Advice Please

I am writing from the UK.  My daughter (now 32) was diagnosed privately with hypothyroidism (not auto-immune)11 years ago, having suffered with numerous symptoms for the previous 9 years.  We have recently discovered that her many symptoms overlap dramatically with coeliac disease and we are now concerned that she may indeed be coeliac as the thyroid treatment has proved largely unsuccessful.  She has had 4 tests (again privately) - Iga (anti-endomysium), IgA and IgG (antigliadin, and IgA (antitransglutamine).  These have come back negative.  She is still very unwell, and I have read that there are sometimes false negatives, and that a biopsy may be necessary.  Can you advise please on any research studies into the reliability of serum testing for coeliac disease, and/or do you have your own literature?  Thank you very much.  Jane