I have a clinic dataset with count data collected on a monthly basis from January 2013 - May 2018. There are 20+ variables. Almost all of them are "number of patients who accepted xyz treatment" in [month, year]. I have 600+ observations for the count variables and for all of them, the variance is much higher than the mean. Some of my variables are zero-inflated. Counts range from about 10/month - 1500/month.
I want to look at the number of clients who accepted xyz treatment by month from 2013 - 2018. I will do this individually for each treatment of interest. I want to test for 1) presence of trend, 2) direction of trend, and 3) magnitude of trend for all of my count variables.
I have access to Stata. What test should I use? I know how to run a poisson regression and negative binomial with count outcomes and categorical variables, but here I'm not using categorical variables so I don't know what to do. As you can probably tell, I'm a relative newbie so simple explanations are appreciated.