside the negative binomial parameter k.
• The findings support the use of negative binomial regression for robust analysis and transparent reporting in public health intervention studies.