"In Asians, HLA class I (A2, B16, B35, B46, B51, B54, C3) and HLA class II (DR2, DR9, DR53, DQ4) genes showed an association with the disease [31, 100, 101, 102, 103, 104, 105].
In Caucasians, HT is associated with HLA class II genes such as DR3, DR4, DR5, DQA1*0301, DQB1*0201 and DQB1*0301 [106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120] but not with the HLA-DP and HLA class I (HLA-A, HLA-B and HLA-C) genes [113, 114, 121]."
Immunogenetics of Hashimoto's thyroiditis -
J Autoimmune Dis. 2005 Mar 11;2(1):1.
I had my HLADR/DQ gene test and from that list above I have HLADR4 and DQB1*0301. I have Hashimoto's thyroiditis as does my mother and sister. My mother has the exact same 10 genes listed as I do. My sister has not had her genes tested.
I have 5 autoimmune diseases, my sister has 4 of my 5 and my mother 2 of my 5.
Autoimmune diseases are a combination of genetics and a trigger (eg: stress, toxins, vaccines, viruses).
I'm no expert on this, but I think the chance of your child having hypothyroidism depends on what is causing your hypothyroidism. This answer will focus on Hashimoto's because that often runs in families and is probably the most common cause of hypothyroidism in the US and other westernized countries.
Hashimoto's is an autoimmune disease where you develop antibodies that attack the thyroid. Unfortunately, Hashimoto's occurs much more often in women than men (7x more often), and men who have Hashimoto's have a greater risk of having kids with the disease.
Genes alone do not mean a person will have Hashimoto's or hypothyroidism - there are twin studies where twins with identical genes end up with one person developing Hashimoto's and the other twin not, indicating the environment and other factors also play a role into whether someone has Hashimoto's or not.
Hashimoto's does not necessarily mean you will develop hypothyroidism, and some people have found success modifying their diet or lifestyle to keep their thyroid functional and Hashimoto's under control without medication (I discovered my problem too late to try this).
I can't give you a chance or percentage, but please know that hypothyroidism has both genetic components as well as other factors that also play a role in who develops the disease and who doesn't. I don't know anyone else in my family with Hashimoto's, so while it can run in families, sometimes it just pops up on its own as well.
The good news is you are aware there could be a problem and if you have Hashimoto's, that is something you can look out for in your child from an early age.
Have you been tested for Hashimoto's? This would be an antibody test looking at thyroid peroxidase and thyroglobulin. I'm assuming since you are now taking medication for hypothyroidism, you've been tested, but if not I would definitely get the antibody test so you know for sure your whether you have Hashi's or not. Hashimoto's is the most frequent cause in the US, but there are other causes as well which could have a genetic component, including pituitary disorders (the pituitary gland makes TSH - thyroid stimulating hormone, and if it's not making enough, you could be hypo), or a defective thyroid gland.
Good luck and take care.
So far we have focused more on the heredity/pregnancy part of your post. I think you need to be aware of a lot more info about your own status. Hypothyroidism is not just "inadequate thyroid hormone". Instead, correctly defined, hypothyroidism is insufficient T3 effect in tissue throughout the body, due to inadequate supply of, or response to thyroid hormone. So it is insufficient TISSUE T3 EFFECT that causes hypothyroidism. TSH is used as a surrogate for your FT4 level; however, due to a high degree of individuality, TSH has only a weak correlation with FT4, and a negligible correlation with symptoms, which are the best available indicator of thyroid status, supported by tests for Free T4 and Free T3. There is no biochemical test that is adequate as a primary diagnostic for thyroid status.
When you say you are taking Euthyrox to keep your TSH under control, that clearly tells me that your doctor is not treating you adequately. There are many scientific studies showing that just bringing TSH back into range, usually results in too low FT4, and even lower levels of FT3, so the patient continues ot have lingering hypothyroid symptoms. There is another study that concluded that, "Hypothyroid symptom relief was associated with both a T4 dose giving TSH-suppression below the lower reference limit and FT3 elevated further into the upper half of its reference range." I doubt that you have been tested for Free T3. Have you even been tested for Free T4? Also, what symptoms do you currently have?
In consideration of the part of the definition of hypothyroidism, there are numerous variables that affect the response to thyroid hormone. Among the more important ones are cortisol, Reverse t3, Vitamin D, and ferritin. Have you been tested for those, as well as Free T4 and Free T3. When already taking thyroid med, a TSH test is not very useful.
If you want to confirm what I have said, click on my name and then scroll down to my Journal and rad at least the one page Overview of a full paper on Diagnosis and Treatment of Hypothyroidism: A Patient's Perspective, for which there is a link.
kevins2... it's important to understand that there's a whole list of autoimmune conditions and although they tend to run in families, not all family members always get the same autoimmune condition(s), if they even get any of them. For instance, neither of my parents had autoimmune conditions; I have 6 siblings and none of them had/have any autoimmune conditions either, but I have 2 of them - Hashimoto's and Pernicious Anemia. My son has Type I Diabetes and my daughter has Lupus, all of which are also autoimmune conditions.
It's also not a given that our children will develop autoimmune conditions just because we have them. I wouldn't not have children from fear of Hashimoto's.