Background and

User’s Guide

Comparative Child/Adult Pharmacokinetic Database based upon the Therapeutic Drug Literature

Dale Hattis, Abel Russ, Prerna Banati, Mary Kozlak, and Rob GobleClark University

and

Gary Ginsberg and Susan SmolenskiConnecticut Department of Public Health

September, 2001

EPA/State of Connecticut Assistance Agreement #827195-0,Dr. Bob Sonawane, EPA Project Monitor

Table of Contents

1.0 Introduction ………………………………………………………………… 11.1 Goals of the Current Project …..…………………………………… 2

2.0 Methods and Approaches Used for Database Development ……………….. 32.1 Compilation and Description of the Database ………...………... 32.1.1 The Central Database …………………………………………….. 82.1.2 Data Files from Individual Papers ……………………………….. 122.1.3 Files Documenting the Regression Analysis ……………..…….. 13

3.0 References ……………………………………………………………………18

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1.0 Introduction

The risks that children incur from environmental chemicals may be quite different than

risks in adults due to a number of factors: 1) the degree of exposure tends to be greater in young

children due to a greater inhalation rate and food ingestion rate (particularly for certain foods)

per body weight, and greater contact with soil, house dust, and other media which may contain

contaminants (USEPA, 1997); 2) once exposure has occurred, the pharmacokinetic (PK)

handling of chemicals is likely to differ from that in the adult with respect to chemical half-life,

clearance, protein binding, and volume of distribution (Morselli, 1989; Besunder, et al., 1988;

Kearns and Reed, 1989) 3) the sensitivity of rapidly developing tissues and systems in neonates

and young children may differ from that in adults leading to pharmacodynamic (PD) differences

(Faustman, et al., 2000; Vesselinovitch, et al., 1979).

While all three areas of child-adult differences need to be addressed, the focus of the

current project is the second area - the potential for PK differences to play a significant role in

modifying risks to children. Physiologic and metabolic factors govern the PK processes of

chemical absorption, distribution, metabolism, and excretion. These processes in turn determine

the effective internal concentration of a chemical and its metabolites, some of which may be

more or less toxic than the parent compound. Given the differences in physiology (e.g., body

size, lipid and water content) between adults and children and the immaturity of many systems

in young children (e.g., liver metabolizing enzymes, plasma protein binding, renal excretion,

blood-brain barrier function), it is likely that substantial PK differences exist in young children,

at least at certain age groups and for certain chemicals.

PK differences across human receptors are currently factored into the risk assessment

process. The existing approach for non-cancer risk assessment is to use a 10 fold uncertainty

factor to reduce exposure for potential inter-individual differences across the human population.

This 10 fold factor can be thought of as constituting a half log (3.2) factor for PK differences

among human receptors and another half log factor for PD differences (Renwick, 1998). The

3.2 fold PK factor is expected to account for racial, ethnic, gender, genetic, and age differences,

as well as inter-individual differences due to disease states, and intake of drugs. This latter

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factor can modify chemical metabolism and fate via enzyme induction, displacement from serum

proteins, and other PK mechanisms. It should be noted that since uncertainty factors are

traditionally not used in cancer risk assessment, there is no attempt to account for PK variability

across individuals in such assessments.

1.1 Goals of the Current Project

The primary goal of the current project is to define the types of parameters and range of

ages where PK differences between children and adults that may be of greatest importance to

risk assessment. To accomplish this goal, a children’s PK database was constructed from the

therapeutic drug literature. The pharmacokinetics of many drugs have been evaluated in

children to determine the dose levels most appropriate for this age group. When combined with

adult PK studies of the same drugs, direct comparisons between adult and child PK can be made.

By evaluating PK datasets across chemicals with differing structures and clearance mechanisms

(e.g., renal excretion, Phase I metabolism, Phase II metabolism), it is anticipated that differences

between adults and children in terms of key metabolism and removal pathways will become

evident.

In addition to evaluating clearance pathways and specific age groupings for possible

differences with adults, the current project uses the children’s PK database to evaluate the

degree of inter-subject variability seen in the children’s and adult PK datasets. Given that

children are rapidly growing, any pre-set age category will include individuals along a

developmental continuum. This creates a type of PK variability that is likely to be more

important in children than in adults, and thus is critical to identify,quantitate, and incorporate

into children’s risk assessments. By evaluating both the difference in mean value of PK

parameters (e.g., clearance, half-life) and also the inter-subject variability in these parameters

across ages, this research endeavors to provide some perspective on whether the 3.2 fold

uncertainty factor intended to account for PK variability in the human population is sufficient

for children.

This User’s Guide provides information on how the database is constructed so that the key

information can be accessed and utilized. Manuscripts recently submitted to peer review

journals further describe the database and 1) how the mean values of children’s PK paramaters

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compare to adult levels (Ginsberg, et al., 2001); and 2) how inter-subject variability among

children in specific age groups creates a distribution of PK function in relation to the mean

function as seen in adults (Hattis et al., 2001). These papers also describe ways in which the

current database may be useful in children’s risk assessments and places the assembled data in

the context of other children’s PK summaries (Renwick, 1998; Renwick et al., 2000; Morselli,

1989, Kearns and Reed, 1989; Gupta and Waldhauser, 1997; Cresteil, 1998).

2.0 Methods and Approaches used for Database Development

This project involved identification of chemicals from the therapeutic drug literature having

pertinent PK data for children, obtaining and evaluating the primary studies to extract key data,

obtaining comparable data for adults, organizing the data into a spreadsheet database, and

analyzing the data across age groups. The key data obtained from reviewed studies included:

number, gender, and age of subjects, type and number of doses, PK findings in terms of half-

life, clearance, volume of distribution, peak and area-under-the-curve blood concentrations, and

individual subject data or group variability statistics. The various steps involved are further

described below.

2.1 Compilation and Description of the Database

Computerized literature searches were conducted to find references to publications

describing children’s pharmacokinetics, using search words such as neonate, infant and children

and crossing these with terms such as pharmacokinetics, metabolism, distribution, excretion.

Additionally, a pediatric pharmacology text (Yaffe and Aranda, 1992 ) and review articles on

children’s PK (Anderson, 1997; Jacqz-Aigrain, 1996, Renwick, 1998) were examined to

identify chemicals for which PK datasets exist for children. Through these sources, a list of

approximately 100 chemicals from the therapeutic drug literature were identified as having at

least some PK data in children. A subset of 44 chemicals was selected for more detailed

analysis based upon being able to obtain the original data sources, these sources having a

reasonable number of subjects, the availability of data for pertinent age groups (especially very

early life stages), and considerations of clearance mechanism.

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The list of chemicals contained in the database and major clearance mechanisms are

shown in Table 1. Clearance mechanisms were identified from pharmacology texts (Dollery,

1999, Goodman and Gilman, 1990) a key review article (Bertz, 1997), as well as primary

literature for individual compounds as shown in the table. The table provides an indication of

the amount of human metabolism of each chemical, with the information generally from PK

studies in adults. Most chemicals are cleared by multiple pathways but typically one or two

routes of metabolism and elimination predominate. The table provides an estimate of the

percentage of parent compound processed by the major fate pathways.

The table indicates that of the 44 chemicals contained in the database, 8 chemicals (antibiotics:

ampicillin, gentamicin, pepracillin, ticarcillin, tobramycin, vancomycin; other drugs: cimetidine,

furosemide) are primarily excreted unchanged in urine and so half-life or clearance information

on these chemicals can be indicative of renal function at different ages. Regarding biliary

function, bromosulfophthalein (BSP) is the best indicator chemical in the current database given

that at least some of dosed BSP is excreted unchanged in bile. BSP has traditionally been used

as a clinical marker of hepato/biliary function. However, a portion of dosed BSP is conjugated

with glutathione prior to excretion in bile so the overall BSP clearance from blood is actually a

composite of these two pathways (GSH conjugation, biliary clearance of unchanged BSP)

(Fehring, et al, 1989).

Chemicals for which cytochrome p-450 (CYP) Phase I metabolism predominates are well

represented in the database, with numerous chemicals having some form of CYP as the primary

route of disposition. The most prevalent type of CYP substrate are those chemicals metabolized

by CYP3A (alfentanil, fentanyl, ketamine, lidocaine, midazolam, nifedipine, quinidine,

remifentanil, teniposide, triazolam), which is the predominant type of CYP in human liver.

Other types of CYPs for which information can be gained from chemicals present in the

database are CYP1A2 (bupivacaine, caffeine, mepivacaine, theophylline), and the CYP2C

family (amobarbital, tolbutamide). Some of the assignments made in the table are based upon

close structural analogy with a chemical or a group of chemicals for which CYP specificity is

known (e.g., remifentanil, mepivacaine).

Finally, chemicals cleared primarily via Phase II conjugation pathways without the need

for prior Phase I metabolism are also included in the database. Glucuronidation substrates total

6 (lorazepam, morphine, oxazepam, paracetamol, valproic acid, zidovudine), while sulfation

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(metoclopramide) and glutatione conjugation (busulfan, BSP) substrates are also contained in

the database. In some cases these assignments may best be described as general Phase II

substrates rather than substrates for a single conjugation pathway. This is exemplified best by

paracetamol, which is a candidate for glucuronidation, sulfation, and glutathione conjugation,

with a shift in pathways if the preferred substrate is not available (Besunder, et al., 1988).

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Table 1. Clearance Pathways for Chemicals in Children’s PK DatabaseChemical % Metabolized Metabolic Pathways Basis

Alfentanil >90% CYP3A4 (70%) Bertz, 97Amobarbital > 70% predom. Cyp 2C19; some gluc. Analogy w/related barbs;Bertz,97;G&G,

90Ampicillin low (75-90% renal) --- Bertz, 97Antipyrene high multiple p450s: 1A2, 2B6, 2C, 3A4 Engel, 96; Tanaka, 98Bromosulfphthalein not available biliary excretion; GSH conjugation Fehring, 1989Bupivacaine approx. 85% 1A2 (major); Cyp 3A4 (minor); Analogy with ropivicaine; Dollery, 99Busulfan >90% 40% GSH conj.; various other metab Dollery, 99; Ohmori, 98Caffeine >90% Cyp1A2 (90%)>>2E1 Bertz, 97Carbamazepine >90% Cyp 3A4 Dollery, 99; Gibbs, 97Chloral Hydrate >90% ADH most important Henderson, 97Cimetidine <30-40%; (70%

renal) Possible minor role for Cyps Bertz, 97

Clavulanic Acid 50 to 60% Unknown Dollery, 99Cotinine extensive Cyp 2A6 and glucuronidation Dempsey, 2000Dapsone 80-90% N-acetyl (50%), unknown cyp, gluc. Dollery, 99Dichloroacetic acid >90% Cyp hydrolysis; redn via radicals Stacpoole, 98Ethanol >90% ADH>Cyp 2E1>Catalase Dollery, 99Fentanyl >90% Major: Cyp 3A4; Minor: 2D6, 2C8/9 Bertz, 97; Guitton, 97Furosemide low (50-80% renal) Glucuronidation 20-50% Bertz, 97Gentamicin low (>90% renal) --- Goodman&Gilman, 90; Bertz, 97Ketamine 90% Cyp 3A and 2D; others possible Dollery, 99Lidocaine >90% Cyp 3A major; Cyp 1A2, 2B1 (minor) Dollery, 99Lorazepam >90% Glucuronidation without Phase I Dollery, 99; Bertz, 97Mepivicaine approx. 85% 1A2 (major); Cyp 3A4 (minor); Analogy with ropivicaine; Dollery, 99Metoclopramide 70% Sulfation (35%) > gluc (<20%) > Cyp Bertz, 97Midazolam >90% CYP3A (primary) Bertz, 97Morphine >90% Glucuronidation without Phase I Bertz, 97Nicotine >90% Cyp 2A6 - 80%; some glucuron. Dempsey, 2000Nifedipine >90% CYP3A4 (primary) Bertz, 97Oxazepam >90% Glucuronidation without Phase I Bertz, 97Paracetamol (acetamin) >90% Gluc (60%)>sulf (35%)>Cyp1A2,2E1 Bertz, 97Piperacillin low (70% renal) --- Goodman & Gilman, 90Quinidine >70% Cyp3A (>50%) Bertz, 97; Tanaka, 98Remifentanil >90% Cyp3A4 (major); 2D6, 2C8/9(minor) Analogy w/fentanyl & other congeners;

Guitton,97Teniposide 50% Cyp3A (primary) Analogy / etoposide, Bertz, 97, G&G,90Theophylline >90% Cyp1A2 (>70%) > 2E1 > 3A4 Bertz, 97Thiopentone >90% predom. Cyp 2C19; some gluc. Analogy w/related barbs;Bertz,97;G&G,

90Ticarcillin <10% (92% renal) --- Goodman & Gilman, 90Tobramycin <10%, (90% renal) --- Goodman & Gilman, 90Tolbutamide >90% Cyp 2C9/10 Bertz, 97Triazolam >90% Cyp 3A Bertz, 97Trichloloethanol extensive Glucuronidation Mayers, 91; Henderson, 97Valproic acid >90% Glucuronidation (20-70%)>Cyps Bertz, 97Vancomycin low (75-90% renal) --- Bertz, 97Zidovudine 60-80% Glucuron. (major) > Cyp3A (minor) Bertz, 97

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2.2 Database Structure and Contents

The database is available in a series of Microsoft Excel 95workbooks as briefly described in the

following listing. Additional details regarding several key workbooks and worksheets within

each workbook are provided thereafter.

Workbook ”chldpk9_01anal.xls”

“Central Database” worksheet: summary compilation of entire child and adult data organized by

drug, parameter, and age group. It provides basic information on study design, group mean

summary data, and literature references. The final two columns of this worksheet provide the

workbook and worksheet locations of any detailed calculations we did in the analyses of

individual papers. These summary data from this database were used in the regression analyses.

“Full Database” worksheet: expanded version of the Central Database in which dummy

variables for drug name, clearance pathway, and age group are included.

“Data Summaries” worksheet: provides summary tables of the content of the Central Database

in terms of the number of data records available for different age groups, clearance pathways,

etc. It also shows calculations of the imputed values we used for the small numbers of cases

where data on standard deviations or numbers of subjects were missing from the original

literature sources. Because different pharmacokinetic parameters had different variability, these

imputation calculations were done separately for elimination half lives, clearances, etc.

“T1/2 Database” worksheet: This is the portion of the “Full Database” that contains elimination

half-life data.

“Clearance Database” “Vd Database” “Cmax Database” and “AUC Database” worksheets:

Similarly these are the subsets of the “Full Database” pertaining to the different types of

pharmacokinetic measurements.

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“Regression Results” worksheet: presentation of regression statistics for the various parameters

analyzed and modes of analysis.

“Clearance Category Anal” worksheet: This shows a classification of the chemicals by adult

clearance—designed to distinguish chemicals whose metabolism might be appreciably limited

by liver flow from less well extracted chemicals whose elimination rates are a smaller fraction of

liver flow. This worksheet also contains regression results for the elimination half-life

parameter for the chemicals separated into the adult clearance rate categories.

Workbooks “chldpkChildOnlyStudies.xls” “chldpk-Adult.xls” and “chldpk-

Combined.xls”: These Excel worksheets include the detailed documentation of the data as

presented by the original source papers, and the calculations made to go from these data to the

entries in the Central Database. These workbooks are organized by drug, with each worksheet

within a workbook containing data describing a single PK study for that drug.

Workbook “chldpk-Individ.xls”: This workbook documents the individual ratios of

child/adult values for clearances and elimination half lives, in cases where data for individual

subjects were provided by the original authors.

2.2.1 The Central Database

The Central Database summarizes the mean values of pharmacokinetic parameters

measured in groups of children of various ages with similar types of data also presented for

adults. The source references were located from a combination of searches on Medline and

Toxline, and reviews of citations to relevant data in secondary sources. Qualifying datasets were

included if they were based on measurements in at least four subjects, with a distinct preference

for datasets that also provided information on the numbers of subjects studied and some measure

of dispersion such as a standard deviation or a standard error (or, even more preferred, the raw

individual values for which distributional statistics could be calculated).

Generally, each of the 340 lines of the “Central Database” represents the arithmetic

average values found in a particular study for a particular age group—although in several cases

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(particularly for adult data) values from two or more studies have been combined. The Central

Database contains all the summary data and so is a convenient listing of the available data for

children and adults for the chemicals contained in the database. The fields (columns) of the file

are described in more detail below. An additional version of the Central Database, labelled

“CDforPrint.xls” is also included. This excel file has the same information as the main Central

Database file but with some columns hidden and notations simplified to make the spreadsheet

easy to print on 8.5 x 14” paper.

A. Chemical—The name of the drug most commonly used in the studies contributing data.

B. Predominant Fate Pathway —The predominant mode of elimination of the drug from the

body inferred from general sources [e.g., Dollery, 1999; Goodman and Gilman, 1990] and in

several cases from the paper contributing data.

C. Metabolic Type Label – this hidden column contains the fate pathway assignment for each

chemical to be used in subsequent regression runs.

D. Parameter—Indicating the type of measurements made, including clearance “C”;

elimination half life “T1/2” (generally for the second or terminal phase if more than one

compartment was indicated in classical pharmacokinetic analysis); Volume of distribution

“Vd” (generally at steady state, if given); the maximum concentration achieved in the blood

after dosing “Cmax”, or the integrated Area Under the Concentration X time curve “AUC”

after dosing.

E. Parameter Standardized - this column reflects the standardized label given to the column

for the purposes of assigning parameters to different regression analyses.

F. Units—These are the units used to express the data. In many cases it was necessary to

convert the original data given in the source papers to common sets of units to assure

comparability across different studies—generally clearances were expressed in mg chemical/

(min-kg body weight); elimination half-lives were expressed in hours, and volumes of

distribution were expressed in liters per kilogram of body weight, etc.

G. Mean—The arithmetic average of the values of the parameter that were given.

H. Log(Mean)—This hidden column contains the Log10 of the arithmetic mean.

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I. Standard Error—Essentially this functions like a standard deviation, but applied to the

mean of some number (N) of values. It is calculated as the standard deviation divided by the

square root of N. Sometimes these values were given directly by the source paper—in other

cases they were calculated from data in the source paper.

J. Coefficient of Variation – this column shows the degree of variability in the data for this

line, expressed as the standard deviation divided by the group arithmetic mean.

K. “In Var Weight (Mean/SE)^2—this column contains the “inverse variance weight” - a

statistical weight used in some of the regression analyses. It is calculated as the square of

[the mean of the parameter (column F) divided by the standard error (column G)] squared.

Dividing the mean value of the parameter by the standard error in this procedure creates a

unitless quantity that, when squared, represents the reciprocal of the variance of the mean. In

several cases, where the standard error in column G is listed as “not given” the corresponding

entry in column H is “Value!”. In these cases, the entries for this column were imputed from

other information specific to the observed uncertainty in the same parameter measured in

other studies. The detailed calculations are provided in the “Data Summaries” worksheet,

colmuns AT through BE.

L. “Sqrt N Weight”—This is an alternative weight used in some regression analyses. One

possible concern with the inverse variance weight in column H is that it depends heavily on

the authors’ reports of standard deviations of their measurements. Because these standard

deviations are based on relatively modest numbers of data points they are themselves subject

to appreciable statistical uncertainty. Therefore this column is a weight that depends only on

the number of subjects in the group giving rise to the data—N0.5.

M. N—This is the number of subjects studied to give rise to the reported average. In some cases

this information was not supplied in the source paper, and a value of 9 (shown in italics) was

imputed from the median study size of papers that did provide their N’s. Of 340 total data

sets, there were imputed values for group size (median = 9) in only3 cases.

N. Child Age Range shows the range of ages of the children studied or “adults” if the group

consisted of people over 18 years of age.

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O. Mean Child Age (yrs) is the mean age of the children subjects that was reported or could be

calculated.

P. Reference gives short references to the source paper, allowing identification of the full

references in the bibliography.

Q. (Blank)

R. (Blank)

S. (Blank)

T. (Blank)

U. Workbook—Shows the Excel workbook containing the detailed documentation (for cases

with stars, the mean and standard deviation/standard error data were entered into the Central

Database without separate calculations). There are three workbooks—one for child data; one

for adult data, and one for papers that combined child and adult data (child.xls, adult.xls, and

combined.xls, respectively).

V. Worksheet—This gives the specific worksheet for the detailed calculations within the

workbook cited in column U.

An overview of the contents of the Central Database is provided in the spreadsheet titled

Data Summaries, and also in one of the submitted manuscripts (Ginsberg, et al., 2001). Age

groupings were developed in an effort to capture the rapid physiological and

biochemical/metabolism changes that occur in the first weeks to months of life. Given the

evidence that changes occur in liver cytochrome P-450 (CYP) enzymes and other systems within

the first hours to days of life (Cresteil, 1998; Tanaka, 1998), it was important to determine

whether PK changes could be detected in the first week vs. the 1 week to 2 month age

comparison. Further, the fact that premature infants have many underdeveloped systems at birth,

it was important to evaluate them as a separate group. The age groupings beyond the neonatal

period were intended to represent a developmental continuum, although the number of groups

possible and the age cutoffs were a function of the data available for these ages (i.e., there would

be no point in having an age group with too few data points for statistical evaluation). A large

age group encompassing 10 years was used to characterize children beyond the toddler stage up

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until adolescence. This appeared reasonable based upon initial judgements that there was not a

large degree of variability in the PK parameters under study over this broad age range. Further,

there was not much data available for older children. In summary, the age groupings used to

organize and summarize the children’s PK data are as follows:

Neonates (first week of life, full term); Neonates (first week of life, premature); Newborns (1 week to 2 months of age); Early infants (2 –6 months of age); Crawlers/Toddlers (6 months – 2 yrs of age); Pre-Adolescents (2-12 yrs of age); Adolescents (12-18 years of age); Adults

Of course, individuals within any age group are at slightly different developmental stages, with

such inter-individual differences evaluated in the variability analysis (Hattis, et al., 2001).

2.2.2 Data Files From Individual Papers

Three Excel workbooks comprise the “original study” database which represents an

extraction of key data from the PK studies themselves. The information extracted included data

on study protocol, subject ages, group size, and PK results. The three workbooks consist of

papers that (1) provided only adult data for comparison (“chldpk-adult.xls”) (2) provided only

data for groups of children, (“chldpkchild.xls”) or (3) provided data for both adults and children

(“chldpk-combined.xls). Within each workbook, analyses of specific papers are filed in

individual worksheets titled with the name of the chemical/drug studied. In addition, some

worksheets—usually labeled “comb” for combination—document our aggregation of data across

different experimental groups. In most cases the methodology used is self-explanatory—simple

unit conversions (to obtain data in comparable units), and calculations of means, standard

deviations, standard errors, and geometric standard deviations (the latter as measures of

interindividual variability, usually represented on the spreadsheet in bold face, and calculated as

the standard deviation of the logarithms of individual parameter values). Where combinations

were made across studies, in cases where the individual data points were not available, combined

group standard errors were calculated from a weighted average of the variances indicated for the

measurements in each experimental group (for an example, see the “Alfentanil” worksheet in the

“chldpkChild.xls” workbook, cell F14).

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2.2.3 Files Documenting the Regression Analysis

While one may be able to make general inferences of child/adult PK differences from

data presented in the Central Database, regression analysis was used to develop a statistical

description of trends in mean parameter values over different age groups. The main

documentation for regression analyses is contained in the spreadsheet labeled “Regression

Results”. Regressions were run in a multiple regression engine from SAS, Inc. called JMP,

Version 3.1.6.

The regression analysis was conducted across all chemicals in the database by

normalizing the results for each chemical back to a single reference chemical (theophylline was

arbitrarily chosen). In this way, the inherent differences between chemicals in terms of clearance

or half-life were normalized to the respective values for theophylline. The regression equation

(see below) used dummy variables to normalize for chemical identity against theophylline. This

then allows the inter-age differences in clearance or half-life to be evaluated for all chemicals in

the database simultaneously. To accomplish this the regression equation also used dummy

variables to normalize for age group relative to adults. The regression coefficient for each age

group represents that age group’s composite (across all chemicals) ratio compared to adults with

respect to that PK parameter. Since the regression equation is performed as a Log function, the

antilog of the regression coefficient provides the ratio to adults.

The worksheet labeled “Full database” consists of the basic data contained in the Central

Database file discussed earlier, plus a few items added in preparation for the regression analysis:

Columns B through AS are a series of “dummy” (0 or 1) variables for each drug/chemical in

the analysis—given a value of “1” if the chemical corresponds to the label in row A and “0” if it

doesn’t. This allows the regression analysis to control for differences among chemicals in the

typical values of studied parameters (e.g., clearance, half life) and draw overall inferences about

the multiplicative differences associated with specific age categories.

Columns AV through BH are similar “dummy” variables designating different predominant

modes of elimination. In the actual regression these variables were mainly used for quick sorting

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of the database, rather than to control for elimination types as was done for the chemical specific

dummies.

Columns BU through CB provide another set of “dummy” variables related to the age group of

the children (or adults) included in each data group. The classifications are based on either the

mean age or the center of the age range given in the previous columns. Once again, the value of

“1” is used to designate that the targeted age group is being analyzed and “0” if some other age

group is represented.

Column BO provides calculations of coefficients of variation (that is, the standard deviation

divided by the mean) in cases where standard errors or individual data have been provided by the

source reference. The results in this column are used in later calculations of imputed values for

the inverse variance weights for data groups where the source reference did not provide

individual data or measures of dispersion such as standard errors or standard deviations.

The worksheet “Data summaries” characterizes the database by chemicals, parameters,

numbers of subjects, etc., and provides the foundation for the data imputation calculations.

Unfortunately, the number of subjects in a group was not available in all cases. Based

upon the number of subjects per study group where this information was provided, the judgment

was made that there was no clear evidence of a tendency for median group sizes to be

appreciably larger for some parameters than for others. Therefore the overall median value of 9

was used for assigning statistical weights for all data groups where the source paper did not

provide this information.

The regression analysis was run in several formats to test the effects of prioritizing or

weighting those papers that had larger numbers of subjects (“N”) or less variability. Without

such weighting, the regression technique gives equal weight to studies of varying robustness and

statistical confidence. To weight according to number of subjects per study group, the square

root of N was used (N=9 used as default if no N given). To weight according to variability the

“inverse variance weight” (see Central Database, Column H description) was used. This statistic

is an indicator of the coefficient of variation (arithmetic standard deviation divided by the

arithmetic mean) and so is a useful index of the spread of the data around the mean value.

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Since not all papers provided dispersion information (standard deviation or standard

error) to include such papers in our variance weighting procedure, it was necessary to provide a

default estimate of study variability. To gain some insight on this, Table 2 shows the median

coefficients of variation across measurements of different PK endpoints.

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Table 2Median Coefficient of Variation for Different PK Endpoints

PK Parameter Median Coeff. of variation*

AUC 0.3777

Clearance 0.3707

Cmax 0.3004

t1/2 0.3086

Vd 0.3398

All 0.3428

*Coefficient of variation is the arithmetic standard deviation divided by the arithmetic mean.

The table indicates differences in coefficients of variation across these different endpoints

which might not be entirely negligible, which suggests that different parameters could be subject

to systematically different amounts of experimental measurement error per individual studied.

Therefore in our imputations for the inverse variance weights we elected to use the parameter-

specific median coefficients of variation for cases where the source paper did not provide

dispersion information . The imputation calculations themselves are documented in the “inverse

variance weight” columns of the worksheets which yields the final databases used for regression

analyses for each individual parameter (see, especially, the worksheets labeled “Clearance

database”, “T1/2 dataabase, and “Vd database”).

The worksheet labeled Regression Results” in this workbook documents our full

regression results. For each parameter we used a conventional multiple regression model of the

form:

Log(Mean) = B0 + B1*(1 or 0 for chemical 1) + B2*(1 or 0 for chemical 2) + … + Ba*(1 or 0 for age group 1) + Bb*(1 or 0 for age group 2) + …

In this model, the chemical-specific “B’s” correct for differences among chemicals in average

clearance (or other parameter) relative to a specific reference chemical (e.g., theophylline).

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Similarly, the age-group-specific “B’s” assess the average log differences between each age

group and the reference group (adults).

In the table provided for each regression run, the central estimates of the “B” coefficients

are provided under the column labeled “estimate”, with conventional standard errors, t statistics,

and P values provided in subsequent columns. The key information for each table is contained in

the column labeled “Antilog”. This is the best estimate of the ratio of the values of each

parameter found for the data in each age group, relative to the corresponding values for adults. It

is calculated simply as 10B where B is the regression estimate for the age group involved.

The three types of regression runs done for each parameter are presented as follows: (1)

simple unweighted regressions are provided in columns A through F; (2) Square Root of N

weights were used for the results in columns H through M; and finally (3) full Inverse variance

weights were the basis for the regressions reported in columns O through T. It can be seen from

the R values and the P values for the age group coefficients that the regressions using the most

sophisticated inverse variance weights performed appreciably better, although the central

tendencies of the results of all the weighting schemes are similar.

Results of regression runs for different parameters and data subsets are provided in

different sets of rows of the worksheet. Clearance results for the whole data set are provided

beginning at Row 10, half-life results for the whole data set begin at row 528, Vd results for the

whole data set begin at row 1200, and AUC results begin at row 1600. There was insufficient

data for similar regression analyses of Cmax.

Finally, the remaining sections of the spreadsheet show the results of regression runs for

the Clearance and T1/2 parameter for various subsets of the data by predominant elimination

types (renal clearance, “Any P450”, and conjugation). For these runs, only the best-performing

inverse square weightings were used.

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