There are two main classes of IUDs: the copper T 380A IUD and the levonorgestrel-releasing IUD.

Q1: Paragard vs. Mirena?

In what situations is a copper T 380A intrauterine device (ParaGard) preferred over a levonorgestrel-releasing intrauterine device (Mirena)?

Patient with 1) Severe Cirrhosis, and 2) Breast cancer.

“Women with severe cirrhosis or liver cancer should not use the levonorgestrel-releasing IUD, and the copper T is preferred. Hormonal contraceptives, in general, should be avoided in women with severe liver disease, as there is a known association between oral contraceptive use and the growth of hepatocellular adenoma, and this risk is thought to extend to other types of hormonal contraceptives (SOR C).

Breast cancer is another contraindication to use of the levonorgestrel-releasing IUD, and the copper T would be preferred. There is no difference in risk between the copper T and levonorgestrel-releasing IUD with regard to deep vein thrombosis/pulmonary embolism. However, the IUD is preferable to contraceptives containing estrogen.” ABFM

The risk of DVT / PE is the same for both types of IUD.
Women who smoke may use either IUD.
Women with controlled HTN may use either IUD.
In women with uncontrolled HTN, there is a small risk from using of the levonorgestrel-releasing IUD, although the benefits 
outweigh the risks.

Q2: What are the contraindications to using an IUD?

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Q3: How long should I use backup contraception after a Mirena IUD?

You do not need to use backup contraception if your IUD is inserted within 7 days after your menstrual bleeding started (i.e. within 7 days from LMP). If the levonorgestrel IUD is inserted more than 7 days after menstrual bleeding starts, the patient needs to abstain from sexual intercourse or use additional contraceptive protection for the next 7 days.

 

Reference

Centers for Disease Control and Prevention (CDC): US medical eligibility criteria for contraceptive use, 2010. 

Intrauterine devices: An update. Am Fam Physician 2014;89(6):445-450.

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