The FDA runs stability tests for drugs to determine their expiration date. They operate under a rule that if there is a 10% degradation in the amount of drug in the product, then it is no longer appropriate to use. Their tests assume the storage instructions are followed.
The FDA expiration date is the that at, under those specified conditions, they feel comfortable they can guarantee a consumer is getting more than 90% of the drug. In order to protect public health, they err on the side of caution.
In fact, the likely hood that the drug will have decomposed a full 10% at that time depends upon the drug.
For example
Is it a liquid - probability goes up.
Require refrigeration - probability goes up.
Multiple dose item which might get contaminated with microbe - a whole extra worry you don't want to mess with.
Exposed to too high a temperature /light / high humidity - probability goes up.
As to determining the fact of how much of an active ingredient has decomposed - you would have to do a
chemical assay of that product.
As a professional, it would not be ethically appropriate to recommend using drugs beyond their expiration date. Yet for one reason or another we recognize many people do. Sometimes is is to save cost, other times for their convenience.
In the case of any drug where an under dose is likely to matter - like an oral antibiotic. Just no way, Don't risk it.
If it is say, a tube of neosporin or an anti-fungal foot cream, some is still better than none but as it is not a solid it will go bad faster - any funny color or odor and you should pitch it..
In cases like the common pain killers like Aspirin, Tylenol, and NSAIDs - is it really relevant if you got 10% less? I have known pharmacology teachers rightly point out that it might take decades for say, a sealed acetaminophen bottle, to actually degrade.
The real point is, after the expiration date. You can't be SURE you're getting enough drug anymore. Most solid OTC preparations should be good for some time after. But you can never tell. With something like "will this help my headache/muscle ache" the answer is certain to be yes. Ultimately though, these
are all pretty inexpensive. If you have to use old meds because they are all you have on hand, best to get a new bottle (maybe a smaller one) on your next trip out
As far a prescription drugs, you really don't want to risk not getting enough, ever.