Rule Of Exponents Research Articles

UNVEILING HIDDEN MISCONCEPTIONS: A NEW PERSPECTIVE ON FIRST-YEAR STUDENTS' ALGEBRAIC UNDERSTANDING

This study aims to uncover and analyze hidden misconceptions in algebraic understanding among first-year students in the Mathematics Education Department at a private university in Malang. Conducted from January to March 2024, the research involves two first-year students as subjects. The first subject exhibits the misconception known as "illegal canceling," while the second subject demonstrates the "assumption of distributivity of exponents." Utilizing a qualitative research methodology, diagnostic interviews and problem-solving tasks were employed to identify and understand these misconceptions. Our findings indicate that these hidden misconceptions significantly hinder the students' ability to correctly solve algebraic problems and understand underlying concepts. For the first subject, the error in illegal canceling often led to incorrect simplifications, while the second subject's erroneous application of exponent rules resulted in fundamentally flawed solutions. By systematically categorizing these misconceptions, the study offers tailored instructional strategies to effectively address and correct them.This research highlights the critical need for early detection and targeted intervention in mathematical education. By providing a deeper insight into specific algebraic misunderstandings, the study suggests practical approaches for educators to enhance their teaching methodologies, ultimately improving students' overall algebra comprehension. The novelty of this research lies in its detailed focus on hidden misconceptions and the provision of actionable solutions, offering a fresh perspective on improving algebra education for first-year university students.

Effect of Zinc on the Tensile Properties, Microstructure and characteristics in Aluminum Alloys

The existing work characterizes the consequence of Zinc increase of the precise structure, thermal and mechanical characteristic of Aluminum by supplement 60% Zinc and 10 % Zinc to fine Aluminum alloy to gained Zinc-40Aluminium and Zinc-90Aluminium. The study presented that the superplasticity of Zinc-90Aluminium is reduced compared with Zinc-40Aluminium. The strain rate (SR; .) and temperature (T) are having extremely influence on tensile figure. Too (SR; .) and (T) donate excellent Young's modulus (Y), ultimate tensile stress (UTS), yield stress (σy), and fracture strength (breaking strength) σf associated with the exponent rule σ =Ce•m; where C is a fixed number and m is the strain average sensitivity index; while strain rate and temperature decrease fracture strain (ef ). The tensile figures are (T) and (SR;  .) dependence. Stress-strain characteristics of Zinc-40Aluminium and Zinc-90Aluminium alloys were investigated at various strain rates (SR, e•) from 5.0×10-4 to 6.4×10-3 s-1 and deformation temperatures from 298 to 393 K. In case of Zinc-90Aluminium; it has higher ultimate tensile stress (UTS) i.e. Zinc-40Aluminium is more in elongation (ductility) than Zinc-90Aluminium. A common decrease of strain eT with (SR;  .) is characterized by the equation eT =Aexp(-λe•m); A and λ are constant. The results depend on variation precise structure. The Zinc supplement from 10% to40% refines the precise structure, enhancing the mechanical properties, and form increase the ductility.

Interspecies Scaling of Antibody-Drug Conjugates (ADC) for the Prediction of Human Clearance.

Allometric scaling is a useful tool for the extrapolation of pharmacokinetic parameters from animals to humans. The objective of this study was to predict human clearance of antibody–drug conjugates (ADC) allometrically from one to three animal species and compare the predicted human clearance with the observed human clearance. For three animal species allometric scaling, the “Rule of Exponents” (ROE) was used. The results of the study indicated that three-species allometric scaling in association with the ROE provides acceptable prediction (within 0.5–2-fold prediction error) of human clearance. The two-species allometric scaling resulted in substantial prediction error. One-species scaling using a fixed exponent of 1.0 provided acceptable prediction error (within 0.5–2-fold) by monkey, rat, and mouse, in which monkey and rat were comparable. Overall, the predicted human clearance values of ADCs from animal(s) was good. The allometric method proposed in this article can be used to predict human clearance from the animal data and subsequently to select the first-in-human dose of ADCs.

On certain dynamic properties of difference sequences and the fractional derivatives

Recently, the notion of difference operators based on fractional‐order is being extensively used in linear algebra, approximation theory, the theory of fractional calculus (FC), and many others. In this paper, an attempt has been taken for studying the convergence of difference sequence and hence analyzing the consistency and validity of certain related formulas. Investigations on basic results involving convergence, linearity, exponent rule, topological properties, Leibniz, and chain rules for fractional derivatives have been incorporated. In this context, some well‐known results have been demonstrated and verified with the help of some illustrative examples.

Prediction of Human Pharmacokinetics of Antibody-Drug Conjugates From Nonclinical Data.

Prediction of human pharmacokinetics (PK) based on preclinical information for antibody–drug conjugates (ADCs) provide important insight into first‐in‐human (FIH) study design. This retrospective analysis was conducted to identify an appropriate scaling method to predict human PK for ADCs from animal PK data in the linear range. Different methods for projecting human clearance (CL) from animal PK data for 11 ADCs exhibiting linear PK over the tested dose ranges were examined: multiple species allometric scaling (CL vs. body weight), allometric scaling with correction factors, allometric scaling based on rule of exponent, and scaling from only cynomolgus monkey PK data. Two analytes of interest for ADCs, namely total antibody and conjugate (measured as conjugated drug or conjugated antibody), were assessed. Percentage prediction errors (PEs) and residual sum of squares (RSS) were compared across methods. Human CL was best estimated using cynomolgus monkey PK data alone and an allometric scaling exponent of 1.0 for CL. This was consistently observed for both conjugate and total antibody analytes. Other scaling methods either underestimated or overestimated human CL, or produced larger average absolute PEs and RSS. Human concentration‐time profiles were also reasonably predicted from the cynomolgus monkey data using species‐invariant time method with a fixed exponent of 1.0 for CL and 1.0 for volume of distribution. In conclusion, results from this retrospective analysis of 11 ADCs indicate that allometric scaling of CL with an exponent of 1.0 using cynomolgus monkey PK data alone can successfully project human PK profiles of an ADC within linear range.

TIPE-TIPE KESALAHAN SISWA DALAM MENYELESAIKAN SOAL MATEMATIKA PADA ATURAN EKSPONEN DAN SCAFFOLDINGNYA: STUDI KASUS DI SMKN 11 MALANG

Types of Students’ Errors on Completing Math Problems in the Exponent Rules and its Scaffolding: Case Study in SMKN 11 Malang. This research aims to analyze errors made by students on applying exponent rules and to describe the form of scaffolding to overcome these errors. The method was a descriptive method with a qualitative approach. Furthermore, a test and an interview were used to collect data from students at class X Nurse 1 in SMKN 11 Malang. Data were analyzed by taking notes of answers, identifying factors that become thoughts, classifying student difficulties, and drawing conclusions. The results showed that the types of student errors on applying exponent rules were basic errors, missing information, and partial insight. Meanwhile, the forms of scaffolding given to students were environmental provisions, reviewing and restructuring, and developing contextual thinking. The research concluded that the learning process was very important for student learning success.

A note on fractional difference operators

In the present article, following on very recent and new approach of fractional difference operator by Baliarsingh (2016), we establish some new ideas involving the exponent rules of this operator. In fact, the new results are sufficient enough to describe the results obtained by Baliarsingh and also provide certain improvements on them.

Retrospective and Prospective Human Intravenous and Oral Pharmacokinetic Projection of Dipeptidyl peptidase-IV Inhibitors Using Simple Allometric Principles – Case Studies of ABT-279, ABT-341, Alogliptin, Carmegliptin, Sitagliptin and Vildagliptin

The purpose of this exercise was to explore the utility of allometric scaling approach for the prediction of intravenous and oral pharmacokinetics of six dipeptidy peptidase-IV (DPP-IV) inhibitors viz. ABT-279, ABT-341, alogliptin, carmegliptin, sitagliptin and vildagliptin. The availability of intravenous and oral pharmacokinetic data in animals enabled the allometry scaling of 6 DPP-IV inhibitors. The relationship between the main pharmacokinetic parameters [viz. volume of distribution (Vd) and clearance (CL)] and body weight was studied across three or four mammalian species, using double logarithmic plots to predict the human pharmacokinetic parameters of CL and Vd using simple allometry. A simply allometry relationship: Y = aWb was found to be adequate for the prediction of intravenous and oral human clearance/volume of distribution for DPP-IV inhibitors. The allometric equations for alogliptin, carmegliptin, sitagliptin, vildagliptin, ABT-279 and ABT-341 were 1.867W0.780, 1.170W0.756, 2.020W0.529, 1.959 W0.847, 0.672 W1.016, 1.077W 0.649, respectively, to predict intravenous clearance (CL) and the corresponding equations to predict intravenous volume of distribution (Vd) were: 3.313W0.987, 6.096W0.992, 7.140W0.805, 2.742W0.941, 1.299W0.695 and 5.370W0.803. With the exception of a few discordant values the exponent rule appeared to hold for CL (0.75) and Vd (1.0) for the predictions of various DPP-IV inhibitors. Regardless of the routes, the predicted values were within 2-3 fold of observed values and intravenous allometry was better than oral allometry. Simple allometry retrospectively predicted with reasonable accuracy the human reported values of gliptins and could be used as a prospective tool for this class of drugs.

Superdiffusion and transport in two-dimensional systems with Lévy-like quenched disorder.

We present an extensive analysis of transport properties in superdiffusive twodimensional quenched random media, obtained by packing disks with radii distributed according to a Lévy law. We consider transport and scaling properties in samples packed with two different procedures, at fixed filling fraction and at self-similar packing, and we clarify the role of the two procedures in the superdiffusive effects. Using the behavior of the filling fraction in finite size systems as the main geometrical parameter, we define an effective Lévy exponent that correctly estimates the finite size effects. The effective Lévy exponent rules the dynamical scaling of the main transport properties and identifies the region where superdiffusive effects can be detected.

Contrasting toxicokinetic evaluations and interspecies pharmacokinetic scaling approaches for small molecules and biologics: applicability to biosimilar development

1. A 2-fold threshold typically used for prediction accuracy of interspecies scaling of clearance (CL) may be too liberal when using pharmacokinetic similarity in animals to advance biosimilar candidate selection for clinical testing. The purpose of this review is to identify interspecies scaling methods for use in de-risking biosimilar development prior to clinical testing.2. Scaling approaches for predicting macromolecule CL were identified through literature review. Reports that evaluated predicted and observed human CLs for ≥5 individual compounds were considered. Absolute average fold-error (AAFE) was calculated for each method along with the proportion of compounds with individual fold-error values within a tighter threshold of 0.7–1.3.3. Traditional simple allometry with a minimum of three species and the rule of exponents performed inconsistently with some groups of compounds resulting in a greater than 2-fold error (i.e. AAFE > 2). For monoclonal antibodies (mAbs), simplified allometric approaches employing a single species (monkey) with a fixed exponent of 0.85 consistently resulted in lower AAFEs and a higher proportion of compounds within the tighter range of 0.7–1.3.4. For macromolecules, and particularly mAbs, employing single-species monkey “simplified” allometric approaches with a fixed exponent of 0.85 may be more appropriate than traditional allometric approaches.

Interspecies scaling of biliary excreted drugs: prediction of human clearance and volume of distribution

Interspecies differences in biliary excretion and the differences in bile flow rates make scaling across species difficult for drugs that are excreted in the bile. The objective of this study is to predict clearance (CL) and volume of distribution (V) for humans from animals for drugs that are excreted in the bile. Clearance values of 10 drugs known to be excreted in the bile were selected from the literature. Scaling of CL was performed using at least three animal species. Using simple allometry and the rule of exponents (ROE), clearances of studied drugs were predicted in humans. Besides using the ROE, a 'correction factor' was applied adjusting bile flow rate based on the species body weight (bile flow mL/day/kg body weight) or liver weight (bile flow mL/day/kg liver weight). Using the ROE and combining it with the 'correction factor', the clearances of biliary excreted drugs were predicted for humans. V for 15 drugs (without any correction factor) that are excreted in the bile was also predicted for humans. The results of the study indicated that the ROE in association with the correction factors developed for the biliary excreted drugs substantially improved the prediction of human clearance for drugs that are excreted in the bile. In this study, there was no indication (unlike clearance) that the prediction of volume of drug distribution was affected (systematically under- or over-prediction) because of biliary excretion. The clearance of drugs that are excreted in the bile can be predicted with reasonable accuracy using ROE and a correction factor.

Preclinical Pharmacokinetics of MI-219, a Novel Human Double Minute 2 (HDM2) Inhibitor and Prediction of Human Pharmacokinetics

The two purposes of this study were evaluating preclinical pharmacokinetics of MI-219 and predicting clearance (CL) and volume of distribution at steady-state (Vdss) of MI-219 in humans. Pharmacokinetic studies were conducted on mice, rats, dogs, and monkeys. Human CL of MI-219 was predicted using allometric scaling (SA), multi-exponential allometric scaling (ME), rule of exponents (RoE), single species scaling, two-term power equation (TTPE), physiologically based in vitro-in vivo extrapolation (IVIVE), and fu corrected intercept method (FCIM). In vitro assays were conducted to determine in vitro intrinsic CL, protein binding, and blood-plasma partition coefficients. To estimate half-life of MI-219, plasma concentration-time profile in humans was predicted using kallynochron and apolysichron time transformation (Dedrick plots) and normalization with MRT and Vdss (Wajima's method). In addition, simultaneous interspecies scaling of CL, Vdss and concentration-time profile were performed by using Nonlinear Mixed Effects Modeling (NONMEM). Preclinical studies showed that the elimination of MI-219 was mainly through metabolism. The validation using observed monkey CL and Vdss showed that MA, IVIVE and Oie-Tozer methods were accurately than the other methods. Human CL of MI-219 predicted by ME and IVIVE was between 0.237-0.342 L*h⁻¹*kg⁻¹. Human Vdss predicted by Oie-Tozer method and allometric scaling of unbound volume of distribution of tissues (VT/fuT) method was between 0.93-1.40 L*kg⁻¹. Superimposition of rat, monkey and dog data was observed in Dedrick plots and Wajima's transformations. The predicted human pharmacokinetics is useful for the design of first-in-human study.

Towards a Better Prediction of Peak Concentration, Volume of Distribution and Half-Life after Oral Drug Administration in Man, Using Allometry

It is imperative that new drugs demonstrate adequate pharmacokinetic properties, allowing an optimal safety margin and convenient dosing regimens in clinical practice, which then lead to better patient compliance. Such pharmacokinetic properties include suitable peak (maximum) plasma drug concentration (C(max)), area under the plasma concentration-time curve (AUC) and a suitable half-life (t(½)). The C(max) and t(½) following oral drug administration are functions of the oral clearance (CL/F) and apparent volume of distribution during the terminal phase by the oral route (V(z)/F), each of which may be predicted and combined to estimate C(max) and t(½). Allometric scaling is a widely used methodology in the pharmaceutical industry to predict human pharmacokinetic parameters such as clearance and volume of distribution. In our previous published work, we have evaluated the use of allometry for prediction of CL/F and AUC. In this paper we describe the evaluation of different allometric scaling approaches for the prediction of C(max), V(z)/F and t(½) after oral drug administration in man. Twenty-nine compounds developed at Janssen Research and Development (a division of Janssen Pharmaceutica NV), covering a wide range of physicochemical and pharmacokinetic properties, were selected. The C(max) following oral dosing of a compound was predicted using (i) simple allometry alone; (ii) simple allometry along with correction factors such as plasma protein binding (PPB), maximum life-span potential or brain weight (reverse rule of exponents, unbound C(max) approach); and (iii) an indirect approach using allometrically predicted CL/F and V(z)/F and absorption rate constant (k(a)). The k(a) was estimated from (i) in vivo pharmacokinetic experiments in preclinical species; and (ii) predicted effective permeability in man (P(eff)), using a Caco-2 permeability assay. The V(z)/F was predicted using allometric scaling with or without PPB correction. The t(½) was estimated from the allometrically predicted parameters CL/F and V(z)/F. Predictions were deemed adequate when errors were within a 2-fold range. C(max) and t(½) could be predicted within a 2-fold error range for 59% and 66% of the tested compounds, respectively, using allometrically predicted CL/F and V(z)/F. The best predictions for C(max) were obtained when k(a) values were calculated from the Caco-2 permeability assay. The V(z)/F was predicted within a 2-fold error range for 72% of compounds when PPB correction was applied as the correction factor for scaling. We conclude that (i) C(max) and t(½) are best predicted by indirect scaling approaches (using allometrically predicted CL/F and V(z)/F and accounting for k(a) derived from permeability assay); and (ii) the PPB is an important correction factor for the prediction of V(z)/F by using allometric scaling. Furthermore, additional work is warranted to understand the mechanisms governing the processes underlying determination of C(max) so that the empirical approaches can be fine-tuned further.

Comparative Assessment of Empirical and Physiological Approaches on Predicting Human Clearances

The empirical and physiological predictive approaches to human clearance were evaluated using preclinical in vitro and in vivo data of various datasets to establish a methodology for the prediction of clearance. Among the examined empirical approaches, an allometric scaling method with the rule of exponent (ROE), based on the exponent in simple allometry, provided better prediction. The effect of lipophilicity (clog P) and clearance on the predictivity was investigated using the ROE method. High predictivity was found for a low lipophilic compound with clog P < 0 and for a compound with moderate or high clearance. As a physiological approach, the in vitro-in vivo scaling method using metabolic stability in liver microsomes and hepatocytes was evaluated, and the predictivity taking the plasma protein binding and the nonspecific binding in incubation into consideration was compared with the ROE method. The two methods appeared to show comparable predictivity, although the in vitro-in vivo scaling was conducted under limited conditions like the use of physiological scaling factor and lipophilicity-derived nonspecific binding data. The ROE method could be an alternative predictor of the human clearance of compounds to which a physiological approach cannot be applied, in addition to low lipophilic compounds, with acceptable accuracy.

Human Pharmacokinetic Prediction of UDP-Glucuronosyltransferase Substrates with an Animal Scale-Up Approach

The aim of the current study was to evaluate the accuracy of allometric scaling methods for drugs metabolized by UDP-glucuronosyltransferases (UGTs), such as ketoprofen, imipramine, lorazepam, levofloxacin, zidovudine, diclofenac, furosemide, raloxifene, gemfibrozil, mycophenolic acid, indomethacin, and telmisartan. Human plasma clearance (CL) predictions were conducted from preclinical in vivo data by using multiple-species allometry with the rule of exponents and single-species allometric scaling (SSS) of mice, rats, monkeys, or dogs. Distribution volume at a steady state (V(ss)) was predicted by multiple-species allometry or SSS of V(ss). Oral plasma clearance (CL(po)) was calculated under the assumption that F(a) × F(g) was equivalent across species. Each of the results was compared with the observed parameter calculated from the clinical data after intravenous or oral administration. Multiple-species allometry and SSS of mice, rats, and dogs resulted in a similar accuracy of CL and CL(po) predictions. Monkeys tended to provide the most accurate predictions of human CL and CL(po). The ability to predict the half-life, which was determined from CL and V(ss) predictions, was more accurate in SSS of rats and monkeys. The in vivo fraction metabolized by glucuronidation (f(m,UGT)) in bile duct-cannulated monkeys was relatively similar to that of humans compared with other animal species, which likely contributed to the highest accuracy of SSS prediction of monkeys. On the basis of the current results, monkeys would be more reliable than other animal species in predicting human pharmacokinetics and f(m,UGT) for drugs metabolized by UGTs.

Projecting human pharmacokinetics of therapeutic antibodies from nonclinical data

The pharmacokinetics (PK) of therapeutic antibodies is determined by target and non-target mediated mechanisms. These antibody-specific factors need to be considered during prediction of human PK based upon preclinical information. Principles of allometric scaling established for small molecules using data from multiple animal species cannot be directly applied to antibodies. Here, different methods for projecting human clearance (CL) from animal PK data for 13 therapeutic monoclonal antibodies (mAbs) exhibiting linear PK over the tested dose ranges were examined: simple allometric scaling (CL versus body weight), allometric scaling with correction factors, allometric scaling based on rule of exponent and scaling from only cynomolgus monkey PK data. A better correlation was obtained between the observed human CL and the estimated human CL based on cynomolgus monkey PK data and an allometric scaling exponent of 0.85 for CL than other scaling approaches. Human concentration-time profiles were also reasonably predicted from the cynomolgus monkey data using species-invariant time method with a fixed exponent of 0.85 for CL and 1.0 for volume of distribution. In conclusion, we expanded our previous work and others and further confirmed that PK from cynomolgus monkey alone can be successfully scaled to project human PK profiles within linear range using simplify allometry and Dedrick plots with fixed exponent.

Predicting Total Clearance in Humans from Chemical Structure

A conceptually simple, fully in silico model to predict total clearance of new compounds in humans is described. Based on the premise that similar molecules will exhibit similar pharmacokinetic properties, we used a k-nearest-neighbors (kNN) technique to predict total clearance by comparison with known reference agents. Molecular similarity was defined using readily calculated one- and two-dimensional molecular descriptors, and the reference set was obtained by combining the Obach and Berellini sets of human pharmacokinetic data. Neutral molecules and drugs whose biological activity is associated with a metal center were removed from the combined set. The remaining 462 compounds were partitioned into a training and external test set of 370 and 92 compounds, respectively. For acids, bases, zwitterions, and quaternary ammonium/pyridinium ions, average prediction accuracy was within two-fold of observed for the external test set (n = 92). Using a collection of 20 drugs from the literature with > or =3 preclinical animal species allometric scaling data, accuracy of the in silico kNN model was not as good as the rule of exponents, but better than simple allometry (SA), and approached that of combination multiexponential allometry (ME) as defined by the number of predictions with < or =50% error. For a collection of 18 drugs with two species (rat-dog) data, the kNN model outperformed both SA and combination ME using the same performance standard. Since the model is fully in silico and, therefore, capable of generating total clearance predictions in the absence of any experimental data, it can be used to help guide early drug discovery research efforts, such as virtual compound library screening, and analogue prioritization prior to chemical synthesis and biological evaluation. Model validation was accomplished using the external test set, three- and five-fold cross-validation and two different y-randomization techniques (y-shuffling and random number pseudodescriptors).

Prediction of human clearance of therapeutic proteins: simple allometric scaling method revisited

In this report, the utility of a commonly used interspecies scaling method to predict the systemic clearance (CL) of therapeutic proteins in humans was evaluated. Based on analysis of a pharmacokinetic data set of 34 therapeutic proteins, including 12 monoclonal antibodies (mAbs) and Fc fusion proteins, human CL can generally be predicted reasonably well with simple allometric scaling and a fixed exponent of 0.8: approximately 95% of the cases predicted values within 2-fold of the observed values when using CL data from multiple species, or approximately 90% simply using CL from monkeys. Specific to mAbs/Fc fusion proteins, scaling from monkey CL using a fixed exponent of 0.8 gave an excellent prediction; all predicted CL values were within 2-fold of the corresponding observed values. Compared with the simple allometric scaling method that uses a fitted exponent from CL data of > or =3 preclinical species, the fixed exponent approach with 1-2 preclinical species is simple, resource-saving and minimizes systematic bias. Together with its overall satisfactory prediction accuracy, especially in the absence of non-linear pharmacokinetics and species-specific clearance mechanisms, this fixed exponent method affords a viable alternative to other published allometric methods, including the Rule of Exponents (ROE).

Role of Fixed Coefficients and Exponents in the Prediction of Human Drug Clearance: How Accurate are the Predictions from One or Two Species?

Pharmacokinetic (PK) interspecies scaling is generally conducted using PK data from at least three animal species but three animal species may not be always available. In a recent manuscript, Tang et al. have described the methods to predict human drug clearance using one or two animal species. The authors claim that their proposed methods are better than the rule of exponents (ROE) which uses at least three animal species for the prediction of human drug clearance. A thorough examination of Tang et al.'s manuscript indicates that the data analysis may not be accurate. Considering that Tang et al.'s method may be of value, the objective of this study was to extend Tang et al.'s proposed methods for drugs given both intravenously and orally. The results of this study indicate that human drug clearance cannot be predicted with reasonable accuracy for most of the drugs by Tang et al.'s proposed methods and the accuracy of the prediction obtained from the ROE remains more accurate (based on average fold-error) than the one or two-species methods. This manuscript also clarifies some incorrect views regarding ROE presented by Tang et al. in their manuscript.

Application of Fixed Exponent 0.75 to the Prediction of Human Drug Clearance: An Inaccurate and Misleading Concept

Considering the controversy surrounding the exponent of 0.75 for the prediction of human drug clearance and lack of any systematic evaluation of the aforementioned proposal, the objective of this study was to determine whether the exponent 0.75 is indeed the most suitable exponent for the prediction of human drug clearance as compared to allometric scaling using the rule of exponents (ROE). Three methods were used to predict human drug clearance. Besides evaluating the exponent of 0.75, an arbitrarily selected exponent of 0.65 was also tested. ROE was also used to predict human drug clearance, and predicted values by all three methods were compared with observed human drug clearance. The results indicate that the exponent 0.75 is not the best approach for the prediction of human drug clearance. Both exponents 0.75 and 0.65 predicted human drug clearance with uncertainty, although on average the prediction of human drug clearance by 0.65 was better than the exponent 0.75. ROE provided far more accurate prediction of human drug clearance than either of the exponents. Although exponent 0.75 occasionally provided a good prediction of human drug clearance for a given drug for a given species, overall, the method is highly erratic and unreliable.