Download Role of Dosimetric Scaling and Species

Role of Dosimetric Scaling and Species Extrapolation in Evaluating
Risks Across Life Stages
II. Pharmacokinetic Dosimetric Considerations in Old Age
Report to the U.S. Environmental Protection Agency
Under RFQ No. DC-03-00009
Dale Hattis, Abel Russ
Clark University
November 2003
Acknowledgement: This report is part of work prepared for the Office of Research and
Development of the U.S. Environmental Protection Agency. However the report has not yet
been reviewed by EPA. The views it contains are solely those of the author. Additionally, some
material in Section 3 of this report was also included in a recent report to the New Zealand
Ministry of Health on pharmacokinetic modeling issues related to the estimation of long-past
TCDD exposures for residents of a community in that country.
2
Table of Contents
Executive Summary ........................................................................................................................ 3
1.
Introduction ............................................................................................................................. 5
2. Description and Analysis of a New Data Base of Classical Pharmacokinetic Parameters in
Relation to Age in Adults ............................................................................................................... 7
2.1 Identification and Screening of Data Sources ....................................................................... 8
2.2 Classification of Drugs by Primary Modes of Elimination .................................................. 9
2.3 Description of the Data Base ................................................................................................ 9
2.4 Age-Related Changes in Classical Pharmacokinetic Parameters--Regression Analysis
Methods and Results ................................................................................................................. 13
2.5 Relationships between Age and Interindividual Variability in Pharmacokinetic Parameters-Departures of Individual Values From Geometric Mean Model Fits ...................................... 19
2.6 Assessment of Potential Age-Related Differences in Pharmacokinetic Parameters for
Drugs Eliminated by Different Broad Groups of Mechanisms ................................................ 25
2.7 Exemplary Analysis of Birth-Elderly Age Group Data for One Particular Drug—
Theophylline ............................................................................................................................. 30
3. Analysis of NHANES3 Body Mass Index Data to Estimate Changes in Fat Content by Sex
and Age—Implications for Age-Related Changes in Elimination Rates of Poorly Metabolized
Highly Lipophilic Chemicals ........................................................................................................ 33
3.1 Distributions of % Body Fat for U.S. Adults by Age and Sex Inferred from NHANES3
Data ........................................................................................................................................... 34
3.2 Toward More Mechanistically Plausible Representations of the Effects of % Body Fat on
the Rate of Elimination of Poorly Metabolized Lipophilic Environmental Chemicals (e.g
2,3,7,8-Tetrachloro-Dibenzo-Dioxin—TCDD) ........................................................................ 46
4.
Conclusions ........................................................................................................................... 52
5.
References ............................................................................................................................. 53
Appendix A—Data Source References ........................................................................................ 55
Appendix B--Contents of the Data Base/Analysis File (Excel Workbook Titled
“PKeldforanal.xls”)....................................................................................................................... 60
3
Executive Summary
This is the second report in a project intended to contribute to the improvement of the risk
assessment methods available to EPA scientists for assessing toxic risks from exposures at
various life stages.
The present report is divided into two analytical sections intended to deal with issues
posed by (1) relatively rapidly-eliminated hydrophilic, and (2) slowly-eliminated liphophilic
compounds, respectively. The toxicokinetics of rapidly eliminated hydrophilic compounds are
reasonably analogous to pharmaceuticals, and for them we apply similar methods for empirical
analysis of changes in kinetic parameters in the elderly that we previously used to assess
pharmacokinetic differences in infancy and childhood. We develop and analyze a new empirical
database of age-related differences in classical pharmacokinetic parameters [Clearance, HalfLife, Volume of Distribution, and Area Under the Concentration-time curve (AUC)] for 46 drugs
tested in humans.
From this analysis we conclude that internal integrated measures of concentration X time
product per mg/kg dose average about 60% more in 65-85 year olds compared to of that
observed in 18-24 year olds. Similarly, the analysis of clearance rates indicates that 18-24 year
olds average about 47% greater clearance rates per kg body weight than 65-85 year olds. Also in
line with these findings, elimination half-lives appear to be increased by an average of about
40% in 65-85 year olds relative to 18-24 year olds. In each case the differences appear more
pronounced in the 80-84 year age group. By contrast, there is no apparent pattern of systematic
change with age in Volume of Distribution measurements. There is also no apparent pattern of
change with age in the interindividual variability of these pharmacokinetic parameters.
4
Because most of the drugs covered are relatively hydrophilic, we supplement this with
observations of body mass index and estimated body fat content based on an extensive
representative sample of the U.S. population—the National Health and Nutrition Survey III.
Body fat contents systematically increase with age leading to a tendency for decreased
elimination rates with age of TCDD and (likely) other poorly metabolized lipophilic compounds,
other things being equal. Distributions of body fat content tend to narrow in elderly age groups
compared to younger adults, probably in part because of increased age-specific mortality rates
with higher body fat content. We also find room for improvement in the typical regression
equations used to date to model the effect of body fat content on the elimination rates for
lipophilic compounds. From fundamental mechanistic considerations, we suggest a simple
transformation for potential application to refined regression analyses of available empirical data
on this topic.
1. Introduction
This is the second report in a project intended to contribute to the improvement of the risk
assessment methods available to EPA scientists for assessing toxic risks from exposures at
various life stages. The first report (Hattis et al., 2003a) deals with pharmacokinetic changes in
the period from birth through adolescence. This report covers the changing pharmacokinetics of
people from early adulthood (age 18) through old age. A third report will deal with the
distinctive pharmacokinetic changes during pregnancy, and a fourth will discuss
pharmacodynamic issues.
Several previous reviews are available of the effects of ageing on various physiological
systems. Notably, Masoro and Schwartz (2001) have recently prepared an extensive, albeit
largely qualitative, organ-system-by-organ-system review of age-related changes in a wide
variety of functions. More quantitatively, Price et al. (2003) have developed an extensive set of
equations that allow modeling of interindividual variability of the physical size and blood flows
needed for human PBPK modeling on the basis of the extensive NHANES III sample of the U.S.
population. In addition, age-related changes are reviewed in a number of handbooks, reports of
longitudinal studies of defined populations, and studies related to the development of
phamacokinetic models (O’Flaherty, 2000; Mayersohn, 1994; Masoro, 1995; Bernstein and
Bernstein, 1991; Cristofalo, 1985; Cooper et al., 1991; Greenblatt et al., 1982; Lamy, 1982;
Sotaniemi et al., 1997; Rowe et al., 1976).
The principal contribution of this report is to develop and analyze a new empirical
database of age-related differences in classical pharmacokinetic parameters [Clearance, HalfLife, Volume of Distribution, and Area Under the Concentration-time curve (AUC)] for 46 drugs
tested in humans. This analysis is presented in Section 2. Because most of the drugs covered
are relatively hydrophilic, we supplement this in Section 3 with observations of body mass index
and estimated body fat content based on an extensive representative sample of the U.S.
population—the National Health and Nutrition Survey III. Body fat content is an important
determinant of long-term storage and (inversely) the rate of excretion of highly lipophilic and
poorly metabolized environmental toxicants such as 2,3,7,8-tetracholordibenzodioxin (TCDD)
6
(Michalek and Tripathy, 1999). In this connection, we offer some observations that indicate the
potential for improved modeling of TCDD elimination as a function of age and body fat content.
7
2. Description and Analysis of a New Data Base of Classical
Pharmacokinetic Parameters in Relation to Age in Adults
This section applies methods we previously used to analyze age-related patterns of
change in pharmacokinetic parameters in infants and children (Hattis et al. 2003b; Ginsberg et
al., 2002; Ginsberg et al., 2003 in press) to the study of age-related changes during adulthood.
Briefly, we assembled a database of individual and group mean observations of pharmacokinetic
parameters for 46 drugs, and fit the data with the following regression equation:
Log(Mean) = B0 (intercept) + 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) + …
Where the “Mean” is either an individual value in cases where individual values were available,
or the arithmetic mean of the observed values of the particular dependent variable under study
(i.e., AUC, clearance, elimination half-life, or volume of distribution) where no individual data
values were given in the source paper. Group mean values are weighted in the regression by the
square root of the number of subjects contributing to each mean.
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 age group (young adults, ages 18-24). This analytical
technique allowed us to bring data from many different chemicals together to assess geometric
mean ratios of the values seen for particular ages in relation to the reference group of 18-24 year
olds.
8
Below, subsection 2.1 first documents the identification and screening of papers used as
data sources for this analysis. 2.2 then indicates how we classified drugs by primary modes of
elimination. Subsection 2.3 provides a series of quantitative descriptions of the data base by
dependent variable measured, primary mode of elimination, and age group. The main results of
our regression analyses, and some additional details of the regression analysis methodology, are
provided in Subsection 2.4. Subsection 2.5 then assesses age-related changes in the departures
of data for individual people from the overall model expectations. Subsection 2.6 explores the
possibility that drugs with different primary modes of elimination have different patterns of agerelated changes in key pharmacokinetic parameters. Finally, 2.7 shows an exemplary analysis of
the elimination half lives for a single drug (theophylline) for both child and adult age groups.
2.1 Identification and Screening of Data Sources
Papers were selected in several ways. An important first source was a store of papers we
had previously analyzed for our database of human interindividual variability in pharmacokinetic
and pharmacodynamic parameters (Hattis et al., 2002; 1999a; 1999b). This allowed us to
efficiently assemble a relatively large body of data consisting of values for individual subjects.
Beyond this we did searches of the recent pharmaceutical literature, with emphasis on drugs that
we had previously studied in our earlier work. This emphasis was maintained in order to have as
many drugs as possible where we already knew or could readily determine the primary mode of
elimination from the body.
Some papers or datasets within papers were excluded from the analysis if they seemed to
reflect grossly unrepresentative collections of subjects within particular age groups. In
9
particular, we excluded data from subjects known in advance of pharmacokinetic measurements
to have little or know kidney function (e.g., kidney dialysis patients).
Data source references are listed in Appendix A. The full database and the detailed
results of all regression analyses will be made available via the web in a Microsoft Excel file at
http://www2.clarku.edu/faculty/dhattis. The detailed contents of the Excel file are listed in
Appendix B.
2.2 Classification of Drugs by Primary Modes of Elimination
Table 1 lists our conclusions for the primary mode of elimination of the drugs in the data
base. These conclusions were based on information contained in two editions of a general
reference work by Dollery et al. (1991, 1999), and Goodman and Gilman (Hartman and Limbiro,
2001), supplemented with drug-specific searches in Medline where information in the general
reference works was missing or inconclusive. The details of the information sources for
classification of individual chemicals are given in the “Metabolic Classifications” worksheet in
the Excel workbook stored on the website.
2.3 Description of the Data Base
Table 2 provides an overview of the data base, sorted by the four parameters that are used
as dependent variables for our age-specific analyses. Overall there are 885 individual values for
single persons; but for each parameter, much larger numbers of people are included in the form
of group averages for sources that did not provide individual data.
Table 3 shows a breakout of the data base by major routes of elimination from the body.
Table 4 shows the same information grouped into larger categories of types of elimination. It
10
Table 1
Classification of Principal Routes of Elimination of Drugs in the Data Base
Chemical
amikacin
Route of elimination Chemical
Renal
lidocaine
Route of elimination
Cyp3A or 3A4
amitriptyline
ampicillin
antipyrene
CYP2D6
lisinopril
Renal
lithium
CYP--mixed/unkown meperidine
Fecal
Renal
Esterase
atracurium
Esterase
mephobarbital-r
CYP2C19
benazepril
Renal
mephobarbital-s
CYP--mixed/unkown
bromazepam
bupivicaine
CYP--mixed/unkown mianserin
CYP1A2
midazolam
CYP2D6
CYP3A or 3A4
chlorpheniramine
CYP2D6
nortriptyline
CYP2D6
chlorzoxazone
CYP2E1
oxazepam
Copper
Renal
oxytocin
Conjugation
Other--Sulfhydryl
reduction and
aminopeptidase
diazepam
dicumarol
CYP2C19
Unclassified
paracetamol
pethidine
Conjugation
Esterase
enalapril
Renal
phenylbutazone
Conjugation
enalaprilat
Renal
phenylpropanolamine
Renal
erythromycin
fentanyl
gentamicin
CYP3A or 3A4
Cyp3A or 3A4
Renal
piroxicam
propanolol
teicoplanin
CYP2C9
CYP2D6
Renal
grepafloxacin
ibuprofen
ketanserin
ketoprofen
ketorolac
Unclassified
CYP2C9
Unclassified
Conjugation
Renal
terfenadine
theophylline
valproic acid
vancomycin
viloxazine
Renal
CYP1A2
Conjugation
Renal
Unclassified
11
Parameter
AUC
Clearance
Table 2
Overview of the Data Base For Various Parameters
Number of
Individual
Subjects in Data Total Number of
Drugs
Data Points Data Groups
Groups
Subjects
17
163
21
317
480
31
210
59
1003
1213
T1/2
44
359
84
Vd
26
153
51
Total
46
885
215
1312
1671
996
1149
not summed to avoid double
counting
12
Table 3
Size of the Data Base (Including All Parameters) for Chemicals With Different
Predominant Routes of Elimination
Route of
Number of
Individual
Data
Subjects in Data Total Number
Elimination
Drugs
Data Points
Groups
Groups
of Subjects
Conjugation
5
122
6
60
182
CYP1A2
CYP2C19
2
2
113
0
6
24
60
228
173
228
CYP2C9
2
34
22
280
314
CYP2D6
5
156
6
93
249
CYP2E1
CYP3A or 3A4
CYP-mixed/unkown
1
4
34
30
0
14
0
109
34
139
3
22
54
1545
1567
Esterases
Fecal
Renal
Other--sulfhydryl
reduction
Unclassified
Total
3
1
13
0
18
260
18
0
51
114
0
892
114
18
1152
1
4
46
18
78
885
0
14
215
0
247
3628
18
325
4513
13
Table 4
Summary of the Database by Aggregate Groups of Predominant Modes of Elimination
Number Individual
Subjects in Data Total Number
Route of Elimination of Drugs Data Points Data Groups
Groups
of Subjects
All CYPs
19
389
126
2315
2704
Conjugation
5
122
6
60
182
Other Metabolism
4
18
18
114
132
Renal and/or Fecal
Elimination
14
278
51
892
1170
Unclassifed
4
78
14
247
325
Total
46
885
215
3628
4513
should be noted that the numbers of individual data points and data groups in these tables
represent sums for all parameters. In some cases the same people contributed information for
more than one parameter, so there is some double counting of individuals, though not of actual
data points available for analysis.
On the same basis, Table 5 shows a breakdown of the data base by 5-year age groups. It
can be seen that the data base includes relatively more observations for the youngest adult age
groups and age groups from 65-85; and a somewhat smaller density of observations for age
groups between 35 and 64. In the subsequent regression analyses we have sometimes used 5year age groups, and sometimes 10-year age groups depending on the availability of information
for particular parameters and elimination routes.
2.4 Age-Related Changes in Classical Pharmacokinetic Parameters--Regression Analysis
Methods and Results
Tables 6-9 show the main age-related results of applying the regression equation shown
in the introduction to this section to the full data base for each of our dependent variables. In all
cases, each data point is weighted according to the square root of the number of subjects
14
Table 5
Summary of the Database by 5-Year Age Groups
Age Group
18-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
Total
Individual
Data Points
177
134
93
39
29
47
33
37
36
90
67
64
24
15
885
Data Groups
26
39
22
12
2
6
5
4
5
30
37
12
12
3
215
Subjects in Total Number of
Data Groups
Subjects
227
404
1033
1167
188
281
282
321
20
49
272
319
57
90
202
239
90
126
353
443
392
459
208
272
274
298
30
45
3628
4513
15
Table 6
Regression Estimates of the Effect of Age on Area Under the Concentration X Time Curve
Per Mg/kg Dose
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Sum of weights—N1/2
Age Group
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
Antilog of
Estimate
1.202
1.054
1.110
0.975
1.297
1.329
0.835
1.306
1.578
1.608
1.442
2.075
1.362
0.986
0.983
0.177
0.729
240.1
Estimate
0.080
0.023
0.045
-0.011
0.113
0.123
-0.078
0.116
0.198
0.206
0.159
0.317
0.134
Std Error
0.049
0.060
0.070
0.089
0.070
0.076
0.095
0.070
0.045
0.043
0.060
0.083
0.135
t Ratio
1.64
0.38
0.64
-0.12
1.62
1.63
-0.82
1.65
4.4
4.82
2.64
3.83
0.99
Prob>|t|
0.10
0.70
0.52
0.90
0.11
0.11
0.41
0.10
<.0001
<.0001
0.0090
0.0002
0.32
16
Table 7
Regression Estimates of the Effect of Age on Drug Clearance Rates (ml/min/kg body
weight)
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Sum of weights—N1/2
Age Group
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
Antilog of
Estimate
0.927
0.796
0.926
0.804
0.862
0.834
0.769
0.771
0.650
0.684
0.674
0.541
0.733
0.979
0.975
0.169
-2.620
430.2
Estimate
-0.033
-0.099
-0.034
-0.095
-0.065
-0.079
-0.114
-0.113
-0.187
-0.165
-0.171
-0.267
-0.135
Std Error
0.032
0.038
0.044
0.106
0.052
0.064
0.054
0.055
0.035
0.035
0.045
0.046
0.072
t Ratio
-1.03
-2.62
-0.76
-0.9
-1.24
-1.23
-2.11
-2.05
-5.34
-4.75
-3.82
-5.75
-1.88
Prob>|t|
0.30
0.01
0.45
0.37
0.22
0.22
0.04
0.04
<.0001
<.0001
0.0002
<.0001
0.06
17
Table 8
Regression Estimates of the Effect of Age on Drug Elimination Half Lives (hours)
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Sum of weights—N1/2
Age Group
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
Antilog of
Estimate
1.005
1.080
0.945
1.095
0.979
0.989
1.022
1.087
1.354
1.329
1.413
1.632
1.196
0.967
0.962
0.162
1.007
660.9
Estimate
0.002
0.033
-0.025
0.040
-0.009
-0.005
0.009
0.036
0.132
0.124
0.150
0.213
0.078
Std Error
0.025
0.029272
0.035307
0.03879
0.032326
0.038137
0.038399
0.041906
0.029
0.029
0.034
0.040
0.068
t Ratio
0.08
1.14
-0.70
1.02
-0.28
-0.13
0.24
0.87
4.6
4.27
4.43
5.37
1.15
Prob>|t|
0.94
0.26
0.49
0.31
0.78
0.90
0.81
0.39
<.0001
<.0001
<.0001
<.0001
0.25
18
contributing information to the analysis. The upper part of each table shows statistics describing
the fit achieved; while the lower part gives the detailed estimates of the “B” coefficients and
related data. The second column of the lower part of each table shows the geometric mean of the
ratio of the values for each age group to the “reference” age group of 18-24 year olds. These
numbers are the antilogs of the underlying “Bage group” regression estimates in the third column.
The remaining columns—the standard error, t ratio, and P value (for the difference from the
reference group) are conventional statistics related to the log10 regression estimates in the third
column.
All the regressions also generated a set of drug-specific “B’s” for the differences between
the log parameter values for individual drugs and a “reference” drug (theophylline, in the cases
of the analyses summarized in Tables 6-9. These estimates are of little intrinsic interest for the
age group analysis here, but are provided as part of the full set of results in the “regression
results” worksheet on the web site.
Each of the first three regressions (Tables 6, 7, and 8) shows a similar pattern of modestly
increased sensitivity for people in the 65-85 year age groups. The differences from 18-24 year
olds are generally highly statistically significant (P<.01 to P < .0001 for the different 5-year age
groups treated separately. For AUC (Table 6), the enhanced internal integrated concentration X
time product per mg/kg dose is about 60% more in 65-85 year olds compared to of that observed
in 18-24 year olds. Similarly, the clearance analysis (Table 7) indicates that 18-24 year olds
average about 47% greater clearance rates per kg body weight than 65-85 year olds. Elimination
half lives (Table 8) appear to be increased by an average of about 40% in 65-85 year olds relative
19
to 18-24 year olds. In each case the differences appear more pronounced in the 80-84 year age
group.
By contrast, despite the fact that lean body mass appears to decline with age (Forbes and
Reina, 1970), and some previous reports of decreased volume of distribution for some drugs
(e.g., for antipyrine--Greenblatt et al., 1982), our data reveal no systematic pattern of change of
volume of distribution with age (Table 9). With little or no age-related difference in volume of
distribution, age-related differences in clearance (Table 7) appear to be directly reflected in agerelated differences in half-life (Table 8). The consequence is that data for all three predictors of
internal dose (AUC, clearance, and elimination half-life) indicate a similar excess in elderly
sensitivity per unit of external dose expressed as mg/kg body weight.
It should be noted that this conclusion neglects any age-related changes that occur in
exposures. Such changes are likely to the degree that metabolic and activity rates decline, and
are reflected in age-related changes in the intakes of food, air, and water. We have not explored
these likely changes in exposure factors quantitatively.
2.5 Relationships between Age and Interindividual Variability in Pharmacokinetic
Parameters--Departures of Individual Values From Geometric Mean Model Fits
An important finding of our work on pharmacokinetic parameters in children was that
interindividual variability was markedly larger in the youngest age groups (up through about 6
months of age) than in later childhood or adulthood. Figures 1-4 and the accompanying Tables
10-13 analyze the distributions of departures of individual values for our four dependent
20
Table 9
Regression Estimates of the Effect of Age on Drug Volume of Distribution (liters/kg body
weight)
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
Age Group
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
Antilog of
Estimate
1.024
1.024
1.007
0.822
0.898
1.063
0.899
1.039
0.967
0.961
0.944
1.008
1.019
0.975
0.969
0.165
-0.005
355.2
Estimate
0.010
0.010
0.003
-0.085
-0.047
0.027
-0.046
0.017
-0.015
-0.017
-0.025
0.003
0.008
Std Error
0.038
0.045
0.050
0.105
0.051
0.078
0.060
0.061
0.042
0.043
0.047
0.053
0.086
t Ratio
0.27
0.23
0.06
-0.81
-0.92
0.34
-0.76
0.27
-0.35
-0.4
-0.53
0.07
0.09
Prob>|t|
0.79
0.82
0.95
0.42
0.36
0.73
0.45
0.79
0.73
0.69
0.59
0.95
0.92
21
Figure 1
Scatter Plot of Observed - Model Expected
AUC/(mg/kg Dose) vs Age
0.6
y = - .0115 + .00028x R^2 = 0.002
Obs - Model Exp log(AUC)
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
15
25
35
45
55
65
75
85
Age (Yr)
Table 10
Age-Related Differences in the Standard Deviation of Expected Vs Observed Log(AUC)
Age Group
18-34
35-64
65+
Total
obs -exp Dif in Std Dev obsLog(AUC)
exp dif
-0.0035
0.1425
-0.0016
0.1611
0.0106
0.1384
0.0028
0.1441
N
61
34
68
163
22
Figure 2
Obs - Model Exp log(Clearance/kg BW)
Scatter Plot of Observed vs Model Expected
Log(Clearance/kg Body Weight)
0.6
y = -.0269 - .00050x R^2 = 0.005
0.4
0.2
0.0
-0.2
-0.4
-0.6
15
35
55
75
Age (Yr)
Table 11
Age-Related Differences in the Standard Deviation of Expected Vs Observed
Log(Clearance/kg BW)
Age Group
18-34
35-64
65+
Total
obs -exp Dif in Std Dev obsLog(Clearance)
exp dif
0.0187
0.1641
-0.0010
0.1241
-0.0148
0.1535
0.0048
0.1539
N
109
41
60
210
23
Figure 3
Scatter Plot of Observed vs Model Expected
Log(Elimination Half Life)
Obs - Model Exp log(T1/2)
0.5
0.0
-0.5
y = .01545 - .00056 R^2 = 0.005
-1.0
15
35
55
75
Age (Yr)
Table 12
Age-Related Differences in the Standard Deviation of Expected Vs Observed
Log(Elimination Half-Life)
Age Group
18-34
35-64
65+
Total
obs -exp Dif in Std Dev obsLog(T1/2)
exp dif
-0.0023
0.1524
-0.0076
0.1532
-0.0248
0.1406
-0.0104
0.1414
N
156
117
86
359
24
Figure 4
Scatter Plot of Observed - Model Expected
Log(Volume of Distribution--L/Kg)
0.4
Obs - Model Exp log(Vd)
y = .0238 - .00058x R^2 = 0.007
0.2
0.0
-0.2
-0.4
15
35
55
75
95
Age (Yr)
Table 13
Age-Related Differences in the Standard Deviation of Expected Vs Observed Log(Volume
of Distribution—L/kg)
Age Group
18-34
35-64
65+
Total
obs -exp Dif in Std Dev obsLog(Vd)
exp dif
0.0047
0.1415
0.0282
0.1532
-0.0333
0.1557
-0.0023
0.1488
N
78
29
46
153
25
variables from corresponding model predictions (corrected for drug and age group) in the adult
age groups used in the present analysis. In contrast to the observations in children, there is no
systematic tendency for variability in any of our studied parameters from model predictions to
increase with age.
2.6 Assessment of Potential Age-Related Differences in Pharmacokinetic Parameters for
Drugs Eliminated by Different Broad Groups of Mechanisms
We have also done a substantial number of analyses of subsets of the data—for groups of
drugs thought to be eliminated by different primary pathways/mechanisms. Tables 13-16 show
some of these results for elimination half lives; Tables 17-20 for clearance data. With only one
exception, these subset analyses indicate patterns of age-related sensitivity differences that are
similar to those found in the overall data set for all drugs. The one exception is the set of drugs
that are thought to be eliminated primarily by Phase II metabolism (e.g., glucuronide and sulfate
conjugation) pathways. For these drugs there is no apparent age-related difference in elderly
people for either elimination half lives (Table 14) or clearance (Table 18).
Finally we have done a series of analyses of the overall data differentiating between the
sexes. We find no systematic differences attributable to separating the data in this way (data not
shown).
26
Table 13
Regression Estimates of the Effect of Age on Drug Elimination Half Lives (hours
Subset—All Drugs Eliminated Primarily by CYP (P450) Enzymes
RSquare
0.948
RSquare Adj
0.940
Root Mean Square Error 0.150
Mean of Response
0.956
1/2
Sum of weights—N
332.0
Age Group
25-34
35-44
45-54
55-64
65-74
75-84
85+
Antilog of
Estimate
1.071
0.924
0.956
1.024
1.405
1.781
0.943
Estimate
0.030
-0.034
-0.019
0.010
0.148
0.251
-0.025
Std Error
0.030
0.039
0.036
0.040
0.030
0.042
0.154
t Ratio
0.99
-0.88
-0.54
0.26
4.99
5.9
-0.17
Prob>|t|
0.32
0.38
0.59
0.80
<.0001
<.0001
0.87
Table 14
Regression Estimates of the Effect of Age on Drug Elimination Half Lives (hours
Subset—All Drugs Eliminated Primarily by Phase II Conjugation
RSquare
0.971
RSquare Adj
0.964
Root Mean Square Error 0.123
Mean of Response
0.882
1/2
Sum of weights—N
62.3
Age Group
25-34
35-44
45-54
55-64
65-74
75-84
85+
Antilog of
Estimate
0.680
1.026
0.943
0.835
1.054
0.950
0.918
Estimate
-0.168
0.011
-0.026
-0.078
0.023
-0.022
-0.037
Std Error
0.057
0.087
0.087
0.082
0.066
0.057
0.071
t Ratio
-2.94
0.13
-0.29
-0.95
0.34
-0.39
-0.52
Prob>|t|
0.01
0.90
0.77
0.35
0.73
0.70
0.60
27
Table 15
Regression Estimates of the Effect of Age on Drug Elimination Half Lives (hours
Subset—All Drugs Eliminated Primarily by Renal Excretion
RSquare
0.986
RSquare Adj
0.983
Root Mean Square Error 0.161
Mean of Response
1.139
1/2
Sum of weights—N
191.4
Age Group
25-34
35-44
45-54
55-64
65-74
75-84
85+
Antilog of
Estimate
0.998
1.134
1.085
1.090
1.214
1.476
Estimate
-0.001
0.055
0.036
0.038
0.084
0.169
Std Error
0.040
0.052
0.050
0.057
0.049
0.050
t Ratio
-0.02
1.04
0.71
0.66
1.71
3.37
Prob>|t|
0.99
0.30
0.48
0.51
0.09
0.00
Table 16
Regression Estimates of the Effect of Age on Drug Elimination Half Lives (hours
Subset—All Drugs Eliminated by Unclassified Mechanisms
RSquare
0.744
RSquare Adj
0.639
Root Mean Square Error 0.212
Mean of Response
1.266
1/2
Sum of weights—N
36.2
Age Group
25-34
35-44
45-54
55-64
65-74
75-84
85+
Antilog of
Estimate
1.301
1.883
1.370
1.508
1.582
1.760
1.575
Estimate
0.114
0.275
0.137
0.179
0.199
0.245
0.197
Std Error
0.143
0.152
0.147
0.175
0.179
0.189
0.256
t Ratio
0.8
1.81
0.93
1.02
1.12
1.3
0.77
Prob>|t|
0.43
0.08
0.36
0.32
0.28
0.21
0.45
28
Table 17
Regression Estimates of the Effect of Age on Drug Clearance (ml/kg BW)
Subset—All Drugs Eliminated Primarily by CYP (P450) Enzymes
RSquare
0.958
RSquare Adj
0.951
Root Mean Square Error 0.195
Mean of Response
-2.768
1/2
Sum of weights—N
251.7
Age Group
25-34
35-44
45-54
55-64
65-74
75-84
85+
Antilog of
Estimate
0.806
0.912
0.785
0.699
0.600
0.483
0.958
Estimate
-0.094
-0.040
-0.105
-0.155
-0.222
-0.316
-0.019
Std Error
0.045
0.063
0.062
0.061
0.044
0.058
0.201
t Ratio
-2.07
-0.63
-1.68
-2.53
-5.07
-5.44
-0.09
Prob>|t|
0.04
0.53
0.09
0.013
<.0001
<.0001
0.93
Table 18
Regression Estimates of the Effect of Age on Drug Clearance (ml/kg BW)
Subset—All Drugs Eliminated Primarily by Phase II Conjugation
RSquare
0.992
RSquare Adj
0.990
Root Mean Square Error 0.082
Mean of Response
-2.965
Sum of weights—N1/2
35.3
Age Group
25-34
65-74
75-84
85+
Antilog of
Estimate
1.055
0.956
0.979
0.938
Estimate
0.023
-0.020
-0.009
-0.028
Std Error
0.047
0.056
0.043
0.051
t Ratio
0.49
-0.35
-0.22
-0.55
Prob>|t|
0.63
0.73
0.83
0.59
29
Table 19
Regression Estimates of the Effect of Age on Drug Clearance (ml/kg BW)
Subset—All Drugs Eliminated Primarily by Renal Excretion
RSquare
0.881
RSquare Adj
0.854
Root Mean Square Error 0.214
Mean of Response
-2.827
1/2
Sum of weights—N
94.3
Age Group
25-34
35-44
45-54
55-64
65-74
75-84
Antilog of
Estimate
1.141
1.375
0.972
0.588
0.721
1.042
Estimate
0.057
0.138
-0.012
-0.231
-0.142
0.018
Std Error
0.069
0.119
0.227
0.136
0.072
0.101
t Ratio
0.83
1.16
-0.05
-1.69
-1.98
0.18
Prob>|t|
0.41
0.25
0.96
0.096
0.053
0.86
Table 20
Regression Estimates of the Effect of Age on Drug Clearance (ml/kg BW)
Subset—All Drugs Eliminated Primarily by Unclassified Mechanisms
25-34 is the Reference Age Group for This Table Only
RSquare
0.898
RSquare Adj
0.839
Root Mean Square Error 0.211
Mean of Response
-0.606
1/2
Sum of weights—N
33.3
Age Group
35-44
45-54
55-64
65-74
75-84
Antilog of
Estimate
0.729
0.785
0.739
0.732
0.637
Estimate
-0.138
-0.105
-0.131
-0.136
-0.196
Std Error
0.151
0.143
0.140
0.177
0.134
t Ratio
-0.91
-0.74
-0.94
-0.77
-1.47
Prob>|t|
0.38
0.48
0.37
0.46
0.17
30
2.7 Exemplary Analysis of Birth-Elderly Age Group Data for One Particular Drug—
Theophylline
There are a few individual drugs for which we can do a combined analysis of
pharmacokinetic data from childhood through elderly age groups. Theophylline is a leading
example. For theophylline elimination half lives, combining data for the present and previous
studies, we have available 91 individual and group observations; representing 256 total subjects
in age categories ranging from 1 week to 87 years of age.
Table 21 shows the results of a regression analysis of these data similar to those
presented earlier, with the 18-24 year group as the reference category. Figure 5 shows the same
results in graphical form. Half lives start out in early infancy averaging about four times longer
than the reference group. Results for the 2-6 month age group are still elevated (about 1.5 fold).
Statistically both of these differences are significant at less than P = .005. There follows a
period from about 6 months to 12 years of age in which half lives are significantly (35-45%)
shorter than the reference group. In adulthood, the data suggest (P < .1) some lengthening
(about 40%) of elimination half lives by the 55-65 year age group, with the trend becoming
highly statistically significant (1.8 – 2 fold) in the 65-84 year age groups.
31
Table 21
Regression Estimates of Theophylline Halt-Life for All Age Groups (1 Week – 87 Years)
Response:
Log(Mean T1/2 hrs)
Summary of Fit
RSquare
0.810
RSquare Adj
0.784
Root Mean Square Error
0.155
Mean of Response
0.932
Observations (or Sum Wgts)
126.1
Term
Intercept
1 wk - 2 mo
2 - 6 mo
6 mo - 2 yr
2 -12 yr
25-34
35-44
45-54
55-64
65-74
75-84
85+
Antilog of
Estimate
4.056
1.540
0.653
0.544
1.071
0.819
1.050
1.399
1.800
2.051
1.079
Estimate
0.818
0.608
0.188
-0.185
-0.264
0.030
-0.087
0.021
0.146
0.255
0.312
0.033
Std Error
0.026
0.043
0.059
0.070
0.059
0.043
0.064
0.068
0.082
0.080
0.074
0.157
t Ratio
31.24
14.18
3.2
-2.64
-4.49
0.68
-1.35
0.31
1.78
3.18
4.21
0.21
Prob>|t|
<.0001
<.0001
0.002
0.010
<.0001
0.50
0.18
0.76
0.078
0.002
<.0001
0.83
32
Figure 5
Log Plot of Theophylline Half Life Regression
Results for All Age Groups (1 Week -87 Years)
1.6
1 wk-2 mos, 4X T1/2 of reference group
1.4
75-84 yrs, 2X T1/2 of reference group
Log(T1/2 hrs)
1.2
2-6 mos, 1.5X T1/2 of reference group
1.0
0.8
Error bars are ± 1 standard error
18-24 yrs, reference group
0.6
2-12 yrs, 0.54X T1/2 of reference group
0.4
0
20
40
60
Age (yrs)
80
33
3. Analysis of NHANES3 Body Mass Index Data to Estimate Changes in
Fat Content by Sex and Age—Implications for Age-Related Changes in
Elimination Rates of Poorly Metabolized Highly Lipophilic Chemicals
Most of the drugs whose pharmacokinetics were analyzed in the previous section are
relatively hydrophilic, and have half lives that are conveniently measured in hours. However an
important group of environmental chemicals (e.g, halogenated aromatic compounds such as
dioxins, dibenzofurans, and polychlorinated biphenyls) is highly lipophilic, and has elimination
half-lives that are more usually expressed in years.
Body fat content is an important determinant of the pharmacokinetics of this set of
chemicals. Below (Section 3.1) we first draw on the nationally representative NHANES3 data to
assess age- and sex-related changes in the population distributions of body fat content for U.S.
adults. Then (Section 3.2) we draw on literature related to the pharmacokinetics of 2,3,7,8dibenzodioxin (Michalek and Tripathy, 1999; Pinsky and Lorber, 1998; Rhode et al., 1999) to
make some suggestions about how population distribution estimates of body fat should be used
in more mechanistically plausible pharmacokinetic modeling of dioxin elimination rates than
have been done in the past. These suggestions help avoid predictions of anomalously slow or
impossible negative elimination rates that follow from some previously developed statistical
formulae for describing dioxin elimination when applied to older and higher-fat segments of the
population. Such models are particularly needed for assessing long-past exposures to this group
of environmental chemicals.
34
3.1 Distributions of % Body Fat for U.S. Adults by Age and Sex Inferred from NHANES3
Data
The available NHANES3 data for adults (18 – 90) include kg body weight weight and
height measurements in cm for 9407 women and 8266 men. Similar data are also provided for
5151 females and 4981 males between 2 and 17 years of age. Each observation is accompanied
by a statistical weight that represents the number of people in the U.S. population that is
represented. These statistical weights allow estimation of the values of measured parameters
corresponding to defined percentiles of a representative sample of U. S. residents.
These data indicate that while vertical growth of people in the U.S. stops relatively
abruptly at age 15 or 16 on average (Figure 6), growth of body weight continues into middle
age—showing a broad plateau between approximately 40 and 60 years of age, followed by a
decline thereafter (Figure 7).
Together, weight and height are used to create a term called the “Body Mass Index”
(BMI)—the body weight in kilograms divided by the square of the height in meters. The body
mass index is very commonly used to estimate % body fat in people in epidemiological studies
where much more time consuming measurements (such as underwater weighing) are not
practical. Figure 8 shows mean body mass index data for males and females from the
NHANES3 study.
,Several different formulae have been used to estimate % body fat from BMI information
in the context of modeling TCDD elimination relationships. The first of these—by Knapik et al.
(1983), was used in the original analyses of observations of the Ranch Hand study participants
35
Figure 6
Population-Weighted Differences in Mean
Height for NHANES3 Subjects of Different Ages
18 0
Age 16
Mean Height (cm)
16 0
Age 15
14 0
Male Ht (cm)
Female Ht (cm)
12 0
10 0
80
0
10
20
30
40
50
Age (yrs)
60
70
80
90
36
Figure 7
Population-Weigted Differences in Mean Weight
for NHANES3 Subjects of Different Ages
10 0
Mean Weight (kg)
80
60
Male Weight (kg)
Female Weight (kg)
40
20
0
0
10
20
30
40
50
Age (yrs)
60
70
80
90
37
Figure 8
Population-Weighted differences in Mean Body
Weight Index for NHANES3 Subjects of Different Ages
35
Body Mass Index
30
25
20
Male BMI
Female BMI
15
10
0
10
20
30
40
50
Age (yrs)
60
70
80
90
38
(male veterans exposed to TCDD via herbicides used in Vietnam.) The most recent paper in this
series assessing TCDD elimination (Michalek and Tripathy, 1999), covering the 15 year followup of the Ranch Hand observations, continues with this older relationship:
% Body Fat = 1.264*BMI – 13.305
This formula was probably a natural choice for use when the Ranch Hand study started.
From the title of the Knapik paper, it appears that it was derived from observations of relatively
young people entering the U.S. military. There was no need for a treatment of sex because all
the Ranch Hand study participants were male. However, the lack of a term for age effects has
the potential to distort relationships in a longitudinal study lasting a few decades. The effect of
predictions using this formula on expected average body fat content in U.S. males can be seen in
Figure 9, in comparison with predictions using the formulae of Durenberg et al. (1991) and Lean
et al. (1996), which do include age terms. There is a conspicuous difference, in that the Knapik
formula does not predict an age-related increase in % body fat for U.S. males, contrary to
findings of studies that measure body fat by good methods (e.g. Lean et al.) and longitudinal
studies that indicate declining lean body mass with age (Forbes and Reina, 1970). Figure 10
compares the Durenberg and Lean equations (discussed below) for mean % body fat for U.S.
women.
39
Figure 9
Comparison of Projections of U.S. Male Mean
Body Fat From the Formulae of Durenberg et
al. (1991), Lean et al. (1996), and Knapick (1983)
(All Using NHANES3 Body Mass Index Data)
40
Estimated Mean % Body Fat
Durenberg US Male % BF
Lean US Male % BF
Knapik US Male % BF
30
20
10
15
25
35
45
Age (Yrs)
55
65
40
Figure 10
Comparison of Projections of U.S. Male Mean
Body Fat from the Formulate of Durenberg et
al. (1991) and Lean et al. (1996)--(Both Using
NHANES3 Body Mass Index Observations)
50
Durenberg US Female % BF
Lean US Female % BF
% Body Fat
40
30
20
15
25
35
45
Age (Yrs)
55
65
41
Another formula that has been used to estimate % body fat is taken from Durenberg et al.
(1991):
(1.2 x BMI) + (0.23 x age) - (10.8 x sex) - 5.4 (where “sex” for males = 1, females = 0)
It can be seen that in this formula the same coefficient is used for both sexes for the relationships
between BMI and age. The only difference in predictions between males and females comes
from the larger negative constant term used for males (-16.2%) compared to –5.4% for females.
A more recent paper that includes Durenberg as a coauthor (Lean et al., 1996) is based on
underwater weighing observations of 63 men and 84 women (age range 16.8-65.4) and separate
analysis of the data for the two sexes, resulting in:
% Body Fat (males) = 1.33*BMI + 0.236*age – 20.2
% Body Fat (females) = 1.21*BMI + 0.262*age – 6.7
It can be seen in Figures 9 and 10 above that these newer formulae do not seem to make
an appreciable difference in population mean body fat content predictions for U.S. adults
(particularly men). Nevertheless, it seems preferable to utilize these formulae from the more
recent paper with the apparent separate treatment of data for the two sexes.
Both figures 9 and 10 are limited to the age ranges actually studied by Lean et al. (1996).
Figure 11 shows the implications of extending the same formulae for predicting body fat content
42
to ages beyond 65 years. In this region the age-related increase in estimated mean % body fat
tends to flatten out.
A population distributional analysis sheds light on the likely reason for this flattening,
and also provides information of direct usefulness for risk assessments that need variability
estimates.
Figures 12-13 show lognormal probability plots of estimated % body fat in male and
females in the reference age group (18-24 years) vs 65-74 and 75-84. In this type of plot, the Zscore represents the number of standard deviations above or below the median of a theoretical
lognormal distribution fitted to the underlying data. The fitted lognormal distributions are
represented by the straight lines in the figures (and the fit of the points to the corresponding lines
is a quick qualitative indicator of how well the fitted lognormal distributions describe the data.
The regression constants can also be used to estimate body fat content in any desired percentile
of each population group). In the accompanying equations, the intercept is an estimate of the log
of the geometric mean, and the slope is an estimate of the log of the geometric standard
deviation. The steeper the lines (higher slopes) the greater the indicated interindivdual
variability in estimated % body fat.
It can be seen in these figures that lognormal distributions appear to describe the data
very well, with the possible exception of the body fat estimates for 18-24 year old females. Of
greater significance, both figures indicate shallower slopes (less variability) for the older age
groups. While the intercepts (log geometric means) of the fitted lines continue to increase with
age, the slopes decrease. One likely reason for this is that individuals with relatively higher body
fat content are being preferentially lost from the population with advancing age, tending to bring
43
Figure 11
Average % Body Fat vs Age in Men and Women
--Estimates from NHANES3 Body Mass Index
Data Using the Formulas of Lean et al. (1996)
50
% Body Fat
40
30
Female % Body Fat
Male % Body Fat
20
10
0
15
25
35
45
55
Age
65
75
85
44
Figure 12
Females--Lognormal Plots of Body Fat Distributions Estimated from Body
Mass Index Data for NHANES3 Females in Young vs Elderly Age Groups
Log(Female 75-84 % BF) y = 1.655 + 0.0599x R^2 = 0.998
Log(Female 65-74 % BF) y = 1.581 + 0.1064x R^2 = 0.999
Log(Female 18-24 % BF) y = 1.446 + 0.1031x R^2 = 0.965
1.90
Log(% Body Fat)
1.80
1.70
1.60
1.50
1.40
1.30
-2
-1
0
1
Z-Score
2
3
45
Figure 13
Males--Lognormal Plots of Body Fat Distributions Estimated from Body
Mass Index Data for NHANES3 Males in Young vs Elderly Age Groups
1.8
Log(Male 75-84 % BF)
Log(Male 65-74 % BF)
Log(Male 18-24 % BF)
y = 1.512+ 0.0672x R^2 = 0.999
y = 1.498 + 0.0819x R^2 = 0.998
y = 1.204 + 0.1467x R^2 = 0.998
Log(% Body Fat)
1.6
1.4
1.2
1.0
-3
-2
-1
0
Z-Score
.
1
2
3
46
the upper percentile ends down relative to the median and lower percentile ends of the
distributions. This is qualitatively consistent with our understanding of the contributions of
obesity (and associated conditions such as type II diabetes) to cardiovascular mortality.
3.2 Toward More Mechanistically Plausible Representations of the Effects of % Body Fat
on the Rate of Elimination of Poorly Metabolized Lipophilic Environmental Chemicals (e.g
2,3,7,8-Tetrachloro-Dibenzo-Dioxin—TCDD)
In the past, a couple of different empirically-fit equations have been used to represent the
dependence of TCDD elimination on body fat content. The first is attributed to the 10-year
follow-up of the “Ranch Hand” subjects (exposed to TCDD in the course of military service in
Vietnam) by Michalek et al., (1996). This takes the form,
k(t) = ke + k1(F(t) - 25)
where ko is the elimination rate (year-1) for a person with 25% body fat; k1 is a constant reflecting
the change in elimination rate with body fat (year-1); and F(t) is the percentage body fat at year
‘t’ in an individual’s life. Michalek et al reported values ko = 0.0665 and k1 = -0.00314
predicting a 2378-TCDD half-life of 10.4 years for a person with 25% body fat.
Pinsky and Lorber (1998) used the same elimination rate formula but derived the values
of ko = 0.0775 and k1 = -0.00313. Using these constants, a lower half-life of 8.9 years is
calculated for a person with 25% body fat.”
47
A difficulty with both of these formulae is that they predict impossible negative
elimination rates at body fat content levels that are within the range of fat contents that are
present in appreciable numbers of people. For the Michalek et al., relationship, negative
elimination rates are predicted above about 47% body fat; for the Pinsky and Lorber (1998)
estimates, this occurs above a fat content of about 50%.
Table 22 shows estimated population
percentiles of body fat content in the U.S. for adults under 65, and our two older 65-74, and 7584 age groups.
TCDD is eliminated from the body in part via the gastrointestinal tract, and probably in
part via liver metabolism. A third pathway is also possible, but has not been quantitatively
assessed as far as is known to the author. That is, via exfoliation of the outer layers of skin.
An earlier analysis of the gastrointestinal elimination of TCDD was done based on data
of Rhode et al. (1999) in six volunteer subjects indicated that the rate of elimination via the
gastrointestinal tract appeared somewhat smaller in subjects with greater estimated body fat
content (Figure 14). Overall, however the elimination rate calculated from these data suggests a
value that at most appears to correspond to half the total elimination rate observed in the Ranch
Hand veterans.
How and why should one expect that the size of the fat compartment would influence the
rate at which lipophilic compounds are eliminated from the body—either via feces or via liver
metabolism or by some third pathway? Essentially we should expect elimination to be smaller in
48
Table 22
Estimated Cumulative Percentiles of US Males and Females Below Various Body Fat
Contents in Designated Age Groups
18-64 Years of Age
% Body Fat
10
15
20
25
30
35
40
45
50
55
60
65
70
Cumulative % US Males Age 18-64 Cumulative % US Females Age 18-64
(N = 6133)
(N = 7084)
0.38
5.9
20.6
0.34
44.4
5.7
68.5
19.8
85.2
37.8
93.8
57.2
97.0
74.5
98.5
86.4
99.2
93.7
99.6
96.9
98.4
99.4
65-74 Years of Age
% Body Fat
20
25
30
35
40
45
50
55
60
65
70
Cumulative % US Males Age 65-74 Cumulative % US Females Age 65-74
(N = 1118)
(N = 1128)
0.94
10.7
36.0
5.2
70.9
37.8
92.2
57.2
97.5
74.5
99.3
86.4
99.8
93.7
96.9
98.4
99.4
49
Table 22, Continued
Estimated Cumulative Percentiles of US Males and Females Below Various Body Fat
Contents in Designated Age Groups
75-84 Years of Age
% Body Fat
25
30
35
40
45
50
55
60
65
Cumulative % US Males Age 75-84 Cumulative % US Females Age 65-74
(N = 776)
(N = 887)
4.5
29.0
68.5
2.6
92.3
19.6
97.8
51.0
99.7
78.3
93.1
97.6
99.5
50
Figure 14
Data of Rohde et al. (1999) on the Relationship of
Fecal 2,3,7,8-TCDD Clearance and Estimated % Body Fat
0.05
Fract Fecal Elim/Year
y = 0.09735 - 0.00282x R^2 = 0.752
0.04
0.03
0.02
20
21
22
23
% Body Fat
24
25
26
51
individuals with more fat because the pathways to elimination both depend on the redistribution
of the TCDD from fat to other compartments (liver or gut contents, respectively). The basic
notion is that the TCDD in the fat should be sequestered and not subject to direct elimination
either physically or chemically. Therefore, the larger the storehouse of (presumed inert) fat, the
smaller the proportion of total body TCDD that should be contained in the relatively small
compartments where elimination takes place (gut contents, liver, and possibly epidermis).
Let L be the fat-equivalent size (liters of fat equivalents based on steady state TCDD
partitioning capacity) of the body compartments responsible for TCDD elimination (gut contents,
liver, etc.) and F be the size of the fat compartment in the same units. Then let us assume that
TCDD elimination depends on the fraction of total TCDD that is in L rather than F. The rate of
loss of total body stores of TCDD per year in this case would be given by
Kelim (year-1) = constant * TCDD in L/(TCDD in F + TCDD in L)
If we increase the percentage body fat content from F to some multiple M X F, the fraction of
TCDD that is in L is reduced (assuming M is greater than 1) and the new elimination rate is
Kelim (year-1) = constant*original TCDD in L/(MF + TCDD in L)
If the amount of TCDD in L is very small relative to the amount in fat, and assuming L does not
change with an increase in the relative size of the fat compartment, then the elimination rate will
be reduced simply in inverse proportion to the M-fold increase in the body fat TCDD holding
capacity. Otherwise the equation can be simplified for application to data by taking the
reciprocal of each side of the equation:
1/Kelim (year-1) = MF/(constant * Original TCDD in L) + 1/constant
52
MF here can probably be simply replaced by % Body Fat, and the remaining terms
become familiar linear regression constants. Further analyses of the Ranch Hand and other data
sets describing TCDD elimination might there fore benefit from application of this reformulation
of the equation used in regression analyses. This can be pursued in further work, provided that
raw data are available for such a reanalysis.
4. Conclusions
Several conclusions have emerged from this work.
In Section 2 we found that for typical relatively hydrophilic compounds whose
pharmacokinetics are analogous to drugs, a reasonable central tendency estimate is that the effect
of aging is to increase the typical ratio of internal integrated concentration X time per unit of
external dose by approximately 1.5 fold in 65-85 year old people relative to 18-24 year olds—
with corresponding changes in elimination half life and clearance. No systematic change is
indicated for the volume of distribution of these chemicals. An apparent exception to this pattern
is for drugs eliminated primarily by phase II conjugation reactions, for which there is no apparent
change in clearance or half life with age. Additionally, there does not appear to be any
systematic change in the interindividual variability of key pharmacokinetic parameters in older
vs younger age groups.
In Section 3 we found that for highly lipophilic, poorly metabolized compounds a key
determinant of elimination rates is the body fat content. Body fat contents systematically
increase with age leading to a tendency for decreased elimination rates with age, other things
being equal. Distributions of body fat content tend to narrow in elderly age groups compared to
younger adults, probably in part because of increased age-specific mortality rates with higher
body fat content. We also found room for improvement in the typical regression equations used
53
to date to model the effect of body fat content on the elimination rates for lipophilic compounds.
We suggested a simple transformation for potential application to refined regression analyses of
available empirical data on this topic.
5. References
Bernstein C, Bernstein H. 1991. Aging, Sex, and DNA Repair Academic Press, Inc., Harcort
Brace Jovanovich, New York.
Cooper RL, Goldman JM, Harbin TJ, eds. 1991. Aging and Environmental Toxicology—
Biological and Behaviioral Perspectives Johns Hopkiins University Press, Baltimore
Cristofalo VJ. 1985. CRC Handbook of Cell Biology of Aging CRC Press, Inc, Boca Raton, FL
Deurenberg P, Weststrate JA, Seidell JC. Body mass index as a measure of body fatness: ageand sex-specific prediction formulas. British Journal of Nutrition 1991; 65(2): 105-14.
Dollery, C. 1991. Therapeutic Drugs Churchill Lingstone, London Volumes 1 and 2
Dollery, C. 1999. Therapeutic Drugs Churchill Lingstone, London Volumes 1 and 2
Forbes FB, Reina JC. 1970. Adult lean body mass declines with age: Some longitudinal
observations. Metabolism 19: 653-663.
Ginsberg G, Hattis D, Sonawane B, Russ A, Banati P, Kozlak M, Smolenski S, Goble R. 2002.
Evaluation of child/adult pharmacokinetic differences from a database derived from the
therapeutic drug literature. Toxicological Sciences 66: 185-200.
Ginsberg G, Hattis D, Miller R, Sonawane B. 2003 in press. Pediatric pharmacokinetic data:
implications for environmental risk assessment for children,” Pediatrics (in press).
Greenblatt DJ, Divoll M, Darrell BS, Abernathy R, Shader R. 1982. Physiologic changes in old
age: relation to altered drug disposition. J. Am Geriatrics Soc. Suppl 30:S6-S10.
Harpman JG and Limbiro LE, eds. 2001. Goodman & Gilman's The Pharmacological Basis of
Therapeutics, 10th ed. Mcgraw Hill, New York.
Hattis D, Banati P, Goble R. 1999a. “Distributions of individual susceptibility among humans for
toxic effects--for what fraction of which kinds of chemicals and effects does the traditional 10fold factor provide how much protection?” Annals of the New York Academy of Sciences 895:
286-316.
54
Hattis D. Banati P, Goble R, Burmaster D. 1999b. Human interindividual variability in
parameters related to health risks. Risk Analysis 19: 705-720.
Hattis D, Baird S, Goble R. 2002. “A Straw Man Proposal for a Quantitative Definition of the
RfD,” in Final Technical Report, U.S. Environmental Protection Agency STAR grant #
R825360, “Human Variability in Parameters Potentially Related to Susceptibility for Noncancer
Risks,” Full version available on the web at http://www2.clarku.edu/faculty/dhattis; shortened
version Drug and Chemical Toxicology 25: 403-436.
Hattis D, Walker K, Russ A, Goble R. 2003a. Role of Dosimetric Scaling and Species
Extrapolation in Evaluating Risks Across Life Stages. I. Dosimetric Considerations in
Childhood. Draft Report to the U.S. Environmental Protection Agency Under RFQ No. DC-0300009
Hattis D, Ginsberg G, Sonawane B, Smolenski S, Russ A, Kozlak M, Goble R. 2003b.
Differences in pharmacokinetics between children and adults—ii. children’s variability in drug
elimination half-lives and in some parameters needed for physiologically-based pharmacokinetic
modeling, Risk Analysis 23: 117-142.
Lamy PP. 1982. Comparative pharmacokinetic changes and drug therapy in an older population.
J. Am Geriatrics Soc. Suppl 30:S11-S19.
Lean MEJ, Han TS, Deurenberg P. 1996. Predicting body composition by densitometry from
simple anthropometric measurements. Am J. Clin. Nut. 63: 4-14.
Masoro EJ, Schwartz JB. 2001. Exploration of Aging & Toxic Response Issues. Report of
Contract No. 68-C-99-238, Task Order 15, Prepared for Risk Assessment Forum, U. S.
Environmental Protection Agency, by Versar, Inc., Springfield, VA, February 15, 2001.
Masoro EJ, ed. 1995. Handbook of Physiology, Section 11, Aging Oxford University Press,
New York.
Mayersohn M. 1994. Pharmacokinetics in the elderly. Environmental Health Perspectives
102(Suppl. 11): 119-124.
Michalek JE, Tripathi RC 1999. Paharmacokinetics of TCDD in veterans of Operation Ranch
Hand: 15-year follow-up. J. Toxicol. Environmental Health, Part A 57: 369-378.
O’Flaherty EJ. 2000. Modeling normal aging bone loss, with consideration of bone loss in
osteoporosis. Toxicological Sciences 55: 171-188.
Pinsky P, Lorber MN. 1998. A model to evaluate past exposure to 2,3,7,8-TCDD. J. Exposure
Anal. Environ. Epidemiol 8: 187-.
Price PS, Conolly RB, Chaisson CF, Gross EA, Young JS, Mathis ET, Tedder DR. 2003.
Modeling interindividual variation in physiological factors used in PBPK models of humans. Crit
Rev Toxicol. 33(5): 469-503.
55
Rohde S, Moser GA, Papke O, McLachlan MS. 1999. Clearance of PCDD/Fs via the
gastrointestinal tract in occupationally exposed persons. Chemosphere 38: 3397-3410.
Rowe JW. 1995. Handbook of the Biology of Aging, 4th ed, Academic Press, San Diego, Calif.
Rowe JW, Andres R, Tobin JD, Norris AH, Shock NW 1976. The effect of age on creatinine
clearance in men: A cross-sectional and longitundinal study. J. Gerontology 31:m155-163.
Sotaniemi EA, Arranto AJ, Pelkonen O, Pasanen M. 1997. Age and cytochrome P450-linked
drug metabolism in humans: An analysis of 226 subjects with equal histopathologic conditions.
Clinical Pharmacology & Therapeutics 61: 331-339.
Appendix A—Data Source References
KS Albert, WR Gillespie, JG Wagner, A Pau, GF Lockwood 1984. Effects of age on the clinical
pharmacokinetics of ibuprofen. Am J Med 6:47-50.
AC Altamura, T Melorio, G Invernizzi, R Gomeni 1982. Influence of age on mianserin
pharmacokinetics. Psychopharmacology 78:380-2.
AC Altamura, T Melorio, G Invernizzi, F Colacurcio and R Gomeni 1983. Age-related
differences in kinetics and side effects of violxazine in man and their clinical implications.
Psychopharmacology 81:281-5.
JB Bentley, JD Borel, RE Nenad, TJ Gillespie 1982. Age and fentanyl pharmacokinetics. Anesth
Analg 61:968-71.
RA Braithwaite, P Crome, S Dawling, RR Lewis 1979. Pharmacokinetics of nortryptiline in
elderly depressed patients and prediction of optimal dosage regimes. Br J Clin Pharmacol 9:3067.
E Chester, RC Reed, HJ Schwartz 1982. The comparative evaluation of a new sustained-release
theophylline preparation, bronkodylar- SR, with a theophylline elixir, elixophylline, in
volunteers. Current Therapeutic Research, 32: 476-491.
JJ Crowley, BJ Cusack, SG Jue, JR Koup, BK Park, RE Vestal 1988. Aging and drug
interactions. II. Effects of phenytoin and smoking on the oxidation of theophylline and cortisol in
healthy men. J Pharmacol Exp Ther 245(2):513-23.
NR Cutler, PK Narang, LJ Lesko, M Ninos, M Power 1984. Vancomycin disposition: the
importance of age. Clin Pharmacol Ther 36(6):803-810.
D Debruyne, MA Moulin, J Tartiere, M-C Bigot, J-L Gerard, H Bricard 1990. Clinical
pharmacokinetics after repeated intrapleural bupivicaine administration. Clin Pharmacokinet
18(3):240-4.
56
ANJA De Groot, TB Vree, YA Hekster, GJ Pesman, FCG J Sweep, PJW Van Dongen, J Van
Roosmalen 1995. Bioavailability and pharmacokinetics of sublingual oxytocin in male
volunteers. J Pharm Pharmacol 47:571-5.
JD de Vries, L Salphati, S Horie, CE Becker and B-A Hoener 1994. Variabilityin the disposition
of chlorzoxazone. Biopharm Drug Disposition 15:587-97.
DG Ferry, LR Gazeley, WJ Busby, DMG Beasley, JR Edwards, AJ Campbell 1990. Enhanced
elimination of piroxicam by administration of activated charcoal or cholestyramine. Eur J Clin
Pharmacol 39:599-601.
RJ Flanagan, A Johnston, AST White, P Crome 1989. Pharmacokinetics of dextropropoxyphene
and nordextropropoxyphene in young and elderly volunteers after single and multiple
dextropropoxyphene dosage. Bt J Clin Pharmac 28:463-9.
A Forrest, S Chodosh, MA Amantea, DA Collins, JJ Schentag 1997. Pharmacokinetics and
pharmacodynamics of oral grepafloxacin in patients with acute bacterial exacerbations of chronic
bronchitis. J Antimicrobial Chemotherapy 40 (supplement A):45-57.
J Gaillot, J-L J Steimer, A J Mallet, J J Thebault, A Bieder 1979. A Priori lithium dosage
regimen using population characteristics of pharmacokinetic parameters. J Pharmacokinetics and
Biopharmaceutics 7(6):579-602
U Gladziwa, U Klotz, K Maumer, R Zollinger, H Mann, H-G Sieberth 1993. Pharmacokinetics
of epoetin (recombinant human erythropoietin) after long term therapy in patients undergoing
haemodialysis and haemofiltration. Clin Pharmacokinet 25(2):145-153.
SE Gould et al. 1990. Could the increased antihypertensive efficacy of ketanserinin th eelderly
be due to altered pharmacokinetics? Cardiovascular drugs and therapy 4:89-92.
DJ Greenblatt, MD Allen, JS Harmatz, RI Shader 1980. Diazepam disposition determinants. Clin
Pharmacol Ther 27(3):301-12.
DJ Greenblatt, DR Abernethy, R Matlis, JS Harmatz, RI Shader 1984. Absorption and
disposition of ibuprofen in the elderly. Arthritis and rheumatism 27(9):1066-9.
PJ Hayball, RL Nation, F Bochner, LN Sansom, MJ Ahern, MD Smith 1993. The influence of
renal function on the enantioselective pharmacokinetics and pharmacodynamics of ketoprofen in
patients with rheumatoid arthritis. Br J Pharmaco 36:185-93.
JF Henry, C Altamura, R Gomeni, MP Hervy, F Forette, PL Moriselli 1981. Pharmacokinetics of
amitriptyline in the elderly. Int J Clin Pharmacol Ther Toxicol 19(1):1-5.
RJ Herman, CB McAllister, RA Branch, GR Wilkinson 1985. Effects of age on meperidine
disposition. Clin Pharmacol Ther 37:19-24.
57
N. Hockings, AA Ajayi and JL Reid 1986. Age and the pharmacokinetics of angiotensin
converting enzyme inhibitors enalapril and enalaprilat. Br J Clin Pharmac 21:341-8.
L Holmberg, I Odar-Cederlof, LO Boreus, L Heyner, M Ehrnebo 1982. Comparative disposition
of pethidine and norpethidine in old and young patients. Eur J Clin Pharmacol 22:175-9.
WD Hooper and MS Qing 1990. The influence of age and gender on the stereoselective
metabolism and pharmacokinetics of mephobarbital in humans. Clin Pharmacol Ther 48:633-40.
SHD Jackson, A Johnston, R Woollard, P Turner 1989. The relationship between theophylline
clearance and age in adult life. Eur J Clin Pharmacol 36:29-34.
NS Jallad, DC Garg, JJ Martinez, EJ Mroszczak, DJ Weidler 1990. Pharmacokinetics of singledose oral and intramuscular ketorolac tromethamine in th eyoung and elderly. J Clin Pharmacol
30:76-81.
PE Johnson, DB Milne, GI Lykken 1992. Effects of age and sex on copper absorption, biological
half-life, and status in humans. Am J Clin Nutr 56:917-25.
A Jorgensen, P Staehr 1976. On the biological half-life of amitriptyline. J Pharm Pharmac 28:624..
F Jorquera, MM Almar, M Pozuelo, D Sansegundo, M Gonzalez-Sastre, J Gonzalex-Gallego
1995. Effects of aging on antipyrene clearance: predictive factors of metabolizing capacity. Clin
Pharmacol 35:895-901.
G Kaiser, R Ackermann, W Dieterle, CJ Durnin, J McEwen, K Ghose, A Richens, IB Holmes
1990. Pharmacokinetics and pharmacodynamics of the ace inhibitor benazepril hydrochloride in
the elderly. Eur J Clin Pharmacol 38:379-85.
MJ Kendall, R Jubb, HA Bird, P le Gallez, J Hill, AJ Taggart, R Rau 1990. A pharmacokinetic
comparison of ibuprofen sustained-release tablets given to young and elderly patients. J Clin
Pharm Ther 15:35-40.
JB Kitts, DM Fisher, PC Canfell, MJ Spellman, JE Caldwell, T Heier, MR Fahey, RD Miller
1990. Pharmacokinetics and pharmacodynamics of atracurium in the elderly. Anesthesiology
72:272-5.
TE Lackner and S Birge 1990. Accuracy of pharmacokinetic dose determination of gentamicin in
geriatric patients. DICP, the annals of pharmacotherapy 24:29-32.
KR Lees, JL Reid 1987. Age and the pharmacokinetics and pharmacodynamics of chronic
enalapril treatment. Clin Pharmacol Ther 41:597-602.
58
G Li, G Treiber, K Maier, S Walker, U Klotz 1993. Disposition of ibuprofen in patients with
liver cirrhosis: stereochemical considerations. Clin Phamacokinet 25(2):154-63.
GR Matzke, JJ Jameson, CE Halstenson 1987. Gentamicin disposition in young and elderly
patients with various degrees of renal function. J Clin Pharmacol 27:216-220.
PA Miglioli, P Pivetta, M Strazzabosco, R Orlando, L Okolicsanyi, P Palatini 1990. Effect of age
on single- and multiple-dose pharmacokinetics of erythromycin. Eur J Clin Pharmacol 39:161-4.
M Miller, KE Opheim, VA Raisys, 1984. Theophylline metabolism: Variation and genetics.
Clin. Pharmacol. Ther., 35: 170-182.
JO Miners, R Penhall, RA Robson, DJ Birkett 1988. Comparison of paracetamol metabolism in
young adult and elderly males. Eur J Clin Pharmacol 35:160-157.
FO Muller, HKL Hundt, M Van Dyk, G Groenewoud, HG Luus 1986. Ibuprofen bioavailability.
S Afr Med J 70:197-9.
A Nies, DS Robinson, MJ Friedman, R Green, TB Cooper, CL Ravaris, JO Ives 1977.
Relationship between age and tricyclic antidepressant plasma levels. Am J Psychiatry 134:790-3.
HR Ochs, DJ Greenblatt, H Friedman, ES Burstein, A Lockniskar, JS Harmatz, RI Shader 1987.
Bromazepam pharmacokinetics: influence of age, gender, oral contraceptives, cimetidine, and
propranolol. Clin Pharmacol Ther 41:562-70.
MB O'Connell, PR Pentel, CL Zimmerman 1989. Individual variability in the blood pressure
response to intravenous phenylpropanolamine: a pharmacokinetic and pharmacodynamic
investigation. Clin Pharmacol Ther 45:252-9.
E Perucca, R Grimaldi, G Gatti, S Pirracchio, F Crema, GM Frigo 1984. Pharmacokinetics of
valproic acid in the elderly. Br J Clin Pharmac 17:665-669.
J Plantier, AW Forrey, MA O'Neill, AD Blair, TG Christopher, RE Cutler 1976.
Pharmacokinetics of amikacin in patients with normal or impaired renal function: radioenzyme
acetylation assay. J Infectious Diseases 134(supp):S323-30.
H-P Platten, E Schweizer, K Dilger, G Mikus, U Klotz 1998. Pharmacokinetics and the
pharmacodynamic action of midazolam in young and elderly patients undergoing tooth
extraction. Clin Pharmacol Ther 63:552-60.
J Posner, M Danhof, MWE Teunissen, DD Breimer, PD Whiteman 1987. The disposition of
antipyrene and its metabolites in young and elderly volunteers. Br J Clin Pharmac 24:51-55.
JP Rho, A Jones, M Woo, S Castle, K Smith, RE Bawdon, DC Norman 1989. Single-dose
pharmacokinetics of intravenous ampicillin plus sulbactam in healthy elderly and young adult
subjects. J Antimicrobial Chemotherapy 24:573-80.
59
DE Rollins, G Alvan, L Bertilsson, JR Gillette, B Mellstrom, F Sjoqvist, L Traskman 1980.
Interindividual differences in amitriptyline demethylation. Clin Pharm Ther 28:121-9
M Rowland, PD Thomson, A Guichard, KL Melmon, 1971. Disposition kinetics of lidocaine in
normal subjects. Ann New York Acad Sci (179):383-98.
M Rowland 1990. Clinical pharmacokinetics of teicoplanin. Clin Pharmacokinet 18(3):184-209.
GR Siber, AL Smith, MJ Levin 1979. Predictability of peak serum gentamicin concentration
with dosage based on body surface area. J Pediatr 94(1):135-8.
KJ Simons, TJ Martin, WTA Watson, FER Simons 1990. Pharmacokinetics and
pharmacodynamics of terfenadine and chlorpheniramine in th eelderly. J Allergy Clin Immunol
85:540-7.
J Sonne, S Loft, M Dossing, S Boesgaard, F Anderson 1991. Single dose pharmacokinetics and
pharmacodynamics of oral oxazepam in very elderly institutionalized subjects. Br J Clin
Pharmac 31:719-22.
EA Sotaniemi, AJ Arranto, O Pelkonen, M Pasanen 1997. Age and cytochrome P450-linked
drug metabolism in humans: an analysis of 226 subjects with equal histopathological conditions.
Clin Pharmacol Ther 61:331-9.
BAM van Schaik, GG Geyskes, PA van der Wouw, HH van Rooij, AJ Porsius 1988.
Pharmacokinetics of Lisinopril in Hypertensive Patients with Normal and Impaired Renal
Function. Eur J Clin Pharmacol 34:61-5.
ES Vesell, JG Page, GT Passanati 1970. Genetic and environmental factors affecting ethanol
metabolism in man. Clin Pharm Ther 12(2):192-201.
ES Vesell 1974. Factors causing interindividual variations of drug concentrations in blood. Clin
Pharm Ther 16(1):135-48.
RE Vestal, AJJ Wood, RA Branch, DG Shand, GR Wilkinson 1979. Effects of age and cigarette
smoking on propanolol disposition. Clin Pharmacol Ther 26(1):8-15.
VE Ziegler, JT Biggs, AB Ardekani, SH Rosen 1978. Contribution to the pharmacokinetics
60
Appendix B--Contents of the Data Base/Analysis File
(Excel Workbook Titled “PKeldforanal.xls”)
(available at http://www2.clarku.edu/faculty/dhattis)
“Metabolic Classifications” worksheet—This records detailed notes of the information that came
from each data source and contributed to the classification of individual chemicals according to
principal routes of elimination.
“Overall Database” worksheet. This is the basic database, with the following fields:
A. Chemical—name of the drug.
B. Route of Elimination—classification of principal mechanism by which the drug is
thought to be eliminated from the body.
C-G—“Dummy” (0 or 1) variables for major categories of elimination mechanisms.
H. Parameter—parameter taken from the original source paper.
I. Parameter Std—standardized parameter term used for analysis
J. Units—units of the original listed parameter given in the source paper
K. Standardized Units—units for the standardized parameter. For AUC, these are (µgh/ml)/(mg/kg dose); for Clearance these are ml/(min-kg body weight), for T1/2 these
are hours, and for Vd, these are liters/kg body weight.
L. Mean—the individual or group mean parameter value, in the original units (column
J).
M. Standardized mean—the mean (or individual) value transformed into the standardized
units of column K.
N. Log(mean)—the logarithm (base 10) of the standardized mean.
O. Stdev—standard deviation (original units)
P. Standardized stdev—standard deviation in standard units
Q. SE—standard error (standard deviation/square root of N)
R. N—the number of individuals contributing to the mean of the data.
S. Sqrt N—the square root of N—used as the statistical weight in the regression
analyses.
61
T. Gender—male, female, both or unknown/not given.
U. Male?—Dummy variable: 1 if the subject(s) were all male; 0 if all female; blank
otherwise.
V. Age (yr)—individual value or group mean, otherwise the midpoint of a stated range,
if the data are only given in that form.
W. Age^2—the square of the age
X. Age stdev or range
Y. GFR flag (0 for normal renal function; 1 for impared renal function; blank for no
information)
Z. GFR (ml/min, usually as creatinine clearance)
AA.
GFR stdev or range
AB.
Reference
AC.
Notes
“Excluded GFR selection” worksheet—This is a repository for data that were excluded from
analysis because the authors deliberately chose people with unusually deficient renal clearance
for study—e.g. kidney dialysis patients.
“Database with Dummies” worksheet—This has the same content of the “Overall Database”
worksheet, with the addition of dummy variables for all the items to be studied in the regression
analysis—particularly the chemical and the age groups.
“Notes” worksheet—miscellaneous notes
“Data Summaries” worksheet—analyses deriving the various summaries of the data presented in
Section 2.3.
“Regression Results” worksheet—complete results for the regression analyses. AUC analyses
are on lines 1-233; clearance analyses are on lines 250-580; T1/2 analyses are on lines 690-1106;
and volume of distribution analyses are on lines 1122 and higher. Ranging in columns the
worksheet, analyses of the whole database for each parameter in 10-year age groups are in
columns A-F; columns H-M show analyses with age 5 year age groups beyond age 65 only, and
columns V-AA show analyses using 5-year age categories throughout. Columns O-T show
analyses using quadratic (age and age2) terms treating age as a continuous parameter. In all
cases these lead to descriptions of the data that are inferior to the use of the dummy variables for
age categories. Finally, the remaining columns show analyses by subsets of the data by
predominant modes of elimination (columns AC-CX), or by sex (columns CU-DG).
62
The remaining worksheets are in pairs. The sheets titled Vd, Half-Life, Clearance, and AUC
give the full databases (including dummy variables) analyzed for each parameter. The
corresponding worksheets with the suffix “ind” include only the data for individuals for each
parameter (group size = 1), and analyze the distribution of the departures of the individual data
points from expected values generated from the overall regression relationships in 5-year age
groups.