if the dose of a medicine is changed to x times the original value then how will the half-life change?

Question

To be more specific if a patient takes 0.5mg of clonezepam what is the half-life.And when he takes 0.25mg of clonezepam what is the halflife.

Also when he takes 1mg,2mg,etc what is the half life.

It would also help if i can get a formula that can give me the relation between old halflife & new halflife when the dose is changed.

Answer 1

The pharmacodynamics & kinetics of any drug is far too varied to give an answer to this specifically.

The half-life of Clonazepam in humans has a very wide range: following the elimination of the drug, the half-life is 22 to 33 hours for children and 19 to 50 hours for adults. It is usually metabolized in the liver and the metabolites excreted as glucuronide or sulfate conjugates.

Therapeutic drug monitoring of the serum levels is necessary to get the information you need for any specific individual.

Answer 2

As Richard said, it is not easy to determine the kinetics/dynamics of a drug.

Let's set aside patient to patient variation and possible complex metabolic pathways of the drug. I do not know the exact details of clonezepam but I assume its action is as simple as possible.
Then the half-life is a fixed value, independent of the exact amount. It it the time required for the drug to reach half of each initial concentration. What changes, is the time required in total for the drug concentration to drop below a certain limit that is either a detectable value in the blood serum or a concentration below which you don't have any physiological/clinical effects.

According to wikipedia its half-life is 30-40 hours

Assuming exponential decay, the amount of drug remaining C after time t, is
C=Co*e^-((tln2)/t1/2))
where Co is the initial concentration/amount of the drug and t1/2 the half life.
t1/2

So if you know the limit (C) and t1/2 you can find the t required to reach that C. If you want C=0 then t will tend to infinity; that's why in practice there are limits below which you consider it to be 0 while actually it has a very small value. My extremely handwaving wild guess would be that such a limit could be the value C when Co = minimum recommended dosage and t=6*t1/2, as than would correspond to a (1/2)^6 = 1.6% of the minimum dose remaining in the blood. This of course applies only to the simplest case of pharmacokinetics.