How can we log custom activity data against lead with REST API?

We have created custom activity with Marketo web portal, and able to create leads with REST API. So now how we can log custom activity data using Marketo REST API. Custom activity structure is as-

{

    "id": 100001,

    "name": "TEST_ACTIVITY",

    "apiName": "test_api_c",

    "description": "",

    "primaryAttribute": {

        "name": "event_id",

        "apiName": "event_id",

        "dataType": "string"

    },

    "attributes": [ {

            "name": "email",

            "apiName": "email",

            "dataType": "email"

        },

        {

            "name": "event_data",

            "apiName": "event_data",

            "dataType": "string"

        } ]

}