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Medical research is often designed to investigate changes in a collection of response variables that are measured repeatedly on the same subjects. The multivariate generalized linear mixed model (MGLMM) can be used to evaluate random coefficient associations (e.g. simple correlations, partial regression coefficients) among outcomes that may be non-normal and differently distributed by specifying a multivariate normal distribution for their random effects and then evaluating the latent relationship between them. Empirical Bayes predictors are readily available for each subject from any mixed model and are observable and hence, plotable. Here, we evaluate whether second-stage association analyses of empirical Bayes predictors from a MGLMM, provide a good approximation and visual representation of these latent association analyses using medical examples and simulations. Additionally, we compare these results with association analyses of empirical Bayes predictors generated from separate mixed models for each outcome, a procedure that could circumvent computational problems that arise when the dimension of the joint covariance matrix of random effects is large and prohibits estimation of latent associations. As has been shown in other analytic contexts, the p-values for all second-stage coefficients that were determined by naively assuming normality of empirical Bayes predictors provide a good approximation to p-values determined via permutation analysis. Analyzing outcomes that are interrelated with separate models in the first stage and then associating the resulting empirical Bayes predictors in a second stage results in different mean and covariance parameter estimates from the maximum likelihood estimates generated by a MGLMM. The potential for erroneous inference from using results from these separate models increases as the magnitude of the association among the outcomes increases. Thus if computable, scatterplots of the conditionally independent empirical Bayes predictors from a MGLMM are always preferable to scatterplots of empirical Bayes predictors generated by separate models, unless the true association between outcomes is zero. [ABSTRACT FROM AUTHOR]

Mediation analysis evaluates the significance of an intermediate variable on the causal pathway between an exposure and an outcome. One commonly utilized test for mediation involves evaluation of counterfactual effects, estimated from separate regression models, corresponding to a composite null hypothesis. However, the “compositeness” of this null hypothesis is not commonly acknowledged and accounted for in mediation analyses. We describe a generalized multivariate approach in which these separate regression models are fit simultaneously in a single parsimonious model. This multivariate modeling approach can reproduce standard mediation analysis and has notable advantages over separate regression models, including the ability to combine distributions in the exponential family with any link functions and perform likelihood-based tests of some relevant hypotheses using existing software. We propose the use of a novel visual representation of confidence intervals of the two estimates for the indirect path with the use of a confidence ellipse. The calculation of the confidence ellipse is facilitated by the multivariate approach, can test the components of the composite null hypothesis under a single experiment-wise type I error rate, and does not require estimation of the standard error of the product of coefficients from two separate regressions. This method is illustrated using three examples. The first compares results between the multivariate method and separate regression models. The second example illustrates the proposed methods in the presence of an exposure-mediator interaction, missing data and confounding, and the third example utilizes these proposed methods for an outcome and mediator with negative binomial distributions. [ABSTRACT FROM AUTHOR]

Different types of outcomes (e.g. binary, count, continuous) can be simultaneously modeled with multivariate generalized linear mixed models by assuming: (1) same or different link functions, (2) same or different conditional distributions, and (3) conditional independence given random subject effects. Others have used this approach for determining simple associations between subject-specific parameters (e.g. correlations between slopes). We demonstrate how more complex associations (e.g. partial regression coefficients between slopes adjusting for intercepts, time lags of maximum correlation) can be estimated. Reparameterizing the model to directly estimate coefficients allows us to compare standard errors based on the inverse of the Hessian matrix with more usual standard errors approximated by the delta method; a mathematical proof demonstrates their equivalence when the gradient vector approaches zero. Reparameterization also allows us to evaluate significance of coefficients with likelihood ratio tests and to compare this approach with more usual Wald-type t-tests and Fisher's z transformations. Simulations indicate that the delta method and inverse Hessian standard errors are nearly equivalent and consistently overestimate the true standard error. Only the likelihood ratio test based on the reparameterized model has an acceptable type I error rate and is therefore recommended for testing associations between stochastic parameters. Online supplementary materials include our medical data example, annotated code, and simulation details. [ABSTRACT FROM AUTHOR]

The prevalence and persistence of adolescent substance use and abuse is a national health issue, and substance use among adolescents is frequently comorbid with other psychiatric disorders. Most studies in this area utilize samples of middle or high school students or from inpatient settings. Less is known about substance use and psychiatric comorbidity among delinquent adolescents. The present study examined data from two cohorts of juvenile offenders collected over a 2-year period (n = 245, n = 299). Participants reported frequency of cigarette, alcohol, marijuana, and other substance use. Participants' parents completed a measure of behavior problems. Path analyses suggested that parental reports of externalizing problems were significantly related to self-reported substance use while parental reports of internalizing problems were not. Results also suggested that smoking and alcohol use act as mediators between externalizing problems and marijuana and other drug use. Although there were some mean differences by gender, the pattern of relationships amongst the variables did not differ by gender. Implications of the findings and future directions are discussed. [ABSTRACT FROM AUTHOR]

Examines attention deficit hyperactivity disorder (ADHD) symptoms in adolescents with conduct disorder and clinically significant substance involvement to determine whether ADHD contributed significantly to their substance involvement, aggression, and delinquency. Risk for conduct disorder; Normal rates of anxiety and depressive disorders.

The author reflects regarding the article "Simulant medication and substance use outcomes; a meta-analysis," by K. L. Humphreys and colleagues. Among the key topics that the authors have discussed include the link between risks of substance use disorder (SUD) and stimulant medication, the implication of stimulant medication treatment in children with attention deficit hyperactivity disorder (ADHD), and the impact of ADHD treatment in increasing the risks of SUD.