Build the args parameter dynamically when don't how/which args

Here’s my issue.
I have a form that has three drop downs.
https://fifteenforty.wpengine.com/learn-page-search/

Cancer Type, Age & Diagnosis and Lessons Learned. These are a custom taxonomy for a custom post type called story.

A visitor can pick from 1 or 2 or 3 dropdowns.
I know how to do the query and that’s working fine. I just am trying to figure out how to built the $args dynamically based upon what is chosen when the form is submitted.

If they just choose from the Cancer Type, then $args would be
‘ $args=array(
‘post_type’ => ‘story’,
‘cancer-type’ => $cancer_type,
‘orderby’ => ‘date’,
‘order’ => ‘DESC’,
‘post_status’ => ‘publish’,
‘posts_per_page’ => -1,
); ‘

If they choose both Cancer Type & Age, $args would be

‘ $args=array(
‘post_type’ => ‘story’,
‘cancer-type’ => $cancer_type,
‘age-diagnosis-range’ => $age,
‘orderby’ => ‘date’,
‘order’ => ‘DESC’,
‘post_status’ => ‘publish’,
‘posts_per_page’ => -1,
);
‘

How do I take the POST and write the $args dynamically? Or am I totally missing the boat here.