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

We performed a simulation study to assess the performance of NLMMs relative to SEMs with respect to bias, coverage probability, and power in the analysis of mediated binary longitudinal outcomes. Both logistic and probit models were evaluated. Models were also applied to data from a longitudinal study assessing the impact of alcohol consumption on HIV disease progression.For the logistic model, the NLMM adequately estimated the total effect of a repeated predictor on the repeated binary outcome and were similar to the SEM across a variety of scenarios evaluating sample size, effect size, and distributions of direct vs. indirect effects. For the probit model, the NLMM adequately estimated the total effect of the repeated predictor, however, the probit SEM overestimated effects.Both logistic and probit NLMMs performed well relative to corresponding SEMs with respect to bias, coverage probability and power. In addition, in the probit setting, the NLMM may produce better estimates of the total effect than the probit SEM, which appeared to overestimate effects.SEMs are a general modeling framework often used in the social sciences to analyze complex relationships between variables, such as mediated relationships between variables. A mediator is a variable in the causal pathway between a predictor and the outcome of interest. SEMs are becoming more common in the clinical research setting and can be used to model hypothesized causal pathways between variables of interest. Extensions of SEMs have been developed to allow for more general types of dependent variables, including binary outcomes [1]. Common statistical techniques for non-mediated longitudinal binary data include non-linear mixed models (NLMM) [2] and generalized estimating equations (GEE) [3]. When interest is primarily in the total effect of a predictor on an outcome, even if mediation may be present, these commonly used techniques may be preferred over SEMs as they specify straightforward predictor-outcome va