Abstract
BackgroundLongitudinal assessments of usage are often conducted for multiple substances (e.g., cigarettes, alcohol and marijuana) and research interests are often focused on the inter-substance association. We propose a multivariate longitudinal modeling approach for jointly analyzing the ordinal multivariate substance use data.MethodsWe describe how the binary random slope logistic regression model can be extended to the multi-category ordinal outcomes. We also describe how the proportional odds assumption can be relaxed by allowing differential covariate effects on different cumulative logits for multiple outcomes. Data are analyzed from a P01 study that evaluates the usage levels of cigarettes, alcohol and marijuana repeatedly across 8 measurement waves during 7 consecutive years.Results1263 subjects participated in the study with informed consent, among whom 56.6% are females. Males and females show significant differences in terms of the time trend for substance use. Specifically, males showed steeper trends on cigarette and marijuana use over time compared to females, while less so for alcohol. For all three substances, age effects appear to be different for different cumulative logits, indicating the violation of proportional odds assumption.ConclusionsThe multivariate mixed cumulative logit model offers the most flexibility and allows one to examine the inter-substance association when proportional odds assumption is violated.
Highlights
Longitudinal assessments of usage are often conducted for multiple substances and research interests are often focused on the inter-substance association
The mixed cumulative logit model is often constructed by first extending the binary logistic regression model to accommodate more than two categories, and augmenting the cumulative logit model with subject level random effects
In the simple case of multivariate binary outcomes, i.e., Yikj takes on values of either 0 or 1, mixed logistic regression model can be written in terms of the log odds of Pr(Yikj = 1):
Summary
Longitudinal assessments of usage are often conducted for multiple substances (e.g., cigarettes, alcohol and marijuana) and research interests are often focused on the inter-substance association. We propose a multivariate longitudinal modeling approach for jointly analyzing the ordinal multivariate substance use data. Usage levels of multiple substances (e.g., cigarettes, alcohol and marijuana) are often collected together and repeatedly over time [1]. These longitudinal outcomes may be modeled using univariate approaches, such as univariate mixed effect models or univariate generalized estimating equations [2, 3]. Research questions often arise in investigating the inter-substance association of these multiple substances and a multivariate longitudinal model offers a more desirable.
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