Task Proposal: Body Fat Analysis
--- by Zhao, Hong About the data set: This data set includes the statistics of 252 men's body measurements which can be used to estimate the percentage of body fat. I got this data set from this address: http://www.stat.cmu.edu/datasets/bodyfat The data were generously supplied by Dr. A.Garth Fisher who gave permission to freely distribute the data and use for non-commercial purposes. This data set is characterized by 15 variables which are: Density determined from underwater weighing Percent body fat from Siri's (1956) equation Age (years) Weight (lbs) Height (inches) Neck circumference (cm) Chest circumference (cm) Abdomen 2 circumference (cm) Hip circumference (cm) Thigh circumference (cm) Knee circumference (cm) Ankle circumference (cm) Biceps (extended) circumference (cm) Forearm circumference (cm) Wrist circumference (cm) Background: Everybody wants to be healthy. So people are paying more and more attention to their health in their daily lifes. Modern people drink low-fat even non-fat milk, eat low-fat cheese, low-fat butter, low-cholesteral food. They do exercises to improve their health condition. "Fat" and "cholesteral seems to become "enemies" of their health. A variety of popular health books suggest that the readers assess their health, at least in part, by estimating their percentage of body fat. Over the last few decades an increasing number of noninvasive methods have become available for assessing body composition and in particular for assessing body fat. All methods rely on various underlying assumptions that may have a greater or lesser degree of validity depending upon the subject. This work compares the results obtained for the estimation of body fat using nine different methods in subjects having a wide range of body composition. Usually there are the following measurement methods: (See referance 3) 1. In vivo neutron activation analysis(IVNAA) for total body nitrogen(TBN). This measurement can be performed using the 252Cf-based instrument. A direct measurement of TBN can be achieved from analysis of the N-to-H gamma-ray counts ratio with internal standardization for body hydrogen. 2. Whole-body counting for total body potassium(TBK). Measurement of K40 TBK can be taken using a shadow-shield whole body counter K42 previously calibrated for sensitivity changes with body size by measurements in a group of healthy normal volunteers. 3. Tritiated water dilution for total body water(TBW). TBW can be of measured by a dilution method following the oral administration tritiated water and analysis of boold and urine samples. 4. Bioelectric impedance(BIA). Bioelectric impedance measurements can be taken using electrodes attached to the wrist and ankle. 5. Near-infrared interactance(IRI). Measurements of IRI can be performed using the Futrex-5000. The interactance measurements can be made in the belly of the bicep located using the arm-band when the subject is seated. 6. Skinfold anthropometry(SF). Skinfold thicknesses can be measured on one side of the body at the biceps, triceps, subscapular and suprailiac sites using the Harpenden Caliper. 7. Predictor equations incorporationg parameters of body habitus for total body fat, which was expressed as a percentage of the body mass. As we can see from the methods above, accurate measurement of body fat, for example, method 1-5, is inconvenient and costly and it is desirable to have easy methods of estimating body fat that are not inconvenient and costly. For example, some health books give the reader tables which can be used to estimate body fat from their age and various skin-fold measurements obtained by using a caliper. Some of them give predictive equations for body fat using body circumference measurements, for example, abdominal circumference, and/or skin-fold measurements(method 6 and 7). The partitioning of the body mass is carried out along the following lines(See reference 4): (a) The intravascular phase is obtained as the sum of plasma volume and red cell volume. (b) The extracellular phase is represented by the extracellular water (ECW), derived from the bromide(chloride) volume of dilution. The extracellular water is paralled by the total exchangeable chloride(Cle) and by the total exchangeable sodium(Nae) out of which approximately 85 per cent is present in the extracellular water. (d) The body cell mass(BCM) is derived from the total exchangeable potassium, according to the formula: BCM = Ke*8.33. Where Ke is the total exchangeable potassium. (e) The fat-free body(FFB) is derived from the formula: FFB = TBW/0.732. This derivation is based upon the assumption that body fat is anhydrous, and that the fat-free body is 73.2 per cent water. (f) Total body fat = B.Wt. - FFB. (B.Wt.: Body weight) (g) Fat-free solids(FFS) = FFB - TBW. (h) Estimated skeletal weight(Dry fat-free bone) is derived from the ratio Ke/FFS. Among the important ratios describing body composition the following may be mentioned: (a) ICW/TBW (b) Nae/Ke Both ratios reflect the balance between extracellular and intracellularphase. Here the author provides a method to estimate the body fat(f). On the other hand, percentage of body fat for an individual can be estimated once body density has been determined. Folks (e.g. Siri, 1956) assume that the body consists of two components -- lean body tissue and fat tissue. Letting D = Body Density (gm/cm^3) L = proportion of lean body tissue F = proportion of fat tissue (L+F=1) l = density of lean body tissue (gm/cm^3) f = density of fat tissue (gm/cm^3) we have D = 1/[(L/l) + (F/f)] solving for F we find F = (1/D)*[lf/(l-f)] - [f/(l-f)]. Using the estimates: l=1.10 gm/cm^3 f=0.90 gm/cm^3 (see Katch and McArdle, 1977, p. 111 or Wilmore (1976), p.123) we come up with "Siri's equation": Percentage of Body Fat (i.e. 100*B) = 495/D - 450. Volume, and hence body density, can be accurately measured a variety of ways. The technique of underwater weighing "computes body volume as the difference between body weight measured in air and weight measured during water submersion. In other words, body volume is equal to the loss of weight in water with the appropriate temperature correction for the water's density"(Katch and McArdle, 1977, p. 113). Using this technique, Body Density = WA/[(WA-WW)/c.f. - LV] where WA = Weight in air (kg) WW = Weight in water (kg) c.f. = Water correction factor (=1 at 39.2 deg F as one-gram of water occupies exactly one cm^3 at this temperature; =0.997 at 76-78 deg F) LV = Residual Lung Volume (liters) Also anthropometry is commoon field method for measuring body density. Brozek & Keys(1951) were the first to publish regression equations with functions of predicting body density with anthropometric variables. Subsequently, numerous investigators have published equations using various combinations of skinfolds and body circumferences. A.S.Jackson and M.L.Pollock are two of them. They published their paper "Generalized equations for predicting body density of men" in 1978 (See "The British Journal of Nutrition", volume 40, Page 497-504, 1978), they gave us eight generalized regression equations for predicting body density of adult men whose ages covered from 18 to 61 years. These 8 equations use different regression variables and have different correlations and standard errors. The equation with the largest correlation and the smallest standard errors is equation 6: BD = 1.1093800 - 0.0008267(X2) + 0.0000026(X2)^2 - 0.0002017(X3) - 0.005675(X4) + 0.018586(X5) R = 0.918 SE = 0.0072 where BD = Body Density X2 = sum of chest, abdomen and thigh skinfolds X3 = age X4 = waist circumference X5 = forearm circumference R = Correlation SE = Stand Error They also mentioned how they used their data: 1. A total of 403 adult men between 18 and 61 years of age volunteered as subjects. The sample represented a wide range of men who varied considerably in body structure, body composition, and exercise habits. 1. Skinfold thickness, body circumferences and body density were measured in samples of 308 and 95 adult men ranging in age from 18 to 61 years. 2. Using the sample of 308 men, multiple regression equations were calculated to estimate body density using either the quadratic or log form of the sum of skinfolds, combining with age, waist and forearm circumference. 3. The multiple correlations for the equations exceeded 0.90 with standard errors of approximately +0.0073 g/ml. 4. The regression equations were cross validated on the second sample of 95 men. The correlations between predicted and laboratory-determined body density exceeded 0.90 with standard errors of approximately 0.0077 g/ml. 5. The regression equations were shown to be valid for adult men varying in age and fatness. 6. The generalized equations were accurate and valid for use with adult men varying in age and body density. So we can predict body density with the predictive equation above. But in my data set I only have "density determined from underwater weighing", and I don't have the skinfolds required in the predictive equation for body density, so I am trying to use different body circumferences to predict the body density as well as percentage of body fat as my additional task. Task: According to the information provided by the web page I mentioned before, these data are used to produce the predictive equations for lean body weight given in the abstract "Generalized body composition prediction equation for men using simple measurement techniques", K.W. Penrose, A.G.Nelson, A.G. Fisher, FACSM, Human Performance Research Center, Brigham Young University, Provo, Utah 84602 as listed in "Medicine and Science in Sports and Exercise", vol. 17, no. 2, April 1985, p. 189. Unfortunately I couldn't find this paper. So I don't know the result of their work. My task is going to be estimation of body fat by multiple regression based on the data set. Also I will use different body circumferences to estimate body density as my additional task. I also got a data set of "percent fat prediction in males from abdomen and neck dircumference" from the book "Body composition and physical performance"(see reference 5). These data can be used as my cross validation samples. References: 1. http://www.stat.cmu.edu/datasets/bodyfat 2. Jackson A.S. & Pollock M.L. "Generalized equations for predictiing body density of Men" in "The Brithish Jounal of Nutrition", Volume 40, Page 497-504. 3. Simon J.S.Ryde, D.Walter Thomas, John L.Birks, Parvaiz A.Ali, Neville H.Saunders, Said Al-Zeibak, Wynford D.Morgan Swansea In Vivo Analysis Research Group Department of Medical Physics and Clinical Engineering, Singleton Hospital, Swansea, SA2 8QA, UK Department of Physics, University College of Swansea, Singleton Park, Swansea, SA2 8PP Department of Medical Physics and Biomedical Engineering, Queen Elizabeth Hospital, Edgbaston, Birmingham, B15 2TH, UK "Assessment of body fat: A comparison of techniques" in "Basic Life Sciences", Volume 60: "Human Body Composition" Edited by Kenneth J.Ellis and Jerry D.Eastman 4. Knud H.Olesen Department of Medicine B, University Hospital, Copenhagen, Denmark "Body composition in normal adults" in "Symposia of the society for the study of human biology" Volume VII: "Human body composition" edited by Josef Brozek 5. "Body composition and physical performance: Applications for the Military Services" Committee on Military Nutrition Research Food and Nutrition Board Institute of Medicine Edited by Bernadette M.Marriott and Judith Grumstrup-Scott
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