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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. 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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.