I would suggest importing a dimension Initiative for each epic. Open an epic issue and describe a link field Initiative from an epic perspective.
Here is a detailed step by step guide on how to import links.
After you imported the Initiative dimension you can build a report using a new dimension Initiative on Rows. The measure Issues created will count linked issues to this initiative. Add dimension Issue type to pages and select Epic. This will limit linked issue count to epics.
Here is my report example. I am using issue link dimension Feature (I am using Features instead of Initiatives). Issue type - Epic selection on Pages and measure Issues created counts linked Epics to Feature.
Please note. I noticed some epics might belong to several Initiatives. If any epic could belong to one initiative only, you can go a step further if needed. You can build the hierarchy Initiative > Epic > Parent > Sub-tasks. You will need to remove the property multiple_values = true, though. See more details on how to update the definition for the field and define the hierarchy in our documentation. Check the example for Hierarchy with epics and Features in particular. This step will allow analyzing any issue down the hierarchy for the initiative.
Daina / support@eazybi.com