Bioequivalence and Bioavailability Forum

Dear Detlew!

❝ ❝ Hopefully not the arithmetic means? Geometric means would make more sense.

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❝ Seems some members of this forum don't share your opinion .

Ooh-ooh; asymptotically unbiased estimator. Don’t understand what Martin meant in referring to Källén’s Figure 3.4 (a plot of geometric means of infusion data of two drugs).
But see the same author (pp48–49; THX to OCR):

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3.5 Population average vs. subject-specific approach
  When describing plasma profiles, mean values can be used. However, values below LOQ cannot simply be considered missing when computing these mean values, since they carry information. It is therefore important that trailing missing values, due to values below LOQ, are replaced with estimates, based on mono-exponentials using the estimated terminal elimination rate discussed in the previous section. Also other values below LOQ need to be filled in with an appropriate algorithm.
  When computing mean values, it is preferable to compute geometric means. Much of the variability resides in dosing, at least from an extravascular site,^* which is a multiplicative factor to the plasma concentration, and by taking the geometric mean, we get the product of the geometric mean of doses and the geometric mean of dose one response curves (assuming linear kinetics).
  It is important to know what a mean value curve represents. Its value at time t represents what the plasma concentration is expected to be, if we take one sample at that time for a randomly chosen individual after having dosed according to the schedule used. There is a potentially important difference between this mean curve and an individual curve. In order to illustrate the difference, assume a situation with a first order absorption profile and a one-compartment model such that all individuals in the world have the same plasma concentration curve, except that there is a time-lag until absorption starts. But assume that this time-lag varies substantially between individuals, so that the absorption starts much later for some individuals as compared to for others.
  This is illustrated in Figure 3.2, in which we have shown five typical subject profiles, the middle of which is thicker than the others. This is a mean parameter curve, in this case the subject profile you get if you take as lag-time the mean value of all individual lag-times. It looks like the other curves and lies in the middle of the family.



The other thick curve is the mean curve, the curve obtained by taking the means of all the other (not only the five shown, but from the whole population). It looks quite different, and does not resemble an individual curve. But it tells us what the mean plasma concentration should be, if we fix a time point and sample many individuals at that time point.
  This curve is the population average curve, and describing it the population average approach to data analysis. The mean parameter curve represents the subject specific approach to data analysis.
  Strictly speaking the difference between the mean parameter curve and the mean curve makes most sense if we discuss a NONMEM application, in which there is a clear meaning of the former. But we can think of a mean parameter curve as “the most typical individual curve”, obtained from “an average individual”.

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Concerning your question in the subject line – and in the spirit of Källén: I don’t know (“other values below LOQ need to be filled in with an appropriate algorithm”). Lag-times & values <LLOQ are nasty.



But on the other hand: Is this really important? We don’t base any conclusions on curves; they are simple illustrations. Experienced pharmacokineticists want to see spaghetti plots anyway. Who never was confronted with a question like “I measured the C_max of test and reference from the plot on page 4 as 65 and 70; so why do you state on page 3 the PE is only 88%?”

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• Wouldn’t say so. More likely F, V, CL. Content uniformity should protect us from substantial variability in D.