anemia (low iron levels) definitely is a major cause of hair falling out. though there are other factors that can come in to play as well.
i had anemia for years and my hair always seemed to be falling out more than it should. got worse after being pregnant and read on the internet somewhere that lack of iron is a cause.
anyway, started taking an iron supplement (cenovis iron plus, which includes other minerals and vitamins) and within 4-6 weeks notices an improvement. it's been 5 months since i started taking them and my hair hasn't been this thick in years. it even starts growing back.
try taking iron supplements and see how you go. it does take a little while before there is a noticable change though so have patience.
good luck