A power comparison between hierarchical and marginal longitudinal logistic regression models: Application to marijuana usage

Marijuana use is a current problem in the U.S., with high rates among young adults, and a range of associated health and cognitive outcomes. Prior studies have found high co-morbidity between Marijuana addiction and other psychological characteristics such as mood, anxiety, and psychotic disorders. Modeling connections between these variables and usage over time is rare, but provides information about individual-level dynamic relationships. Data for this study were collected using Ecological Momentary Assessment (EMA) methods, where participants respond to text messages three times daily for fourteen consecutive days. EMA will lead to longitudinal data, accompanied by many options for longitudinal data analysis. Modeling the binary variable "usage" suggests a logistic regression model is appropriate. But the longitudinal nature of the data can be accounted for using either hierarchical or marginal models. A hierarchical logistic regression model is one that includes additional random terms, typically associated with clustering by group or individual. A marginal longitudinal logistic regression model will include direct modeling of the response error structure to reflect expected associations due to clustering. Based on pilot data, a power analysis was performed to compare a random-intercept hierarchical logistic regression model, a random-slopes hierarchical logistic regression model, and a GEE marginal logistic regression model. The GEE model was applied using auto-regressive, exchangeable, and independent working correlation structures. A comparison of model performance includes consideration of different conclusions allowable for each model. In general the random-intercept hierarchical logistic regression model shows the strongest properties and ultimately was selected for the analysis.