Recent publications have shown that Amazon ran a program in India to copy top brands (Reuters), and places Amazon-owned brands at the top of search results, even when other brands are better reviewed with a longer selling history (The Markup).
It's now more crucial than ever to make sure you're not competing directly against Amazon when launching a new product, but also to see if they've recently entered your space.
Might be time for a self audit.
In the subcategories you compete in, look at the revenue share Amazon has overall. If you want to get more specific, look at the brand details for the subcategory (price tag icon). The chart will automatically be sorted by "Percent Share", the brand's marketshare.
Click on the top brand, then click "Sellers" to see whether Amazon is one of the top sellers of these brands. If they're not, then you know you're in the clear (for now).
If Amazon is a top seller of a top brand, be sure to keep an eye on that one, and maybe consider diversifying away from those product types to keep yourself safe from any encroachment.