I would like to calculate the half-life of a biological drug.

This biological drug is said to have a biological half-life of:

3.33 days when a patient is receiving a dose of 0.04 mg/kg of body weight,
13.4 days when the dose is 0.2 mg/kg
and 14.9 when the dose is 1 mg/kg

How could I extrapolate this information to get biological half-life estimate for 2 mg/kg of body weight?

Could I also graph this? for example in R?

  • 2
    $\begingroup$ This sounds a lot like a homework question. I'm glad you got an answer though. $\endgroup$
    – James
    Jun 15, 2015 at 12:33
  • $\begingroup$ Maybe it does but I'm actually a doctor and I have a patient that has to switch from one clinical trial to another. He may go into the second clinical trial only after a wash-out period of 5 drug half-lifes. and the information I have given - is actually in the drug description. $\endgroup$
    – WojciechF
    Jun 16, 2015 at 4:33

1 Answer 1


I plotted your data using MATLAB and it looks like this:

                  enter image description here

Most degradation or clearance processes happen via first order kinetics. However when the clearance/degradation machinery gets saturated then degradation proceeds via a zeroth order kinetics i.e. it becomes independent of the concentration of the drug. The half life in first order reactions is independent of the initial state. Only in the case of the zeroth order reactions, the half life is directly proportional to initial state (See here). In this graph there is a huge gap in half life, between the first and the second points. We need more data points to say anything conclusively about this observation. However, I am assuming that the clearance reaction is already in the zeroth order kinetics as half life increases with concentration (though at different rates). For a rough calculation let us consider second point onwards. By calculating the slope between second and third points you can obtain the half life corresponding to dosage of 2mg/kg.

$$Slope=\frac{t_3 -t_2}{x_3-x_2}\\ t_4=x_2+slope\times2=17.15\ days$$

There can be other complicated explanations too, such as the drug inhibiting its own clearance etc. But for assuming such models we would require more information.

  • $\begingroup$ does it mean that more drug "clogs" kidney (for example) so that drug stays in blood stream longer? Is it real effect (observable in reality)? $\endgroup$ Jun 15, 2015 at 10:12
  • $\begingroup$ @aandreev I haven't studied that with drugs but if you overexpress proteins beyond a limit then their degradation rates become zero order i.e. independent of concentration of the protein because proteosomes get "clogged". Same goes with drugs and if two drugs require same enzyme for their metabolism then taking them together may be harmful. I guess, that is why most drugs are metabolized slowly when someone has consumed alcohol. $\endgroup$
    Jun 15, 2015 at 10:17

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