Drug Metabolism and Disposition Fast Forward
First published on May 26, 2005; DOI: 10.1124/dmd.105.004127
0090-9556/05/3309-1288-1293$20.00
DMD 33:1288-1293, 2005
ACCURACY OF ALLOMETRICALLY PREDICTED PHARMACOKINETIC PARAMETERS IN HUMANS: ROLE OF SPECIES SELECTION
Huadong Tang1, and
Michael Mayersohn
Department of Pharmaceutical Sciences, College of Pharmacy, The University of Arizona, Tucson, Arizona
(Received February 9, 2005;
accepted May 20, 2005)
 |
Abstract
|
|---|
A general equation was derived, which directly describes the mathematical relationship between the allometrically predicted pharmacokinetic (PK) parameters in humans and the body weights of animal species (along with their corresponding measured PK parameters). It was shown, with use of the derived equation, that the predicted values in humans, based on combinations of animal species commonly used in allometry, are heavily dependent on certain species, for example, the dog. In contrast, parameter values from the rat made no contribution to the predicted human values, as long as the rat was not the smallest species used. Monte Carlo simulations were further performed to examine the species or weight dependence. The cost-effective combinations of animal species, in terms of number and species type, were theoretically examined through simulations. Finally, literature data demonstrated the species or weight dependence predicted from the equation and as illustrated through the Monte Carlo simulations. Appreciation of this species or weight dependence should guide researchers in selecting animal species and designing optimal experiments in the application of allometric scaling.
Allometric scaling is one of the most widely used approaches in predicting human pharmacokinetic (PK) parameters [e.g., clearance (CL), Vd, t1/2] based on values in animals, The basic allometric relationship has been observed to follow the power function: parameter = a (body weight)b, where a and b are a coefficient and an exponent, respectively. The observed power function is empirical, although there is some possible underlying physiological rationale (Boxenbaum, 1982
; Mordenti, 1986). For example, the "3/4 power law" of metabolic rate was theoretically derived from the hydrodynamics and fractal geometry of nutrition-supply network of the organisms (West et al., 1997). However, there are numerous examples of substantial differences between predicted and observed values in humans. Great effort has been focused on how to improve the accuracy of allometric scaling. The various modifications include in vitro correction (Lave et al., 1997), a two-term power function approach (Boxenbaum and Fertig, 1984), maximum life-span potential or brain weight correction (Mahmood and Balian, 1996b), "rule of exponents" (Mahmood and Balian, 1996a), and unbound CL approach (Feng et al., 2000). Unfortunately, none of these modifications is completely satisfactory since there are always deviations from prediction. Basically there are two reasons leading to such deviations. One is the deviations of the values of PK parameters in certain species (animal or human) from the assumed power function. The other is the measurement errors in the reported PK parameters. The former could be considered as a "position error" (though it is not an error), and such an error is fixed for each species. The latter measurement error is a random one.
Power functions are well known for creating substantial errors in data fitting. The log-log transformation of the data will visually minimize the deviations from a regression line. A high R2, greater than 0.90 or even 0.95, does not guarantee that all the data points will be close to the regression line. The extrapolation of this regression line to obtain a predicted human value, which is obtained from fitting data based on a limited number of animal species, may have great uncertainty associated with it. It is also well known that the regression process does not treat the weight of each animal species comparably. The measurement errors in a given parameter from an animal species could lead to significant prediction error in humans as a result of fitting this power function. Therefore, it is necessary and desirable to know how quantitatively a measurement error or a position error in a given parameter in animals affects the regression analysis and the ultimate quantitative prediction in humans.
In this report, we have derived a general equation, which describes the mathematical relationship between predicted PK parameters in humans and the body weights of selected animal species and the values of the corresponding measured PK parameters. Using CL as an example, simulations were performed to examine the dependence of the variability of predicted human CL on the variability of animal CL. Finally, data from the literature were examined to demonstrate the species dependence as derived from theory. Based on these results, some suggestions are proposed for the optimal selection of animal species and the application of animal data in allometric scaling.
|
Materials and Methods
|
|---|
Theory. The function relating predicted PK parameters in humans (Ppredicted) to animal body weights (W) and observed animal PK parameters (Pi) is derived in the following sections.
The log-log transformation of P = a · Wb gives
 | (1) |
Let Y = log P; X = log W; a = 10
; b = ß. Then, eq. 1 can be simplified to
 | (2) |
Suppose n different animal species are used for allometric scaling. Therefore, there are n sets of (X, Y) data to fit using linear regression. Based on the method of least squares for linear regression, and ß can be calculated as
 | (3) |
 | (4) |
Substituting Y = log P; X = log W into eqs. 3 and 4, and further substituting and ß into a = 10; b = ß, expressions of a and b are obtained as
 | (5) |
 | (6) |
where
 | (7) |
 | (8) |
By assuming a human body weight of 70 kg, the predicted P in humans is obtained from
 | (9) |
Direct fitting of power functions with incorporation of a weighting strategy has been shown not to improve the prediction performance by allometric scaling (work not shown). The above log-log transformation and linear regression appears to be the best approach in allometry. In reality, this method is inevitably applied in allometric scaling.
Monte Carlo Simulations. CL was used as an illustrative example of a PK parameter. Typical body weights of animals commonly used in allometry are listed in Table 1. Assuming that there is a perfect allometric relationship, CL = a · Wb, between CL and W, and setting a = 30 ml/min, b = 0.75, "seed values" of CL for each species for Monte Carlo simulations can be obtained (Table 1). Log-normal distribution, N(ln CLseed + CV), is assumed for CL, where the coefficient of variation (CV) is 30% or 100%. Thirty percent and 100% CV are used to assess the effect of the experimental measurement errors and the overall "errors" (including both measurement errors and position errors) on the prediction performance, respectively. The magnitude of the position errors is considered to be much greater than that of the measurement errors. The arithmetic mean and median values of CLpredicted in humans from these simulations are listed for comparison with the theoretically perfect value (726.0 ml/min) predicted from the power function. For some combinations of commonly used animal species, in addition to the simulations where all the Pi values were variables, simulations were also performed by assuming that only one Pi was variable, whereas the others were held constant (at the seed values). This was done to assess the contribution of each species to the prediction performance. Different combinations of animal species from five species to two species were used for simulation purposes to select optimal combinations of animal species. Percentage errors (PEs), which are [(CLpredicted – CLobserved)/CLobserved] x 100%, for over-prediction and [(CLobserved – CLpredicted)/CLpredicted] x 100%, for under-prediction, were used to assess the prediction performance. All the calculations and simulations were performed with MATLAB 6.5 (MathWorks, Inc., Natick, MA).
View this table:
[in this window]
[in a new window]
|
TABLE 1 Animal body weights and the seed values of CLi used for Monte Carlo simulations
CLi is the clearance in the ith species.
|
|
Literature Data Experimentation. Twenty-six sets of allometric scaling data for CL from at least three species, including mouse, rat, and dog, were randomly collected from the literature. CL in humans was predicted by allometry. Percentage change is defined as [(CLremove-ith-species – CLall)/CLall] x 100% for an increase and [(CLall – CLremove-ith-species)/CLall] x 100% for a decrease, where CLall is the CL predicted using all animal species and CLremove-ith-species is the CL predicted by removing the ith species.
|
Results
|
|---|
Theoretical experimentation. The equation,
|
| (9) |
not only directly depicts the relationship between the predicted PK values in humans and those observed in animals, but more importantly it indicates the dependence of the prediction variability on animal body weights, which determine the value noted in the exponent of Pi. Each animal Pi is raised to a specific power, Ai + 1.845Bi. Prediction of CL is used as an example of a parameter, P, in the following discussion, although the principle can be applied to any PK parameter, such as volume of distribution and half-life. A typical example of an animal species combination, mouse, rat, rabbit, and dog, was used to illustrate the body weight dependence suggested by eq. 9. Substituting body weights from these species into Ai + 1.845Bi gives the equation
 | (10) |
The exponent (–0.005357) for rat CL is close to 0, indicating that the CL in the rat would have little effect on the prediction of human CL when this specific set of animals is chosen. In contrast, the CL in the dog would be expected to have a large effect on the predicted CL in humans. For example, a doubling of the values of dog CL results in a 0.75-fold increase in the predicted CL in humans, whereas there is little prediction effect on the predicted value in humans even with a 100-fold change in rat CL (Fig. 1).
View larger version (30K):
[in this window]
[in a new window]
|
FIG. 1. Fold-range in predicted human clearance as a function of the fold-range in clearance in selected animal species. A hypothetical combination of animal species was considered: mouse (long-dashed line), rat (dotted line), rabbit (short-dashed line), and dog (solid line). Note that log-scales are used.
|
|
The roles that different species play in their contribution to the prediction accuracy and variability were also examined by simulations allowing only one Pi to vary at a time. Commonly used species combinations were examined: mouse, rat, rabbit, monkey, dog; mouse, rat, monkey, dog; and mouse, rat, dog (Table 2). The results demonstrate that the prediction of a value in humans is most sensitive to the value in dogs, whereas the rat made essentially no contribution to the prediction. For example, the 30% CV random error in rat CL only generates a mean of 0.01% PE. The mouse also showed a small contribution to the prediction variability. These results are consistent with the results derived from the model equation, which shows that rat CL has a trivial effect on the variability in predicted human CL, whereas a significant effect is observed using the value of CL from the dog.
View this table:
[in this window]
[in a new window]
|
TABLE 2 The effects of variability of species on the prediction performance in humans based on Monte Carlo simulations with 30% CV as input random error and 100 trials
|
|
Literature Data Experimentation. The mouse, rat, rabbit, or dog was individually removed from allometric scaling to examine the effect of deleting one species on the prediction in humans (by using the log-log transformation and linear regression method), since the majority of the 26 allometry data sets used these four species. The rat contributed virtually nothing to the prediction, because all the values of percentage change were very close to 0 after removal of the rat. In contrast, removal of the dog from the allometry resulted in a significant change in predicted CL values in humans (Table 3, Fig. 2).
View this table:
[in this window]
[in a new window]
|
TABLE 3 The effect of removing one species from the combination of animal species on the prediction in humans based on real data
|
|
View larger version (10K):
[in this window]
[in a new window]
|
FIG. 2. Percentage difference in the predicted human value for clearance ("box and whisker" plots) when one individual species is removed from a combination of three or more species. The inset graph illustrates a limited, but the major, range of percentage difference. Analysis is based on real data taken from the literature (Table 3).
|
|
|
Discussion
|
|---|
The equation that has been derived here offers insight into allometric analysis in that it describes quantitatively the dependence of prediction variability on each animal species (i.e., species weight). An immediate practical significance of these findings will allow investigators to recognize such animal species, or body weight dependence, on the predicted human value and permit design of better or more optimal experiments. For example, large variability in the data for dog PK parameters would have a high potential risk for producing large deviations in predicted human values, whereas variability in rat data can essentially be ignored. Having such a quantitative equation available and realizing the magnitude of the species weight dependence, investigators may increase sample size for the species having the most significant effect on the predicted value to improve its accuracy, and appropriately reduce or eliminate completely the sample size for the species with the least effect. As demonstrated by both theoretical and literature experimentation, rats had no significance in predicting human PK parameters as long as the body weight of the rat is not the smallest in the species used in the allometric relationship. Why, then, have rats been widely, almost inevitably, included in allometric scaling? One reason is that the rat is relatively inexpensive and readily available. The other reason may be that investigators rely on the concept "the more, the better," without recognizing the magnitude of improvement in prediction brought by adding more species; the rat, in this discussion. In fairness, however, the role of species weight in allometric prediction has not been recognized until now.
It is apparent and not surprising that the more species used in establishing an allometric relationship, the better the human prediction will be. However, it is costly, time-consuming, and not realistic to design allometric experimentation to include five or more species. A practical and economical approach to minimize the number of animal species is to recognize the role of species weight, while still achieving the desired prediction goal. Monte Carlo simulations using different combinations of animal species were performed to select the "best" or optimal combination of animal species. The results showed, not surprisingly, that, in general, the more species used, the better becomes prediction performance (Tables 4 and 5). By comparing the percentage errors among different combinations of animal species, the following observations, in terms of prediction performance, could be obtained.
View this table:
[in this window]
[in a new window]
|
TABLE 4 Comparison of the prediction performance in humans obtained from different combinations of animal species based on Monte Carlo simulations with 30% CV random error and 100 trials
|
|
View this table:
[in this window]
[in a new window]
|
TABLE 5 Comparison of the prediction performance in humans obtained from different combinations of animal species based on Monte Carlo simulations with 100% CV random error and 100 trials
|
|
- The five-species combination is the best, having the smallest PE mean; however, it offers no significant improvement over the four-species combinations.
- Certain three-species combinations, such as mouse/rat, monkey, and dog, showed a prediction performance similar to that of the four species combinations, whereas some three-species combinations, such as rabbit, monkey, and dog, showed a significantly worse prediction performance.
- The two-species combination showed the worst prediction performance, especially for the combinations of mouse and rat, rabbit and monkey, or monkey and dog, which should be forbidden combinations in allometric scaling.
- Comparison of any combination having more than three species including mouse and rat showed that removal of the rat has little effect on the prediction performance, which is consistent with the previous findings.
- A three-species combination, mouse/rat, rabbit, and dog, or mouse/rat, monkey and dog, may be economically desirable without sacrificing the predictability compared to a five-species combination.
However, investigators should keep in mind that all of the above observations are purely mathematical. The differences or similarities between animal species and humans in terms of anatomy, physiology, biochemistry, etc. are not considered. These differences or similarities would account for different CVs used in the above analyses. Unfortunately, there are still no significant findings, or agreement, regarding these differences/similarities as to what animal species should be used to provide the best prediction in humans.
To summarize, an equation has been derived that relates the accuracy of predicted PK parameters in humans to species weight used in allometric scaling, and the Monte Carlo simulations provided a quantitative approach to appreciate the prediction variability in a species-dependent way (or more generally, body weight-dependent). The awareness that such dependence exists may be helpful in selecting animal species and designing experiments, such as increasing the sample size for species having the greatest effect on the prediction, and reducing or even deleting the species having the smallest effect on the prediction. It is especially noted that rats were found to have no significance in predicting human PK parameters as long as the body weight of rats is not the smallest among the species used in the allometric experimentation. In addition, some economical combinations of three animal species, mouse/rat, rabbit, and dog, or mouse/rat, monkey, and dog, which allow a theoretically reasonable predictability, are proposed.
|
Acknowledgments
|
|---|
We thank Drs. Stacey Tannenbaum (Novartis Pharmaceutical Co.) and Iftekkar Mahmood (U.S. Food and Drug Administration) for providing part of the allometric data used in the analyses.
|
Footnotes
|
|---|
This work was presented at the American Association of Pharmaceutical Scientists Annual Meeting, Baltimore, Maryland, November 8, 2004.
Article, publication date, and citation information can be found at http://dmd.aspetjournals.org.
doi:10.1124/dmd.105.004127.
ABBREVIATIONS: PK, pharmacokinetic; CL, clearance; PE, percentage error.
1 Current address: Bioanalytical Department, Wyeth Research, Pearl River, New York. 
Address correspondence to: Michael Mayersohn, College of Pharmacy, The University of Arizona, 1703 East Mabel Street, Tucson, AZ 85721. E-mail: rxprof{at}frontiernet.net
|
References
|
|---|
Boxenbaum H (1982) Interspecies scaling, allometry, physiological time and the ground plan of pharmacokinetics. J Pharmacokinet Biopharm 10: 201–227.[CrossRef][Medline]
Boxenbaum H and Fertig JB (1984) Scaling of antipyrine intrinsic clearance of unbound drug in 15 mammalian species. Eur J Drug Metab Pharmacokinet 9: 177–183.[Medline]
Busch U, Schmid J, Heinzel G, Schmaus H, Baierl J, Huber C, and Roth W (1998) Pharmacokinetics of meloxicam in animals and the relevance to humans. Drug Metab Dispos 26: 576–584.[Abstract/Free Full Text]
Chung M, Radwanski E, Loebenberg D, Lin CC, Oden E, Symchowicz S, Gural RP, and Miller GH (1985) Interspecies pharmacokinetic scaling of Sch 34343. J Antimicrob Chemother 15 (Suppl C): 227–233.
Duthu GS (1985) Interspecies correlation of the pharmacokinetics of erythromycin, oleandomycin and tylosin. J Pharm Sci 74: 943–946.[Medline]
Feng MR, Lou X, Brown RR, and Hutchaleelaha A (2000) Allometric pharmacokinetic scaling: towards the prediction of human oral pharmacokinetics. Pharm Res (NY) 17: 410–418.
Hussey EK, Donn KH, Daniel MJ, Hall ST, Harker AJ, and Evans GL (1994) Interspecies scaling and pharmacokinetic parameters of 3TC in humans. J Clin Pharmacol 34: 975–977.[Abstract]
Hutchaleelaha A, Chow HH, and Mayersohn M (1997) Comparative pharmacokinetics and interspecies scaling of amphotericin B in several mammalian species. J Pharm Pharmacol 49: 178–183.[Medline]
Kaye B, Brearley CJ, Cussans NJ, Herron M, Humphrey MJ, and Mollatt AR (1997) Formation and pharmacokinetics of the active drug candoxatrilat in mouse, rat, rabbit, dog and man following administration of the prodrug candoxatril. Xenobiotica 27: 1091–1102.[CrossRef][Medline]
Khor SP, Amyx H, Davis ST, Nelson D, Baccanari DP, and Spector T (1997) Dihydropyrimidine dehydrogenase inactivation and 5-fluorouracil pharmacokinetics: allometric scaling of animal data, pharmacokinetics and toxicodynamics of 5-fluorouracil in humans. Cancer Chemother Pharmacol 39: 233–238.[Medline]
Kim SH, Kim WB, and Lee MG (1998a) Interspecies pharmacokinetic scaling of a new carbapenem, DA-1131, in mice, rats, rabbits and dogs and prediction of human pharmacokinetics. Biopharm Drug Dispos 19: 231–235.[CrossRef][Medline]
Kim SH, Kwon JW, and Lee MG (1998b) Pharmacokinetics and tissue distribution of a new carbapenem DA-1131, after intravenous administration to mice, rats, rabbits and dogs. Biopharm Drug Dispos 19: 219–229.[CrossRef][Medline]
Komiya M, Kikuchi Y, Tachibana A, and Yano K (1981) Pharmacokinetics of new broad-spectrum cephamycin, YM09330, parenterally administered to various experimental animals. Antimicrob Agents Chemother 20: 176–183.[Abstract/Free Full Text]
Lave T, Coassolo P, Ubeaud G, Brandt R, Schmitt C, Dupin S, Jaeck D, and Chou RC (1996) Interspecies scaling of bosentan, a new endothelin receptor antagonist and integration of in vitro data into allometric scaling. Pharm Res (NY) 13: 97–101.
Lave T, Dupin S, Schmitt C, Chou RC, Jaeck D, and Coassolo P (1997) Integration of in vitro data into allometric scaling to predict hepatic metabolic clearance in man: application to 10 extensively metabolized drugs. J Pharm Sci 86: 584–590.[CrossRef][Medline]
Lave T, Levet-Trafit B, Schmitt-Hoffmann AH, Morgenroth B, Richter W, and Chou RC (1995) Interspecies scaling of interferon disposition and comparison of allometric scaling with concentration-time transformations. J Pharm Sci 84: 1285–1290.[CrossRef][Medline]
Lee FH, Pfeffer M, Van Harken DR, Smyth RD, and Hottendorf GH (1980) Comparative pharmacokinetics of ceforanide (BL-S786R) and cefazolin in laboratory animals and humans. Antimicrob Agents Chemother 17: 188–192.[Abstract/Free Full Text]
Lin CC, Lim J, Radwanski E, Kim HK, Marco A, Lapiguera A, DiGiore C, and Symchowicz S (1987) Pharmacokinetics and metabolism of an intravenously administered penem (Sch 34343) in humans. Antimicrob Agents Chemother 31: 84–87.[Abstract/Free Full Text]
Mahmood I (1999) Prediction of clearance, volume of distribution and half-life by allometric scaling and by use of plasma concentrations predicted from pharmacokinetic constants: a comparative study. J Pharm Pharmacol 51: 905–910.[CrossRef][Medline]
Mahmood I and Balian JD (1996a) Interspecies scaling: predicting clearance of drugs in humans. Three different approaches. Xenobiotica 26: 887–895.[Medline]
Mahmood I and Balian JD (1996b) Interspecies scaling: predicting pharmacokinetic parameters of antiepileptic drugs in humans from animals with special emphasis on clearance. J Pharm Sci 85: 411–414.[CrossRef][Medline]
Mahmood I and Sahajwalla C (2002) Interspecies scaling of biliary excreted drugs. J Pharm Sci 91: 1908–1914.[CrossRef][Medline]
Matsushita H, Suzuki H, Sugiyama Y, Sawada Y, Iga T, Hanano M, and Kawaguchi Y (1990) Prediction of the pharmacokinetics of cefodizime and cefotetan in humans from pharmacokinetic parameters in animals. J Pharmacobio-Dyn 13: 602–611.[Medline]
McGovren JP, Williams MG, and Stewart JC (1988) Interspecies comparison of acivicin pharmacokinetics. Drug Metab Dispos 16: 18–22.[Abstract]
Mordenti J (1986) Man versus beast: pharmacokinetic scaling in mammals. J Pharm Sci 75: 1028–1040.[Medline]
Mordenti J, Chen SA, Moore JA, Ferraiolo BL, and Green JD (1991) Interspecies scaling of clearance and volume of distribution data for five therapeutic proteins. Pharm Res (NY) 8: 1351–1359.
Murakawa T, Sakamoto H, Fukada S, Nakamoto S, Hirose T, Itoh N, and Nishida M (1980) Pharmacokinetics of ceftizoxime in animals after parenteral dosing. Antimicrob Agents Chemother 17: 157–164.[Abstract/Free Full Text]
Ohshima T, Hasegawa T, Johno I, and Kitazawa S (1991) Protein binding of cefpiramide in the plasma of various species. J Pharm Pharmacol 43: 805–806.[Medline]
Owens SM, Hardwick WC, and Blackall D (1987) Phencyclidine pharmacokinetic scaling among species. J Pharmacol Exp Ther 242: 96–101.[Abstract/Free Full Text]
Patel BA, Boudinot FD, Schinazi RF, Gallo JM, and Chu CK (1990) Comparative pharmacokinetics and interspecies scaling of 3'-azido-3'-deoxythymidine (AZT) in several mammalian species. J Pharmacobio-Dyn 13: 206–211.[Medline]
Paxton JW, Kim SN, and Whitfield LR (1990) Pharmacokinetic and toxicity scaling of the antitumor agents amsacrine and CI-921, a new analogue, in mice, rats, rabbits, dogs and humans. Cancer Res 50: 2692–2697.[Abstract/Free Full Text]
Puigdemont A, Guitart R, de Mora F, and Arboix M (1991) Prediction of the disposition of propafenone in humans and dogs from pharmacokinetic parameters in other animal species. J Pharm Sci 80: 1106–1109.[CrossRef][Medline]
Robbie G and Chiou WL (1998) Elucidation of human amphotericin B pharmacokinetics: identification of a new potential factor affecting interspecies pharmacokinetic scaling. Pharm Res (NY) 15: 1630–1636.
Sawada Y, Hanano M, Sugiyama Y, and Iga T (1984) Prediction of the disposition of beta-lactam antibiotics in humans from pharmacokinetic parameters in animals. J Pharmacokinet Biopharm 12: 241–261.[CrossRef][Medline]
Siefert HM, Domdey-Bette A, Henninger K, Hucke F, Kohlsdorfer C, and Stass HH (1999) Pharmacokinetics of the 8-methoxyquinolone, moxifloxacin: a comparison in humans and other mammalian species. J Antimicrob Chemother 43 (Suppl B): 69–76.[Abstract]
Tsunekawa Y, Hasegawa T, Nadai M, Takagi K, and Nabeshima T (1992) Interspecies differences and scaling for the pharmacokinetics of xanthine derivatives. J Pharm Pharmacol 44: 594–599.[Medline]
Ubeaud G, Schmitt C, Jaeck D, Lave T, and Coassolo P (1995) Bosentan, a new endothelin receptor antagonist: prediction of the systemic plasma clearance in man from combined in vivo and in vitro data. Xenobiotica 25: 1381–1390.[Medline]
Walker DK, Ackland MJ, James GC, Muirhead GJ, Rance DJ, Wastall P, and Wright PA (1999) Pharmacokinetics and metabolism of sildenafil in mouse, rat, rabbit, dog and man. Xenobiotica 29: 297–310.[CrossRef][Medline]
West GB, Brown JH, and Enquist BJ (1997) A general model for the origin of allometric scaling laws in biology. Science (Wash DC) 276: 122–126.[Abstract/Free Full Text]
This article has been cited by other articles:
|
|
|
|
 
H. Tang and M. Mayersohn
Utility of the Coefficient of Determination (r2) in Assessing the Accuracy of Interspecies Allometric Predictions: Illumination or Illusion?
Drug Metab. Dispos.,
December 1, 2007;
35(12):
2139 - 2142.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
H. Tang, A. Hussain, M. Leal, M. Mayersohn, and E. Fluhler
Interspecies Prediction of Human Drug Clearance Based on Scaling Data from One or Two Animal Species
Drug Metab. Dispos.,
October 1, 2007;
35(10):
1886 - 1893.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
I. Mahmood
COMMENTS ON "A MATHEMATICAL DESCRIPTION OF THE FUNCTIONALITY OF CORRECTION FACTORS USED IN ALLOMETRY FOR PREDICTING HUMAN DRUG CLEARANCE"
Drug Metab. Dispos.,
March 1, 2006;
34(3):
507 - 509.
[Abstract]
[Full Text]
[PDF]
|
|
|
|
|
|
|
H. Tang and M. Mayersohn
A MATHEMATICAL DESCRIPTION OF THE FUNCTIONALITY OF CORRECTION FACTORS USED IN ALLOMETRY FOR PREDICTING HUMAN DRUG CLEARANCE
Drug Metab. Dispos.,
September 1, 2005;
33(9):
1294 - 1296.
[Abstract]
[Full Text]
[PDF]
|
|
|
![[Feedback]](/icons/banner/feedbackACT.gif)
![[For Subscribers]](/icons/banner/subscriberACT.gif)
![[Archive]](/icons/banner/archiveACT.gif)
![[Search]](/icons/banner/searchACT.gif)
![[Contents]](/icons/banner/tocACT.gif)
Top
Abstract
Materials and Methods
