A Trivariate Distribution for the Height, Weight, and Fat of Adult Men*

Abstract

Using exploratory data analysis, probability plots, scatterplots, and computer animations to rotate and visualize the data, we fit a trivariate Normal distribution to data for the height, the natural logarithm of body weight, and the body fat for 646 men between the ages of 50 and 80 years as reported by the medical staff of the US Veterans Administration's "Normative Aging Study" in Boston, MA. Although these data do not include any children, women, or young men, the measurements represent the best data that we could find through a 4-year search. We believe that these data are well measured and reliable for men in the specified age range and that these data reveal an interesting statistical pattern for use in probabilistic PBPK models. Introduction and Data

A Weight Index for the Standardized Uptake Value in 2-Deoxy-2-[F-18]fluoro-d-glucose-Positron Emission Tomography

“…Only an additional õ0.006 reduction in the cv of blood SUV was found. There is underlying physiological support for the unimportance of H compared to W: while finding r = 0.49 for % body fat (having a minimal FDG uptake) correlation with lnW, finding only 0.07 without significance for correlation with H [14]. Moreover, the cv of H is only about 1/2 that of W in the adult population.…”

“…Use is made of a small coefficient of variation (cv) of W, namely 0.15, being encountered in adults [14]. Because the approximation ln(1 + x) $ x can be used, it is found that n = w. The population geometric mean weight W geo = exp(the average of the lnW_s) in practice is quite close to the arithmetic average weight W avg .…”

“…In another but related approach, an index m may be defined quite simply as the slope of SUV vs. W. The logarithmic formulation is natural because of both lognormal W [14] and SUV [15] distributions in populations. Since both linear and logarithmic formulations can be convenient, both are treated here.…”

Review of Information Resources to Support Human Exposure Assessment Models

“…Certain correlations (e.g., between body weight and skin surface area) are so well characterized that joint distributions have been established (e.g., Burmaster and Murray 1998). Many other correlations have been qualitatively identified but not extensively quantified (e.g., the correlations between body weight and water intake or food intake).…”

Evaluation of physiologically based pharmacokinetic models for use in risk assessment

“…There are a number of integration algorithms and programming languages currently available for coding and solving PBPK model equations (Table 3), and It is currently used by academic and commercial institutions for constructing mathematical models for research and teaching A computer system where connections between various data libraries in the preparation and post-processing of simulation are executed by macro commands A system that allows the user to create compartmental models based on personal biological knowledge, leaving the construction and numerical solution of the differential equations to the software Numerical integration algorithms developed by the Department for PBPK modeling A visualization software package capable of importing processed resonance images and combining the use of ACSL to create three-dimensional representations of the PBPK of a chemical in an organism This software facilitates the conduct of Bayesian analysis with PBPK models but has no graphical interface personal and portable computers marketed today generally possess sufficient speed, disk space and run time memory required for PBPK modeling. Many of the commercially available software packages routinely make use of integration algorithms to obtain a numerical solution to differential equations (Menzel et al, 1987;Burmaster and Murray, 1998;Easterling et al, 2000;Reddy et al, 2003) such that (for most cases) the modeler or the risk assessor only needs to evaluate that an appropriate algorithm was used. (Most PBPK models are 'stiff' sets of differential equations and, unless it has been shown otherwise, the algorithm should be known to work for such sets of differential equations.)…”