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Background  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.    Methods  We 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.    Results  1263 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.    Conclusions  The multivariate mixed cumulative logit model offers the most flexibility and allows one to examine the inter-substance association when proportional odds assumption is violated.    Supplementary Information  The online version contains supplementary material available at 10.1186/s12874-021-01444-1.

Analysis of multivariate longitudinal substance use outcomes using multivariate mixed cumulative logit model