WASHINGTON, July 28 (Reuters) - Women with low or high levels of a hormone that affects thyroid gland function and thyroid hormone levels may have a higher risk of Alzheimer's disease, researchers reported on Monday.

While it is not clear whether Alzheimer's affects thyroid function or the other way around, the findings dovetail with long-standing knowledge that having an underactive or overactive thyroid can affect memory.

Dr. Zaldy Tan of Hebrew SeniorLife, Beth Israel Deaconess Medical Center and Harvard Medical School in Boston and colleagues looked at measured levels of a thyroid-regulating hormone called thyrotropin in 1,864 healthy men and women with an average age of 71.

They had blood drawn as part of the larger Framingham Health Study in which practically everyone in a Massachusetts town has had their health scrutinized for decades.

Writing in the journal Archives of Internal Medicine, Tan and colleagues said 209 of the volunteers had developed Alzheimer's disease after nearly 13 years.

Women with the lowest and highest levels of thyrotropin had more than double the risk of developing Alzheimer's disease. No such relationship was seen in men.

Changes in the brain caused by Alzheimer's disease may reduce the amount of thyrotropin released, Tan's team said. Alternately, low or high thyrotropin levels could damage brain cells or blood vessels.

They said the findings should be tested in a larger population. (Reporting by Maggie Fox; editing by Todd Eastham)

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