Can I just clarify that you have triple negative IDC? Without seeing the whole letter, particularly the diagnosis which is usually the first line of the letter, and in bold, the paragraph you have supplied is not clear language.
To repeat, it is not for them to dictate to you what procedure you want. Ultimately, your wishes are what is important. If you want a mastectomy, then they should respect this.
Secondly, while your tumour is only 10mm, it might well be bigger once they remove it. Ultrasound initially measured mine as 18mm, and it was actually smidge over 50mm. Your team know there is a very real possibility your tumour could be bigger and in addition and they could end up having to take more tissues. (I recall the first lumpectomy I had at 15, the surgeon with 30 years experience was confident it would be a small scar/easy surgery and take less than an hour. I was in theatre for almost three hours (incidentally, the same time as my mastectomy thirty years later) and the lump was the size of a sausage and due to its positioning, was a far more intricate to remove as he wanted to give the best result and scar possible.
Are you outside London? Not somewhere with a large breast cancer unit? Is your consultant older and male? Sometimes, this demographic are really anti-mastectomies, and not as up to date with all the new advances/surgical techniques. While it is true that most oncoplastic surgeons want to conserve as much of the breast as possible, they should not dismiss what you if you want a mastectomy. What is most shocking to me is the way the letter is written and language used. It is patronising, reductive and not clear. Definitely feed this back to PALS.
If I were you and I wanted a mastectomy, I would keep insisting on this. They cannot operate without your consent, and as it is a grade 3 cancer, they have to do so sooner. Also, what if pathology reports the margins are not clear? They will need to do a second operation a few weeks later. If these margins aren't clear, they will need to do a third. If this is still the case, a mastectomy is them the only option. Obviously, this is worse case scenario, but part of my reasoning for opting for a mastectomy was that it was the least amount of surgery because it removed any option of further surgeries should my margins not be clear.
FYI - it takes around six weeks to recover after a mastectomy/the scar to heal and for the next states of treatment to commence. Recovery for a lumpectomy is about half this time, although the scar can take as long to heal. I think they're trying to scare you into doing what you want. So long as chemotherapy starts within three months of surgery (I think), all is fine.
Personally, I wouldn't be happy with this person being my consultant. I would ask for a referral elsewhere.
Good luck with whatever you decide to do.
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PS. Right breast removal. Remember, only the risk is reduced, not the chance of getting a tumour in your other breast. I have a a rare double BRCA mutation have been told, not even recommended to have my other breast, ovaries and fallopian tubes removed. I have told them no, absolutely not. There is no value for me to have anything removed unless there is an issue because removal does not remove the risk of cancer completely, and besides, despite my terrible genes, I might not even develop cancer in any of these places anyway. Please take heart from this and try to not worry about anything happening with your remaining breast. The one good thing about having cancer is they will monitor you closely for x amount of years afterwards, and should you have a genetic mutation, you will be eligible for a yearly MRI which will find anything suspicious while it is still early and easily treatable.