If you want to pass data to the API, such as the details of a notice you want to create you should pass them as query parameters rather than as JSON in the body. The body of your requests should be empty.

curl -X POST -H "Authorization: Bearer saldjh32ekjhwsdkjh32ekjhsad23kjkjh34" \
	page_name="My Example Status Page" \
	https://api.sorryapp.com/pages

For the most part data-in matches data-out. If you see an attribute listed in a JSON response you can pass that exact same attribute name into a POST/PUT/PATCH request.