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LETTER

COMMENTS ON "A MATHEMATICAL DESCRIPTION OF THE FUNCTIONALITY OF CORRECTION FACTORS USED IN ALLOMETRY FOR PREDICTING HUMAN DRUG CLEARANCE"

Clinical Pharmacology and Toxicology Branch, Office of Drug Evaluation VI, Center for Drug Evaluation and Research, Food & Drug Administration, Woodmont Office Center II, Rockville, Maryland

(Received September 2, 2005; accepted December 2, 2005)

	Abstract

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In a recent paper, Tang and Mayersohn [(2005) Drug Metab Dispos 33:1294–1296] mathematically described the functionality of the correction factors (CFs), maximum life-span potential (MLP), and brain weight (BrW) used in allometric scaling for the prediction of human drug clearance. They found that there is an intrinsic defect in using correction factors because different combinations of species will produce different prediction results. Analysis with real examples reveals that different predicted clearance values observed with different combinations of animal species, with or without CFs, are not due to the intrinsic defect of the correction factors; rather, it is the effect of the species, observed clearance values in the species, and the range of the body weights. Even if one does not use the CF, the predicted clearance by the simple allometry will still vary by severalfold, depending on the species used in the scaling.

To improve the prediction of human drug clearance from animal data, Mahmood and Balian (1996) developed "the rule of exponents." The rule of exponents (ROE) was developed from real observations and behavior of the allometric exponents. The ROE has helped a great deal in improving the human drug clearance over simple allometry (SA), and it has also provided the guidelines for the selection of CFs (before the ROE, these correction factors were applied randomly). However, the ROE is not rigid, and there are many examples where predictions obtained from this method were not accurate but produced less prediction error than SA for the same drug. The ROE is not applicable to renally secreted drugs (Mahmood, 2005a), and physiological correction factors along with the ROE are needed (Mahmood, 2005a) to improve the prediction of human drug clearance for biliary excreted drugs. Although not perfect, at this time, ROE remains the method of choice for the prediction of human drug clearance for a wide variety of drugs after both intravenous and oral administration (Mahmood, 2005b). The objective of this commentary is to 1) highlight and strengthen the important and impressive work of Tang and Mayersohn (2005b) on the mathematical description of the functionality of CFs by some real examples; 2) emphasize the importance of the exponents of the allometry and the need of the correction factors for the prediction of human drug clearance; and 3) clarify the incorrect conclusion of Tang and Mayersohn (2005b) that there is an intrinsic defect in using correction factors because different study designs will produce different results.

	Materials and Methods

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In Table 1, there are five drugs for which human clearances were predicted using mouse, rat, dog, and monkey. Then, the prediction was made using only three species using different combinations of animal species as described by Tang and Mayersohn (2005b). The prediction of human drug clearance was also made using F_MLP and F_Brwt.

	Results and Discussion

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The results of allometric scaling shown in Table 1 confirm many conclusions drawn by Tang and Mayersohn (2005b). Remarkably, almost similar prediction of human drug clearance was obtained by simply multiplying the predicted clearance obtained by SA and F_MLP or F_Brwt, as needed, and ROE. This confirms the mathematically drawn conclusion by the authors that the CF as used in allometry is multiplication of some constant and the predicted clearance by SA. The slight difference in the predicted clearances between ROE and F_MLP or F_Brwt are mainly caused by the different body weights used in the scaling (original body weights of the species rather than fixed body weights). It can be clearly seen that without the application of CF, the error in the predicted clearance for these drugs by SA alone remains comparatively much higher. Many conclusions can be drawn from the study of Tang and Mayersohn (2005a,b) and this author's previous works (Mahmood, 2005c).

• The exponents of SA have no physiological meaning (Mahmood, 2005c). The exponents of SA will widely vary depending on the species used in the scaling. For example, in Table 1 for quinidine, the exponents of SA varied from 0.548 to 1.034, depending on the species used in the scaling. Without CF, the error in the predicted human drug clearance will be much higher. The same is true for all other drugs presented in Table 1 and in many other studies conducted by this author (Mahmood, 2005c). The beauty of the CF is that although it is a constant, it varies depending upon the species. Therefore, with the change in species, CF is adjustable, thus helping in improved prediction of human drug clearance. Without this ability, CF would have been of no practical value.
  
• The application of CF is simply a mathematical manipulation which helps in reducing the prediction error (Mahmood, 2005c). Tang and Mayersohn (2005b), however, incorrectly concluded that there is an intrinsic defect in using CF because different study designs will produce different results. The statement is correct that different study design (in fact, this should be called same study design but with different species) will produce different results, but this is not due to the defect in the correction factors but due to the species used in the allometric scaling (I will not call this a defect, either). For example, if one evaluates the predicted clearance by SA (Table 1), it becomes obvious that the clearance values widely vary even without the application of CF. For quinidine, based on the species used, the predicted clearance using SA ranged from 178 to 747 ml/min, and using ROE, the predicted clearance ranged from 227 to 508 ml/min. The same is true for other drugs. Therefore, different predicted clearance values observed with different combinations of animal species with or without CF are not due to the intrinsic defect of the correction factors; rather, it is the effect of the species, observed clearance values in the species, and the range of the body weights. In other words, even if one does not use the CF, the predicted clearance by SA will still vary by severalfold, depending on the species used in the scaling. Therefore, I disagree with Tang and Mayersohn that there is an intrinsic defect in using CF because different study designs will produce different results.
  
• From Table 1 and the previous studies conducted by this author, it is difficult to assess a priori what is the best combination of animal species for a given drug, to predict human clearance as accurately as possible. At this time, it does not seem that there is any outright answer for this, although in one of their works, Tang and Mayersohn (2005a) have clearly shown the importance of species and body weight on the prediction of human drug clearance.
  
• Is it reasonable to apply MLP to both drugs if the exponent of one drug is 0.71 and the other is 0.99? The answer to this question is yes, because the exponents of the allometry will depend on the body weights and the clearance values of the species. However, one should not assume that the error in the prediction of human drug clearance obtained by SA will proportionally increase with increasing exponent of the allometry. The coefficient of the allometry also plays an important role (although not distinguishable for CF) in the prediction of human drug clearance.
  

In short, in the pharmacokinetic allometric scaling, one must recognize the fact that species, the clearance values in different species, and their body weights will have substantial impact on the prediction of human drug clearance. The predicted human clearance values for a given drug will widely vary depending on the species, with and without correction factors.

	Footnotes

 
The views expressed in this article are those of the author and do not reflect the official policy of the FDA. No official support or endorsement by the FDA is intended or should be inferred.

Article, publication date, and citation information can be found at http://dmd.aspetjournals.org.

doi:10.1124/dmd.105.007187.

ABBREVIATIONS: CF, correction factor; MLP, maximum life span potential; Brwt, brain weight; ROE, rule of exponents; SA, simple allometry.

Address correspondence to: Dr. Iftekhar Mahmood, Clinical Pharmacology and Toxicology Branch, Office of Drug Evaluation VI, Center for Drug Evaluation and Research, Food & Drug Administration, Woodmont Office Center II, Rockville, Maryland. E-mail: Mahmoodi{at}CDER.FDA.GOV

	References

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Mahmood I and Balian JD (1996) Interspecies scaling: predicting clearance of drugs in humans. Three different approaches. Xenobiotica 26: 887–895.[Medline]

Mahmood I (2005a) Interspecies scaling of drugs cleared by the kidneys and the bile, in Interspecies Pharmacokinetic Scaling: Principles and Application of Allometric Scaling pp 105–143, Pine House Publishers, Rockville, MD.

Mahmood I (2005b) Prediction of oral pharmacokinetic parameters in humans, in Interspecies Pharmacokinetic Scaling: Principles and Application of Allometric Scaling pp 144–167, Pine House Publishers, Rockville, MD.

Mahmood I (2005c) Interspecies scaling of clearance, in Interspecies Pharmacokinetic Scaling: Principles and Application of Allometric Scaling pp 39–85, Pine House Publishers, Rockville, MD.

Tang H and Mayersohn M (2005a) Accuracy of allometrically predicted pharmacokinetic parameters in humans: role of species selection. Drug Metab Dispos 33: 1288–1293.[Abstract/Free Full Text]

Tang H and Mayersohn M (2005b) A mathematical description of the functionality of correction factors used in allometry for predicting human drug clearance. Drug Metab Dispos 33: 1294–1296.[Abstract/Free Full Text]

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