Non-linear mixed models in the analysis of mediated longitudinal data with binary outcomes

Area of Science:

• Biostatistics
• Longitudinal Data Analysis
• Statistical Modeling

Background:

• Structural Equation Models (SEMs) are versatile for longitudinal data with mediation.
• Non-linear Mixed Models (NLMMs) offer an alternative for total effect estimation, particularly when causal pathways are unclear or specialized SEM software is unavailable.
• This study evaluates NLMM performance against SEMs in optimal SEM settings.

Purpose of the Study:

• To compare the performance of NLMMs versus SEMs for analyzing mediated binary longitudinal outcomes.
• To assess bias, coverage probability, and power of NLMMs relative to SEMs.
• To evaluate NLMMs in both logistic and probit model contexts.

Main Methods:

• A simulation study was conducted to compare NLMMs and SEMs.
• Performance metrics included bias, coverage probability, and statistical power.
• Analyses were performed on simulated data and a real-world longitudinal study on alcohol consumption and HIV progression.

Main Results:

• For logistic models, NLMMs provided adequate total effect estimates, comparable to SEMs across various scenarios.
• For probit models, NLMMs also adequately estimated total effects.
• Probit SEMs tended to overestimate the effects, while NLMMs offered more accurate estimations.

Conclusions:

• Both logistic and probit NLMMs demonstrated strong performance regarding bias, coverage, and power compared to SEMs.
• NLMMs may yield superior total effect estimates in probit models compared to SEMs, which can overestimate effects.
• NLMMs present a reliable statistical approach for mediated binary longitudinal data analysis.