Enhanced modeling approaches for count data analysis with focus on substance use outcomes.

Area of Science:

• Behavioral medicine
• Biostatistics
• Epidemiology

Background:

• Accurate statistical modeling is crucial for count data analysis in behavioral medicine.
• Traditional Poisson and Negative Binomial models struggle with excess zeroes and U-shaped distributions.
• Zero-inflated and hurdle models offer alternatives for zero-heavy data.

Purpose of the Study:

• To critically examine the limitations of zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) models for adolescent substance use count data.
• To evaluate a wider range of statistical models, including zero-inflated beta-binomial (ZIBB) and beta-binomial hurdle (BBH) models.
• To identify superior models for analyzing sparse count data with complex distributions, such as U-shaped patterns.

Main Methods:

• Analysis of adolescent smoking behavior (
• Days Smoked in the Past Month") from a longitudinal study (N=1263) across eight waves.
• Model identification using the Kolmogorov-Smirnov (KS) test and validation through confirmation studies.
• Regression analysis guided by the Akaike Information Criterion (AIC) across various models: ZIP, PH, ZINB, NBH, ZINB-r, NBH-r, ZIBB, BBH, ZIBB-n, BBH-n, ZIBB-ab, BBH-ab, ZIBNB, and BNBH.

Main Results:

• The zero-inflated beta-binomial (ZIBB) and beta-binomial hurdle (BBH) models demonstrated superior model fitting and regression analysis capabilities.
• The ZIBB model effectively captured the observed U-shaped distribution in adolescent smoking frequency.
• Findings highlight the limitations of commonly used ZIP and ZINB models for complex count data.

Conclusions:

• The ZIBB and BBH models provide more accurate and reliable analyses for count data in behavioral medicine research, especially with excess zeroes and U-shaped distributions.
• Exploring a broader array of statistical models beyond ZIP and ZINB is essential for advancing research accuracy.
• This study advocates for the adoption of advanced models like ZIBB to enhance the interpretation of adolescent substance use and other behavioral data.