You don't get cancer as a result of car crashes. Cancer happens when your cells mutate but don't get cleaned up by your immune system; the mutated cells go out of control, multiply incredibly, and essentially ruin how your body functions.
You could kludge it by saying the doctor treated head trauma sustained in the crash and should have noticed the tumor she already had... but missed it. You might be surprised how many people have brain abnormalities and tumors and don't know.... my ex worked in a research lab that does brain MRI scans, and they had to work up a procedure for notifying the research subjects that they might want to get a medical scan and a doctor to look at it, ASAP. It was not terribly rare (though not common) to notice some abnormality that warranted further investigation. He commented that nobody could believe that one fella was still up and walking around -- half his brain looked cancerous. Yet he had no abnormal indications (they never heard back from him, though they left several voicemails at his contact number).