You would have a hard time buying the claim that the cold you woke up with this morning was caused by sunrise as your cold started after the sun rose. Yet, you would probably assume that, if your doctor prescribed antibiotics for that very same cold and after a few days you felt better, that the antibiotics beat off the cold.
No, cause and effect have not been established. Your cold might have gotten better anyway. Just because you took the antibiotics and you felt better, doesn’t mean that these very same antibiotics worked wonders on a viral illness. There are many other examples in medicine: If a child happens to be diagnosed with autism after an immunization, the immunization did not necessarily cause this awful disease. If your chest hurts less after the third drink, this doesn’t prove that the chest pain is nothing to worry about; conversely if your chest pain improves with aspirin, it doesn’t always imply that the pain is from your heart. If you take Vitamin C and don’t get a cold like your buddies did, this does not prove that Vitamin C worked to prevent that cold.
To prove cause and effect, rigorous studies with enough subjects to be able to provide that statistical power are needed. Ideally, the study should be double blinded, which basically means that neither the patient nor the researcher knows whether dummy pills (placebo) or the real deal was administered. Why? If you believe something will work then you often feel better, regardless whether the medication actually worked. This is called the placebo effect.
What else is needed to prove a medication works? The study should be reviewed by other independent researchers who don’t work directly with the authors. It should be published so that others can review and perhaps try to repeat the findings.
Sometimes, anecdotal evidence ( cause and effect ) can be useful as a springboard for further research. For example. Parkinsons’ patients treated with Amantadine suffered fewer episodes of influenza. Did the Amantadine prevent influenza? Well, after years of research, it was shown that indeed Amantadine worked to prevent the flu.
Yes. it takes time and effort to sort cause and effect out. In the long run however, quality evidence is much better than just hearsay.