Bioequivalence and Bioavailability Forum

Dear All, to whom it concerns,

I have played around with the t_E algorithm of Czismadia/Endrenyi for estimating the lag time, mentioned previously in this thread and I would like to share my experiences.

Short description of the algorithm (see the ref.* for more information):

1. Calculate a first guess of the lag time as mean of the time prior to (t_L) and at first (t_F) measurable concentration.
   
2. Transform the concentrations between tlag and tmax according to
     Y=Conc*exp((t-tlag)/(tmax-tlag))
   
3. Estimate the intersection with the time axis of a linear weighted regression of Y versus time using the weights 1/Y². This intersection is t_E=estimated lag time.
   
4. If t_E<t_L or t_E>t_F then use t_L.

Experiences:
First: It seems a reasonable approach if the absorption is actually (at least approximately) first order. This results then in a concave part at the beginning of the concentration time curve for which the proposed transformation* yields in fact a reasonably straight line if plotted versus time.

Second: The transformation does not work very well (not to say it breaks down totally) if the beginning part of the concentration time curve is first convex and then concave. Let me try to illustrate such a curve character based:
| conc     **
|        *    *
|       *       *
|      *          *
|     *
|   *
-**------------------------------ time
[I hope you will see my point . ]
In case of such curves the transformation* does not yield a straight line and therefore the regression versus time cannot reasonably applied. The algorithm yields in most of such cases t_L as lag time according to step (4) above. This is not worth the extra calculation power needed in the algorithm.

Unfortunately I have seen such shaped curves frequently in cases where the lag time has importance.

And the moral of the story is:
Do not use an algorithm blind. Always check the underlying assumptions.
More or less a platitude, I know. But it cannot told often enough.

Reference:

• Czismadia F, Endrenyi L. Model-independent estimation of lag-times with first-order absorption and disposition. J Pharm Sci. 1998;87:608–612.

BTW: I hope I do not bother anybody with my links to concave/convex, but I always cannot remember which is which .
BTW2: Implementing the algorithm I would suggest to replace the condition: If t_E>t_F then use (t_L+t_F)/2.