What is Hazel's cancer miracle story in The Fault in Our Stars?

We learn the details of Hazel's "cancer miracle story" in Chapter 2, when she relates it to Augustus, her new friend and love interest.

When she was thirteen, Hazel was diagnosed with "Stage IV thyroid cancer." ("Stage IV" means the cancer has already advanced significantly within the body, so it's a very serious diagnosis.) Her doctors use surgery, radiation, and chemotherapy to try to keep her cancer in check, but Hazel comes down with a...

We learn the details of Hazel's "cancer miracle story" in Chapter 2, when she relates it to Augustus, her new friend and love interest.

When she was thirteen, Hazel was diagnosed with "Stage IV thyroid cancer." ("Stage IV" means the cancer has already advanced significantly within the body, so it's a very serious diagnosis.) Her doctors use surgery, radiation, and chemotherapy to try to keep her cancer in check, but Hazel comes down with a serious case of pneumonia and feels like she's drowning from the fluid in her lungs. She is very close to death, even holding her parents' hands and saying her goodbyes to them, when, incredibly, her doctor is able to remove the fluid from her lungs and she survives. At that point, she's given an experimental drug, which are notorious for not working very well, but it works for her and keeps her tumors at bay.

For the year and a half before Hazel has this conversation with Augustus, she has been taking that "miracle" drug, receiving help for her lungs from an oxygen machine, and surviving. She considers her story to be somewhat miraculous, although Hazel's sarcasm may be at play here; she may be indicating that her story is actually pretty common. And she also moderates the heartwarming aspect of the story by thinking about how her time is still limited, that the drug could stop working at any point.

Because this question asks about a main character's backstory, we know to look for the answer near the beginning of the book. But we won't always find a character's backstory in the prologue or the first chapter of a novel. Why? It's more interesting for an author to begin the story with action, with something exciting happening, rather than with all the potentially tedious details of what the character has experienced up until the real beginning of the story. So, one way that authors can include background information in an interesting way is by allowing one character to reveal that information to another character whom she's recently met. For that reason, it's a good idea to look for important conversations between characters who have just met if you need to find their backstories.