Interntionl Journl of Obesity (2003) 27, 498 504 & 2003 Nture Publishing Group All rights reserved 0307-0565/03 $25.00 www.nture.com/ijo PAPER Rtes of weight chnge for blck nd white Americns over twenty yer period TJ Sheehn*, S DuBrv, LM DeChello nd Z Fng w University of Connecticut School of Medicine, Frmington, CT, USA OBJECTIVE: To exmine the rte of weight gin over time mong Americns by ge, gender, nd rce. PARTICIPANTS: Scientific smple of 5117 Americns, ges 25 74 y in 1971 followed for 20 y. RESULTS: Rtes of weight gin estimted by mixed effects models re highest mong young dults nd rtes of weight loss re gretest mong older dults. The overll shpe of the growth curves re similr for men nd women, blck nd white, in terms of both weight gin nd weight loss. Rtes re lso ffected by bseline body mss index (BMI ¼ wt in kg/height in m 2 ). CONCLUSIONS: Americns gin weight until middle ge, stbilize, nd begin to lose weight ner ge. Weight loss during old ge is especilly evident for obese Americns. The bility to ccurtely identify groups with incresed risk nd trget them for obesity prevention will help combt the stedy rise of overweight nd obesity in Americ. Interntionl Journl of Obesity (2003) 27, 498 504. doi:10.1038/sj.ijo.02263 Keywords: obesity; ging; longitudinl studies; body mss index; weight gin; weight loss Introduction Obesity is the number one helth problem in the US 1 nd it hs been worsening. 2 While more nd more Americns re being clssified s obese, little is known bout the pttern of weight chnge in individuls during the dult yers. Who is gining weight? When re they gining? Are the rtes the sme for everyone t ll ges, for men s for women? Are the rtes similr for blck nd white Americns? Answers to these questions could identify who is t risk nd when. While most studies of weight gin in the US popultion hve been cross-sectionl, this study models the pttern of weight gin for dult men nd women longitudinlly. From cross-sectionl surveys of the US popultion conducted between 19 nd 1994, Flegl et l described trend towrd incresing overweight nd obesity in the popultion, with obesity defined by Body mss index (BMI) 425 kg/m 2, similr for ll ge, gender, nd rcil ethnic groups with n overll overweight nd obesity prevlence of 54.9%. 2 In cross-sectionl study of Cndins, Mueller et l concluded *Correspondence: Dr T J Sheehn, Deprtment of Community Medicine nd Helth Cre (MC-6325), University of Connecticut School of Medicine, 263 Frmington Ave., Frmington, CT 030, USA. E-mil: Sheehn@nso.uchc.edu w Now t New York University School of Medicine, USA. Received 22 April 2002; revised 9 October 2002; ccepted 2 December 2002 tht generl ftness in both men nd women increses with ge up to 65, nd then begins to decline. 3 While cross-sectionl studies re useful to describe weight chnge in the generl popultion over time, only longitudinl studies cn estimte rtes of chnge. Both Guo et l nd Chumle et l reported on findings from the Fels Longitudinl study tht men nd women were gining weight up to ge 65. 4,5 Shimokt, in 5 y longitudinl follow-up of prticipnts in the Bltimore Longitudinl Study of Aging lso reported weight gin until bout ge 65 nd weight loss therefter. 6 Willimson et l reported from the first Ntionl Helth Exmintion Follow-up Study (NHEFS) of Americn men nd women tht the lrgest increse in weight occurs between the ges of 25 nd 44 for both men nd women nd tht those over yers of ge show loss of weight. 7 Cornoni-Huntley et l studied chnge in weight for those in the first NHEFS s well, splitting the subjects into quintiles of BMI. 8 They found tht younger persons in the lower quintiles t bseline gined more thn those in the higher quintiles nd older persons in the highest quintile t bseline hve the gretest loss in weight. The estimtes from the third nd fourth wves of the NHEFS included in this pper should extend the work described bove. This pper will estimte rtes of chnge for weight over 20 y period for subjects who were ged 25 74 t bseline nd will ddress ge, BMI, rce, nd gender s possible
contributors to these estimtes. This study provides the most comprehensive description of weight gin mong dult Americns over 20-y period. Methods Subjects were 5117 men nd women from the first Ntionl Helth nd Nutrition Exmintion Survey (NHANES I), who were 25 74 y old t bseline beginning in 1971 nd were surveyed gin beginning in 1982, 1987, nd 1992 s prt of the NHEFS. The first follow-up study ws performed in the homes of the prticipnts, nd weight ws mesured on uniform scles. In the remining follow-up surveys, subjects were sked to report their current weight during telephone interview. Ech prticipnt ws followed for 20 y s the cohort ged from 25 to 74 y of ge t bseline to 45 94 t the fourth follow-up. Since the time intervl between surveys vried for individuls, the subject s ge t the time of ech survey is the mjor independent vrible in this study. NHEFS clssified subjects s Aleutin, Eskimo or Americn Indin, Asin/Pcific islnder, blck, white, nd other. There were 5165 subjects who hd useble dt t ech of the four time points for ech vrible of interest, including 4519 white nd 598 blck subjects, 14 Aleutin, Eskimo or Americn Indins, 34 Asin/Pcific islnders, nd no others. Owing to smll smple sizes, the Aleutin, Eskimo or Americn Indin nd Asin/Pcific islnder subjects were eliminted from ll nlyses, leving smple of 5117 blck nd white subjects who were nlyzed seprtely. Since it ws postulted tht people gin weight most rpidly when they re young, stbilize for while, nd then begin to lose weight s they grow older, the smple of 5117 ws divided into four ge groups, first by dividing the smple into three ge groups of equl size. The youngest group, ges 25 35 t their initil interview, consisted of 1837 subjects, 532 men nd 1305 women. The second ge group consisted of 15 subjects, 498 men nd 1107 women, who were ged 36 to 47 t their initil interview. The third ge group is 1675 subjects, 611 men nd 1064 women, who were 48 74 t initil interview. This third ge group contins roughly the sme number of subjects but spns 26 y insted of 10 or 11 y s the other ge groups do. Also, Willimson et l 7 nd others found chnge in rtes of weight gin or loss round ge. For these resons, the eldest ge group ws split into two ge groups: 48 nd 61 74. The 48 ge group contins 999 subjects, 0 men nd 599 women. The oldest ge group, 61 74, contins 676 subjects, 211 men nd 465 women. We lso divided the smple into six ctegories of BMI: o20, 20 22.49, 22.5 24.99, 25 27.49, 27.5 29.99, nd Z30 kg/m 2. These re stndrd BMI ctegories where vlue of 25 kg/cm 2 or greter is regrded s overweight, nd vlue of 30 kg/m 2 or greter is regrded s the threshold for obesity. 9,10 Hence, the three highest BMI ctegories encompss those who re overweight nd obese. Rtes of weight chnge TJ Sheehn et l Sttisticl nlyses were performed seprtely by gender nd rce, first descriptively with tbles to show the crude growth rtes for blck nd white men nd women by ge groups, nd then by fitting growth models to provide refined sttisticl estimtes of growth rte. Growth models were fit by gender nd rce to estimte the effects of ge, ge squred, nd ge cubed. These models provide more ccurte estimtes of overll rtes of weight chnge thn the crude growth rtes estimted from the descriptive sttistics, but more importntly they test for nonlinerity. If men nd women gin weight up to bout ge nd then begin to lose weight, these models will detect tht nonlinerity. A second set of growth models were fit to estimte the rtes of growth within ech combintion of ge nd BMI ctegory, 24 models for white men nd 24 for white women. Exmining these estimtes revels precisely how rtes of weight chnge vry within ech BMI nd ge ctegory. The smple of 598 blck subjects, 157 men nd 441 women, ws too smll to conduct such detiled nlyses for blck subjects. The fitted models were mixed effects models contining both fixed nd rndom effects. 11 The mixed effects models treted ge s rndom for ech subject. Rndom-effects models llow individul subjects to hve their own intercepts nd slopes, nd these provide more precise modeling for longitudinl weight chnges. For exmple, when considering ge s rndom effect, two subjects with the sme ge cn hve different body weight chnges in the model, which is more precise nd relistic thn fixed effects model where every subject hs the sme chnge in body weight t the sme ge. Another dvntge of using rndom-effects model is the flexibility of the covrite structure vilble for missing dt or unblnced design. In this study, the rndom effects model cn seprte between-subject vritions from longitudinl chnges. When these models relting ge nd weight re fit, the intercept estimtes weight t ge zero. Therefore time ws centered on the men ge, which gives the intercept more mening but leves the slope unchnged. To ddress the possibility tht smll number of persons who experienced extreme weight chnges contributed excessively to these models, Cook s Distnce ws clculted. Cook s Distnce is sttistic tht combines studentized residuls nd leverge vlues to flg extreme observtions, which re defined s hving vlue of Cook s Distnce greter thn or equl to one. This llows investigtion of the possibility tht some extreme subjects re cusing significnt chnges in the estimted growth rtes. 12 Liner, qudrtic, nd cubic mixed effects models were fit using both the LME function in S-PLUS 13 nd Proc Mixed in SAS. 14 Akike s Informtion Criterion (AIC) ws used to compre liner mixed effects models for ech subgroup to models, which lso included ge-squred. AIC is fit index reflecting goodness of fit, which ccounts for prsimony by penlizing for overprmteriztion. If the AIC vlue for the overll qudrtic model is closer to zero thn the AIC for the 499 Interntionl Journl of Obesity
500 Tble 1 Rtes of weight chnge TJ Sheehn et l Averge weight in kg over time by gender, ge ctegories, nd rce NHANES I 71 74 NHEFS 82 84 NHEFS 87 NHEFS 92 Weight chnge kg/y chnge Gender Age White Blck White Blck White Blck White Blck White Blck White Blck 25 35 62.6 69.4 66.2 74.4 67.6 76.7 70.3.3 7.7 10.9 0.39 0.54 36 47 66.2 73.5 68.9 77.6 69.9 78.0 70.8 78.5 4.5 5.0 0.23 0.25 48 66.7 78.5 68.5 77.1 68.5 74.8 67.6 73.5 0.9 5.0 0.05 0.25 61 74 64.9 70.8 64.0 69.4 62.1 67.6 59.0 63.5 5.9 7.3 0.29 0.36 25 35.3 78.0 84.4 84.8 85.7 84.8 87.5 86.2 7.3 8.2 0.36 0.41 36 47 79.8 82.6 83.0 84.8 83.5 85.7 84.4 87.1 4.5 4.5 0.23 0.23 48 79.4.7.7 83.0.7 83.5 79.8 83.5 0.5 2.7 0.02 0.14 61 74 75.8 71.2 76.2 73.0 75.3 73.5 73.0 70.3 2.7 0.9 0.14 0.05 Weight t NHEFS 92 Weight t NHANES I. liner model, then the qudrtic model is the better fit. The best model is reported for ech subgroup. 15 Results Descriptions of the crude weight chnges re shown in Tble 1. Weight chnge hs been defined s the weight t the end minus weight t the beginning of the study. Tble 1 shows the observed chnge in verge weight s well s crude rtes of chnge by rce, gender, nd ge ctegories. Weight increses more rpidly for both men nd women in the first two ge ctegories. White women 25 35 t bseline gined 7.7 kg over 20-y period, or 0.39 kg/y, while men gined 7.3 kg or 0.36 kg/y. The youngest blck women gined 10.9 kg, while the younger blck men gined 8.2 kg, or 0.54 nd 0.41 kg/y, respectively. White men nd women 36 47 t bseline gined 4.5 kg, or 0.23 kg/y. Blck men nd women 36 47 y old t bseline showed similr trends s the white subjects, with 5.0 kg gin for women nd 4.5 kg gin for men, or 0.25 nd 0.23 kg/y, respectively. White men nd women 48 y old t bseline leveled off, with the men gining 0.5 kg, or 0.02 kg/y, nd women gining 0.9 kg, or 0.05 kg/y. Blck women in the 48 ge group were lredy losing weight, while the white women were stble. Blck women lost 5.0 kg, or 0.25 kg/y, while blck men gined 2.7 kg, or 0.14 kg/y. White men nd women in the 61 74 ge group lost 2.7 nd 5.9 kg, respectively, or 0.14 nd 0.29 kg/y. The blck men nd women lost 0.9 nd 7.3 kg, respectively, or 0.05 kg/y nd 0.36 kg/y. This nlysis suggests tht the point t which Americns stop gining nd begin to lose weight is ner ge. Blck women show more extreme pttern of gin: gining weight fster while young, losing weight fster when older, nd beginning to lose weight erlier thn white women. In generl, weight gins re highest for the first two ge ctegories while weight losses re highest for the lst two ge ctegories. Tble 2 contins the prmeter estimtes from fitting mixed models for ech rce nd gender. The models estimte weight chnge s function of ge, ge squred, nd ge cubed. As mentioned erlier, ge hs been men centered prior to nlysis. The estimtes in Tble 2 re fixed effects, Tble 2 Coefficients for fixed effects by sex nd rce Effect White Blck White Blck Intercept 83.2774 83.4396 68.9678 77.9845 Age 0.1417 0.2070 0.1990 0.1354 (Age) 2 0.0068 0.0055 0.0071 0.0119 (Age) 3 0.0001 Coefficient is not significnt t Pr0.05. lthough ech subject hs n individul rndom intercept nd slope tht re not included in the tble. The estimted effects re consistently positive for ge nd negtive for ge squred, with ge cubed significnt for white women only. While Tble 2 contins estimtes of the fixed effects prt of the mixed model, the predicted weights from the combined significnt fixed effects nd rndom effects models re grphed in Figure 1. The squiggled lines combine the fixed effects nd rndom effects estimtes of predicted weights, which re smoothed using the locl liner regression option in SPSS interctive grphics. 16 Although the overll shpes of the smoothed grphs pper similr for men nd women, both blck nd white, the vrition is greter mong blck subjects, especilly blck men who hve the smllest smple sizes, 441 women, nd 157 men. The grphs show weight gins until ge 50 or nd weight losses therefter for ll groups, nd demonstrte the nonliner effects of ge on ll groups. It is cler from Tble 2 nd Figure 1 tht the rte of weight chnge vries with ge nd is nonliner. To clrify how weight chnge vries with ge, while lso exmining how weight might chnge with BMI level s reported by Cornoni- Huntley et l, 8 dditionl nlyses were performed, dividing white men nd women into the four ge ctegories nd six BMI ctegories described erlier. The smples of blck men nd women were too smll to conduct such detiled nlyses. Thus, with four ge ctegories nd six BMI Interntionl Journl of Obesity
Predicted weights (kg) Predicted Weights (kg) Predicted weights for blck men nd women Rtes of weight chnge TJ Sheehn et l 501 90 70 ge ge b Predicted weights for white men nd women 70 Figure 1 ge predicted weight for ge from mixed effects models by rce nd gender. The predictions re bsed on combined fixed nd rndom effects. ge ctegories, 24 seprte models were fit for white men nd women. Tble 3 contins the estimtes relting chnges in weight to ge nd ge-squred for ech combintion of ge nd BMI ctegory. The models shown re those with the best AIC. In ll, 11 of the 48 models contin estimtes for ge tht re not significnt t the 5% level with four of the 11 occurring mong the obese in the first two ge ctegories, indicting lck of evidence for ny significnt weight gin for obese men nd women in the first two ge ctegories. In fct, for obese women in the youngest ge group, 25 35 yers old t bseline, there is negtive effect for ge squred, 0.02, suggesting sttisticlly significnt weight loss over the 20 y study period. For ll other BMI ctegories in the first two ge ctegories, men nd women show their highest rtes of weight gin. The growth rtes in Tble 3 re generlly higher for the younger ge groups, nd show trend towrd slower rtes with incresing BMI ctegories, with no significnt growth mong obese men or women. The rtes hve slowed for women in the 48 ge group; they remin significntly positive for the first three BMI ctegories, but lso show trend towrd significntly negtive ge-squred effects indicting the strt of weight loss by the end of follow-up for the 48 ge group. The highest BMI ctegory hs significnt negtive effect for ge nd negtive effect for ge squred suggesting the declines for the highest BMI levels in the third ge group. For women in the oldest ge ctegory the continuing decline with ge is clerly seen, with significnt negtive estimtes for ge nd ge squred nd Interntionl Journl of Obesity
502 Rtes of weight chnge TJ Sheehn et l <20 20-22.49 22.5-24.99 <20 20-22.49 22.5-24.99 ge ge ge Overweight nd Obese nd 25-27.49 27.5-29.99 >=30 25-27.49 27.5-29.99 >=30 ge ge Figure 2 predicted weight by ge for white subjects only, bsed on the combintion of fixed nd rndom effects. Ech line represents one of six BMI ctegories: o20, 20 22.49, 22.5 24.99, 25 27.49, 27.5 29.99, nd Z30 kg/m 2. These re stndrd BMI ctegories where vlue of 25 kg/cm 2 or greter is regrded s overweight, nd vlue of 30 kg/m 2 or greter is regrded s the threshold for obesity. The bottom pnels show chnges for overweight nd obese men nd women. ge rtes of decline incresing s BMI ctegories increse. The estimtes suggest tht women in the higher BMI groups begin to lose weight erlier thn those in the lower BMI groups. Similr trends re present for men. The highest BMI group stbilizes the erliest, with nonsignificnt ge effects cross the first two ge groups, which turn negtive for the third ge group, ges 48 t bseline. The lowest BMI group, on the other hnd, is continuing to show significnt positive ge effects into the 48 ge group nd levels off in the 61 74 ge group. Figure 2 grphs the overll estimtes of the mixed effects models presented in Tble 3, but the grphs re limited to Interntionl Journl of Obesity
Tble 3 Coefficients for fixed effects by ge nd BMI t bseline for white subjects only Rtes of weight chnge TJ Sheehn et l 503 Age ct BMI ct N Intercept Age Age 2 N Intercept Age Age 2 25 35 >20 20 70.15 0.65 257 55.03 0.37 20 22.5 94 75.09 0.43 0.01 354 61.28 0.42 0.01 22.5 25 130 81.06 0.42 223 65.99 0.43 0.01 25 27.5 125 85.81 0.35 138 73.45 0.42 27.5 30 66 92.18 0.24 57 c 79.11 0.26 Z30 53 106.87 0.04 b 117 96.49 0.01 b 0.02 36 47 >20 18 63.78 0.44 111 55.99 0.35 20 22.5 56 72.41 0.33 0.01 254 61.05 0.29 22.5 25 98 77.07 0.24 225 66.17 0.27 25 27.5 139 82.55 0.20 131 71.53 0.24 27.5 30 88 91.21 0.17 83 78.04 0.25 Z30 50 99.22 0.005 b 138 92.50 0.10 b 48 >20 20.24 0.21 44 52.14 0.09 0.01 20 22.5 33 72.20 0.21 0.02 109 59.57 0.08 0.01 22.5 25 86 75.79 0.05 0.01 120 64.46 0.10 0.01 25 27.5 115 81.29 0.06 b 0.01 91 68.44 0.03 b 27.5 30 52 86.90 0.05 b 66 74.85 0.07 b Z30 48 96.14 0.17 b 101 86.00 0.29 0.01 61 74 >20 8 c 58.20 0.02 b 22 d 47.75 0.11 0.02 20 22.5 18 c 69.89 0.14 b 0.05 62 54.01 0.14 0.01 22.5 25 62 71.05 0.14 0.02 111 59.55 0.24 0.01 25 27.5 52 77.46 0.10 90 c 65.09 0. 0.02 27.5 30 39.37 0.23 67 69. 0.37 0.01 Z30 14 e e e 64 76.27 0.62 0.02 Effect not included due to incresed AIC. b Coefficient is not significnt t Pr0.05. c Model fit with vrince component covrince structure. All others hve been fit using unstructured covrince. d 105.87 0.82x 0.05x 2 +0.005x 3 hs lower AIC. e Estimted G mtrix is nonpositive definite. gender nd BMI ctegory. The grphs omit ge ctegories for severl resons. Age is lredy represented on the horizontl xis nd the shpe of the curves reflects how rtes chnge with ge nd to include grphs for ge ctegories would entil n dditionl 36 grphs. In ech pnel, the squiggled lines combine the fixed nd rndom effects; the smooth lines were computed using locl liner regression within SPSSs interctive grphics. There is one pnel for ech BMI ctegory. The grphs for obese men nd women, BMI 30 kg/ m 2 or higher, stnd out from the other BMI groups. While the other BMI groups gin weight until pproximtely y of ge, obese men nd women do not show erly gin. Their curves re either flt or lredy in decline well before the rest of the popultion joins them in losing weight t bout ge. To ddress the issue of whether extreme observtions were unduly influencing the estimtes, especilly for models with smll smple sizes, Cook s Distnce ws clculted. All subjects hd vlues of Cook s Distnce below one t ll time points. The highest vlue of Cook s Distnce ws 0.296, nd only three of the 20 468 observtions hd Cook s Distnce greter thn 0.10, suggesting tht extreme observtions re not concern here. Discussion Of the longitudinl studies of weight chnge vilble tht we re wre of, this study uses dt on the lrgest smple followed for the longest time. The follow-up period of 20 y trcks chnges in weight for 5117 subjects who were between the ges of 25 nd 74 t the strt nd who were between the ges of 45 nd 95 y of ge t the finish. The use of liner nd qudrtic mixed models provided estimtes for weight chnge overll. When grphs of the fitted models re shown together in Figure 1, nonliner pttern emerges for ll groups ccelerting upwrd, leveling off, nd turning downwrd round ge. The use of ctegories of BMI hs llowed for the possibility tht obese Americns re not gining or losing weight t the sme time nd rte s others. The dt show tht obese men nd women chnge the lest before ge nd then lose weight more rpidly thn others fter ge. These models suggest tht the gretest risk for weight gin occurs during young dulthood. Since obesity is such helth hzrd, trgeting men nd women between the ges of 25 nd 50 for weight mngement could be the most productive. There is need for effective obesity prevention t younger ges, s mny Americns re lredy obese by ge Interntionl Journl of Obesity
504 25. At the older end of the spectrum there is lso concern. Although weight loss is often considered beneficil to helth, the weight loss mong older dults my be due to the loss of len body mss, even while ft mss increses or remins the sme. 17 For women especilly, losses in bone minerl density cn be prticulrly dngerous nd possibly led to osteoporosis; for both men nd women, the loss of muscle mss cn signl loss of strength nd stbility leding to greter risks for disbility. Acknowledgements This reserch ws supported in prt by grnts from the Arthritis Foundtion nd the Clude Pepper Older Americns Independence Center. We thnk Frnk Dvidoff, MD, Michelle Berlin, MD, MPH, nd Judith Fifield, PhD for helpful comments on n erlier drft. We re lso grteful for the helpful comments of the nonymous reviewers. References Rtes of weight chnge TJ Sheehn et l 1 Friedmn JM. Obesity in the new millennium. Nture 2000; 4: 632 634. 2 Flegl KM, Crroll MD, Kuczmrski RJ, Johnson CL. Overweight nd obesity in the United Sttes: prevlence nd trends, 19 1994. Int J Obes Relt Metb Disord 1998; 22: 39 47. 3 Mueller WH, Wer ML, Hnis CL, Emerson JB, Brton SA, Hewwett-Emmett D, Schull WJ. Which mesure of body ft distribution is best for epidemiologic reserch? Am J Epidemiol 1991; 133: 858 869. 4 Guo SS, Zeller C, Chumle WC, Siervogel RM. Aging, body composition, nd lifestyle: the Fels Longitudinl Study. Am J Clin Nutr 1999; 70: 5 411. 5 Chumle WC, Guo SS, Zeller CM, Reo NV, Siervogel RM. Totl body wter dt for white dults 18 to 64 yers of ge: the Fels Longitudinl Study. Kidney Int 1999; 56: 244 252. 6 Shimokt H, Andres R, Coon PJ, Elhi D, Muller DC, Tobin JD. Studies in the distribution of body ft. II. Longitudinl effects of chnge in weight. Int J Obes Relt Metb Disord 1989; 13: 455 464. 7 Willimson DF. Epidemiologic nlysis of weight gin in US dults. Nutrition 1991; 7: 285 286. 8 Cornoni-Huntley JC, Hrris TB, Everett DF, Albnes D, Micozzi MS, Miles TP, Feldmn JJ. An overview of body weight of older persons, including the impct on mortlity. The Ntionl Helth nd Nutrition Exmintion Survey IFepidemiologic follow-up study. J Clin Epidemiol 1991; 44: 743 753. 9 Allison DB, Fontine KR, Mnson JE, Stevens J, VnItllie TB. Annul deths ttributble to obesity in the United Sttes. JAMA 1999; 282: 1530 1538. 10 Must A, Spdno J, Cokley EH, Field AE, Colditz G, Dietz WH. The disese burden ssocited with overweight nd obesity. JAMA 1999; 282: 1523 1529. 11 Pinheiro JC, Btes DM. Mixed-Effects Models in S nd S-PLUS. Springer: New York, 2000. 12 Drper NR, Smith H. Detection of influentil observtions. In: Brdley H, Kendll, Wtson (eds). Applied regression nlysis, 2nd edn. John Wiley nd Sons: New York; 1981. pp 170 171. 13 Insightful. S-PLUS 6.0. Insightful Corp.: Settle, WA; 1988 2001. 14 SAS Institute. SAS. 8.0. SAS Institute: Cry, NC; 1999. 15 Akike H. A new look t the sttisticl model identifiction. IEEE Trns Automtic Control 1974; 19: 716 723. 16 SPSS Inc. SPSS Interctive Grphics. SPSS Inc.: Chicgo, IL; 1999. p 161. 17 Kyle UG, Genton L, Hns D, Krsegrd L, Slosmn DO, Pichrd C. Age-relted differences in ft-free mss, skeletl muscle, body cell mss nd ft mss between 18 nd 94 yers. Eur J Clin Nutr 2001; 55: 663 672. Interntionl Journl of Obesity