Predictive modelling of crossover trial with a binary outcome and four interventions

I have a clinical crossover trial dataset to analyze in order to investigate the predictors of disclosure of HIV prevention product usage by women to their sexual partners. There are four products (interventions) and the outcome is binary (disclosure). There are a number of covariates in the study that were measured as well. Every month there was a product crossover and a question of disclosure was asked at every visit when the women were crossing over to another product. The women made four visits and an additional visit for their preferred product, making it five visits in total. I want to use a regression model to build a prediction model with other covariates as predictors for disclosure in order to classify the women who are more likely to disclose the usage of the product to their sexual partners. Each product should have its own predictive model. It should be noted that the study is a balanced crossover trial and the order of product usage was randomized. As I earlier indicated, the trial has four interventions (products), translating to 24 possible sequences. I am asking for your suggestions and comments on how best I can analyze these data. I am contemplating using hierarchical Lasso. By the way, I am a Stata user.

Best regards!