Using the Reports endpoint, you can replicate the custom metric feature in the Affluent UI by passing an object as a metric as oppose to a metric name.

You will need the following fields:

alias: Specify the name you want to give the custom metric (this is how it will be labelled in the response). Note, it must start with the prefix custom_.
aggregation: Specify how you want to aggregate your metric(s). All the possible values are
[ SUM, MAX, AVG, MIN ]
calculation: An object containing your operator and your operands.

Note, the possible operator values are +, -, *, and /.

Here's an example of how you could request a custom metric that represents the Net number of Actions driven by New Customers:

"metrics": [
    {
      "alias": "custom_new_actions", // prefix `custom_` is required!
      "aggregation": "SUM",
      "calculation": {
        "operator": "+",
        "operands": [
          {
            "metric": "actionCountNet",
            "filters": {
              "operator": "AND",
              "statements": [
                {
                  "category": "repeatCustomer",
                  "match": "equals",
                  "values": [
                    "FALSE"
                  ]
                }
              ]
            }
          }
        ]
      }
    }
  ]