Latent transition models with latent class predictors: attention deficit hyperactivity disorder subtypes and high school marijuana use

Summary.  Attention deficit hyperactivity disorder (ADHD) is a neurodevelopmental disorder which is most often diagnosed in childhood with symptoms often persisting into adulthood. Elevated rates of substance use disorders have been evidenced among those with ADHD, but recent research focusing on the relationship between subtypes of ADHD and specific drugs is inconsistent. We propose a latent transition model (LTM) to guide our understanding of how drug use progresses, in particular marijuana use, while accounting for the measurement error that is often found in self-reported substance use data. We extend the LTM to include a latent class predictor to represent empirically derived ADHD subtypes that do not rely on meeting specific diagnostic criteria. We begin by fitting two separate latent class analysis (LCA) models by using second-order estimating equations: a longitudinal LCA model to define stages of marijuana use, and a cross-sectional LCA model to define ADHD subtypes. The LTM model parameters describing the probability of transitioning between the LCA-defined stages of marijuana use and the influence of the LCA-defined ADHD subtypes on these transition rates are then estimated by using a set of first-order estimating equations given the LCA parameter estimates. A robust estimate of the LTM parameter variance that accounts for the variation due to the estimation of the two sets of LCA parameters is proposed. Solving three sets of estimating equations enables us to determine the underlying latent class structures independently of the model for the transition rates and simplifying assumptions about the correlation structure at each stage reduces the computational complexity.