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BMC Med Res Methodol. 2012; 12: 5.
Published online Jan 24, 2012. doi:  10.1186/1471-2288-12-5
PMCID: PMC3353200
Non-linear mixed models in the analysis of mediated longitudinal data with binary outcomes
Emily A Bloodcorresponding author1,2 and Debbie M Cheng1
1Department of Biostatistics Boston University School of Public Health 801 Massachusetts Avenue 3rd Floor Boston, MA 02118 USA
2Clinical Research Program, Children's Hospital Boston and Harvard Medical School, 300 Longwood Avenue Boston, MA 02115 USA
corresponding authorCorresponding author.
Emily A Blood: emily.blood/at/childrens.harvard.edu; Debbie M Cheng: dmcheng/at/bu.edu
Received July 15, 2011; Accepted January 24, 2012.
Abstract
Background
Structural equation models (SEMs) provide a general framework for analyzing mediated longitudinal data. However when interest is in the total effect (i.e. direct plus indirect) of a predictor on the binary outcome, alternative statistical techniques such as non-linear mixed models (NLMM) may be preferable, particularly if specific causal pathways are not hypothesized or specialized SEM software is not readily available. The purpose of this paper is to evaluate the performance of the NLMM in a setting where the SEM is presumed optimal.
Methods
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.
Results
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.
Conclusions
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.
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