VBA button to generate numbers based on formula

Why do you want VBa to do this? What's wrong with your formulae? They all seem to work, to me at least.

Try this workbook to see if it does as you want.

The idea is to build your formula into strings and use these to calculate your conditions.
I'm restricted to 2003 at the moment so I have used SUMPRODUCT() instead of COUNTIFS() in this trial workbook.

I've tried to replicate your workbook for testing, it would be useful to have sheets "VGH ED" and "VGH Clinic Intake" with sensitive data disguised/removed.

The code is a first attempt and doubtless could be improved, it isn't linked to a button.

Make some changes in the dummy worksheets then select from the dropdown in Sheet "Analysis VBA" D3 to trigger the code.
If you have say "P 5" selected and make further changes then you'll have to Select it again to update the worksheet.

This is at best a temporary solution.