A dose is related to how much of the drug is needed to achieve a certain concentration in your blood. Most medications need to achieve a certain concentration in order to be effective / do their job / kill all the bacteria / whatever.
The half-life is related to how fast your liver can decompose the medication or substance (alcohol for example). Your liver works 24/7 and decomposes nutrients and chemicals in your blood, and the kidneys sometimes participate in the decomposing, but primarily extract the by-products created by the liver, into your urine.
So basically, each dose is decomposed by the liver within a certain time, which is why you need to take another dose in order to maintain the “working concentration” for the medication to be effective over a period of days or weeks.
Anyway, long half-live means the liver doesn’t decompose it easily. The (normal) dose just goes around in your blood without being taken out by the liver and the kidneys.
Half life and overdose levels aren’t quite related. If you’re given a single, safe dose of the drug at a time (letting the drug completely clear from your body between doses), you’ll never overdose on it, no matter how long the half-life is.
Similarly, the half-life is irrelevant to how much of the drug is needed for an overdose, although a short half-life would also shorten the duration of the overdose.
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