Download 2.2.1 The Central Database

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 Goble
Clark University
and
Gary Ginsberg and Susan Smolenski
Connecticut 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 ………………………………………………………………… 1
1.1 Goals of the Current Project …..…………………………………… 2
2.0 Methods and Approaches Used for Database Development ………………..
2.1
Compilation and Description of the Database ………...………...
2.1.1 The Central Database ……………………………………………..
2.1.2 Data Files from Individual Papers ………………………………..
2.1.3 Files Documenting the Regression Analysis ……………..……..
3
3
8
12
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, bloodbrain 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
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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 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.
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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 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
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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.
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
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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
(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 Database
Chemical
Alfentanil
Amobarbital
% Metabolized
>90%
> 70%
Ampicillin
Antipyrene
Bromosulfphthalein
Bupivacaine
Busulfan
Caffeine
Carbamazepine
Chloral Hydrate
Cimetidine
Metabolic Pathways
CYP3A4 (70%)
predom. Cyp 2C19; some gluc.
Basis
Bertz, 97
Analogy w/related barbs;Bertz,97;G&G,
90
Bertz, 97
Engel, 96; Tanaka, 98
Fehring, 1989
Analogy with ropivicaine; Dollery, 99
Dollery, 99; Ohmori, 98
Bertz, 97
Dollery, 99; Gibbs, 97
Henderson, 97
Bertz, 97
low (75-90% renal)
high
not available
approx. 85%
>90%
>90%
>90%
>90%
<30-40%; (70%
renal)
Clavulanic Acid
50 to 60%
Cotinine
extensive
Dapsone
80-90%
Dichloroacetic acid
>90%
Ethanol
>90%
Fentanyl
>90%
Furosemide
low (50-80% renal)
Gentamicin
low (>90% renal)
Ketamine
90%
Lidocaine
>90%
Lorazepam
>90%
approx. 85%
Mepivicaine
Metoclopramide
70%
Midazolam
>90%
Morphine
>90%
Nicotine
>90%
>90%
Nifedipine
Oxazepam
>90%
Paracetamol (acetamin) >90%
Piperacillin
low (70% renal)
Quinidine
>70%
Remifentanil
>90%
--multiple p450s: 1A2, 2B6, 2C, 3A4
biliary excretion; GSH conjugation
1A2 (major); Cyp 3A4 (minor);
40% GSH conj.; various other metab
Cyp1A2 (90%)>>2E1
Cyp 3A4
ADH most important
Possible minor role for Cyps
Unknown
Cyp 2A6 and glucuronidation
N-acetyl (50%), unknown cyp, gluc.
Cyp hydrolysis; redn via radicals
ADH>Cyp 2E1>Catalase
Major: Cyp 3A4; Minor: 2D6, 2C8/9
Glucuronidation 20-50%
--Cyp 3A and 2D; others possible
Cyp 3A major; Cyp 1A2, 2B1 (minor)
Glucuronidation without Phase I
1A2 (major); Cyp 3A4 (minor);
Sulfation (35%) > gluc (<20%) > Cyp
CYP3A (primary)
Glucuronidation without Phase I
Cyp 2A6 - 80%; some glucuron.
CYP3A4 (primary)
Glucuronidation without Phase I
Gluc (60%)>sulf (35%)>Cyp1A2,2E1
--Cyp3A (>50%)
Cyp3A4 (major); 2D6, 2C8/9(minor)
Dollery, 99
Dempsey, 2000
Dollery, 99
Stacpoole, 98
Dollery, 99
Bertz, 97; Guitton, 97
Bertz, 97
Goodman&Gilman, 90; Bertz, 97
Dollery, 99
Dollery, 99
Dollery, 99; Bertz, 97
Analogy with ropivicaine; Dollery, 99
Bertz, 97
Bertz, 97
Bertz, 97
Dempsey, 2000
Bertz, 97
Bertz, 97
Bertz, 97
Goodman & Gilman, 90
Bertz, 97; Tanaka, 98
Teniposide
Theophylline
Thiopentone
50%
>90%
>90%
Cyp3A (primary)
Cyp1A2 (>70%) > 2E1 > 3A4
predom. Cyp 2C19; some gluc.
Ticarcillin
Tobramycin
Tolbutamide
Triazolam
Trichloloethanol
Valproic acid
Vancomycin
Zidovudine
<10% (92% renal)
<10%, (90% renal)
>90%
>90%
extensive
>90%
low (75-90% renal)
60-80%
Analogy / etoposide, Bertz, 97, G&G,90
Bertz, 97
Analogy w/related barbs;Bertz,97;G&G,
90
Goodman & Gilman, 90
Goodman & Gilman, 90
Bertz, 97
Bertz, 97
Mayers, 91; Henderson, 97
Bertz, 97
Bertz, 97
Bertz, 97
----Cyp 2C9/10
Cyp 3A
Glucuronidation
Glucuronidation (20-70%)>Cyps
--Glucuron. (major) > Cyp3A (minor)
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Analogy w/fentanyl & other congeners;
Guitton,97
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 “chldpkCombined.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).
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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
(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
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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.
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.
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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.
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
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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
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
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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).
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.
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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
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
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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.
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 2
Median 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 parameterspecific 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) + …
16
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).
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.
17
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