Because the cannabinoids and the anticoagulant warfarin (Coumadin) share the same pathway for breakdown by the body, in some situations the Coumadin level can rise slightly with simultaneous cannabis use. This is rarely clinically significant, but occasionally it can be important, especially if other prescription medications are being taken that share the same metabolic route. I don't believe being on Coumadin is a contraindication to medical cannabis use, but patients who are using cannabis regularly should have their INR checked regularly as well to make sure their level of anticoagulation is appropriate.
The cytochrome p450 system accounts for 70 to 80 percent of the enzymes involved in drug clearance, making it the most important system for drug metabolism. Both THC and CBD are competitive inhibitors of three different enzymes in the cytochrome p450 system, two of which are involved in the metabolism of coumadin. This means that CBD and THC are competing for the same receptors as is coumadin. So when coumadin is taken concurrently with CBD and/or THC, coumadin levels could possibly rise. When coumadin levels rise excessively, blood clotting may be compromised leading to signs ranging from frequent bloody noses all the way on up to a potentially fatal event, such as a hemorrhagic stroke or heart attack. https://ghr.nlm.nih.gov/primer/genefamily/cytochromep450
A case report published in 2009 described a patient who was on coumadin therapy for eleven years. He was admitted to the hospital for a severe gastrointestinal bleed when he confessed to consuming much more cannabis than was typical for him; his INR was 10.41 (therapeutic range is usually between 2 and 3); after inpatient treatment, his INR normalized; then, fifteen days after being discharged, he was readmitted with an INR of 11.55; after he quit using cannabis, his INR remained between 1.08 and 4.40 and he suffered no further complications. https://www.ncbi.nlm.nih.gov/pubmed/19531696
Another case report suggested that extremely high doses of CBD can lead to markedly elevated coumadin levels. Enrolled in a clinical trial evaluating CBD as a potential treatment for epilepsy, the test subject was given extremely high doses of CBD. He was first given doses averaging 265mg, which resulted in a slightly elevated coumadin levels; at doses averaging 528mg, the coumadin levels were markedly elevated; after reducing the coumadin dose, INR results normalized. Relevantly, very few patients, if any, would ever take as much CBD. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5789126/
However,as previously mentioned, a highly elevated coumadin level can lead to serious consequences. And because the effects of cannabis on coumadin levels have yet to be sufficiently studied, as Dr. Elkind advised, you should discuss the matter with your prescribing physician and monitor your INR results with additional vigilance.