Analysis of survey on menstrual disorder among teenagers using Gaussian copula model with graphical lasso prior

A high prevalence of menstrual disturbance has been reported among teenage girls, and research shows that there are delays in diagnosis of endometriosis among young girls. Using data from the Menstrual Disorder of Teenagers Survey (administered in 2005 and 2016), we propose a Gaussian copula model with graphical lasso prior to identify cohort differences in menstrual characteristics and to predict endometriosis. The model includes random effects to account for clustering by school, and we use the extended rank likelihood copula model to handle variables of mixed-type. The graphical lasso prior shrinks the elements in the precision matrix of a Gaussian distribution to encourage a sparse graphical structure, where the level of shrinkage is adaptable based on the strength of the conditional associations among questions in the survey. Applying our proposed model to the menstrual disorder data set, we found that menstrual disturbance was more pronouncedly reported over a decade, and we found some empirical differences between those girls with higher risk of developing endometriosis and the general population.