What this means in practice
If you take warfarin, tell whoever monitors it that you are taking glucosamine, and tell them again if you change the amount. The check that would catch a problem is the blood test you are already having.
What people say
Glucosamine is a natural joint supplement, not a drug, so there is nothing to check before adding it to whatever you already take.
What the evidence supports
Reviewers at the US Food and Drug Administration describe a man stable on warfarin for five years whose blood-thinning measurement rose from 2.3 to 4.7 after he tripled his glucosamine and chondroitin dose, and settled back to 2.6 once he stopped the supplement. Searching their own adverse-event database they found 20 further reports of raised measurements, bleeding or bruising in people taking both, and the World Health Organization's database held 21 reports of a raised measurement with glucosamine, 17 of which resolved when it was stopped. Spontaneous reports like these have no denominator and cannot establish cause, and the reviewers say directly that more information is needed to define the interaction.
How it is supposed to work
No mechanism has been established. What is reported is a pattern: the international normalised ratio, the standard blood test for how far warfarin has thinned the blood, rises after glucosamine is started or its dose increased, and falls again when it is stopped.
Which way it runs
The risk runs one way. Glucosamine appears to increase warfarin's effect; warfarin does nothing to glucosamine. Almost every report involves glucosamine taken alongside chondroitin, so which of the two is responsible has not been separated, and the reports name glucosamine because that is the ingredient the reviewers searched on.
What is still missing
The evidence is much too weak to call this an established interaction, which is the reason to act on it rather than the reason not to: mentioning a supplement costs nothing, and the test that would catch a problem is one a warfarin patient already has done routinely.