Actually, I am not Katherine, but I am studying this cancer since I was diagnosed in November. And I am a biochemist so it's easier for me to get the information through my University online library. Last link that I gave gives a comprehensive information about the BC. And it's published this year. I will put this link separately in a thread.
I found the answer to your question. "The rate of progression to muscle invasion or metastasis is 2% to 4% for grade I, 11% to 20% for grade II, and roughly 20% to 50% for grade III tumors. While grade tends to correlate with stage, high-grade Ta lesions are not substantially less dangerous than high-grade T1 lesions." This is the link. www.ncbi.nlm.nih.gov/books/NBK12969/
I just read the original research paper to clear up your question again. Actually, they say that the exposure of mice to BBN (a carcinogen from the cigarette smoke)causes first the CIS tumor (in 3 to 4 months)and then further transformation (more mutations) leads to invasive BC. "evidence clearly demonstrates that basal urothelial stem cells expressing Shh (Sonic hedgehog protein) are the exclusive cell of origin for invasive bladder cancer, expression of Shh is lost by the time invasive carcinomas are formed. So, no mentioning of the non-invasive BC. Will be researching more to answer your question.
I know for sure from reading other articles that the noninvasive can progress to invasive. The risk increases with high reccurency. My impression from this particular research (I maybe mistaken) is that the original mutated stem cell gave rise to precancerous lesions that were hedge hog expressing and the tumor was noninvasive. Further exposure to carcinogens transformed these originally hedge hog expressing cells to non hedge hog expressing cells and without this hedge hog signaling protein the cells became invasive. I actually read the original research paper a few months ago. But i forgot many details. This is a report based on that paper.