Hi,
No answer just a few comments
1)LADA is by it's definition autoimmune,
2) There is an offcial diagnosis for people with T1 and no markers for antibodies: T1b, (idiopathic) . The most reported form of this is found in people of African and Indian origin and in this case it has a very specific form (insulin dependence actually comes and goes)
http://www.diabetestypes.org/type-1-dia ... abetes.htm
This may not be the only form of T1b (just one that has been identified)
3) Reading on forums though there seem to be quite a few people who have all the appearances of T1 (ketosis prone, insulin sensitive) but no antibodies. One lady on another forum has called herself type weird!
4) When children are diagnosed with T1 they are rarely tested for antibodies, so we don't know how many childhood onset T1s would test negative for the markers of autoimmunity. One very recent piece of reseach on children found that out of 900 newly diagnosed T1 children tested within 2 weeks of diagnosis 145 (16.1%) were negative for all five anti-islet autoantibodies, and autoantibody negativity significantly increased with age
http://www.ncbi.nlm.nih.gov/pubmed/21138544
5) In 2007 a 'new' autoantibody for T1 was reported: ZnT8a. Interestingly it was detected in up to 80% of patients with new-onset T1D and 26% of patients with T1D otherwise classified as negative on the basis of existing markers.
http://www.ncbi.nlm.nih.gov/pubmed/17942684 (really difficult paper for us non specialists!) I don't think that testing for this is available, or indeed whether subsequent research has backed up the original findings.
6) There is always the possibility of MODY which is not T1, is genetic and will often respond well to oral medications.
Hope all this isn't too confusing, but there aren't any simple answers!
edit; missed out a figure