Timing and magnitude of adolescent growth in height and weight in Cape Coloured children after kwashiorkor One hundred sixteen patients who had had kwashlorkor between the ages of 5 months and 4~;, years and 89 controls were the subjects of Q 15-year follow-up study ofthelr growth and development. We report the findings of a longltudlnal analysis of 53 (30 females) of the ex-patlents and 30 (15 females) of the Controls, selected because at the end of 15 years of study they conformed to the criteria of (1) adult secondary sexual characteristics, (2) helght veloclty <2 cm/yr, and (3) completeness of data. Nonlinear curve-fittlng technlques were applled to the helght and welght data for these subjects using the PreeceBalnes model I growth function to determine the tlmlng and magnltude of adolescent growth spurts and the asseciated blologlc changes. Both expatients and controls grew below the 2w percentile of British longitudinal standards, but the male ex-patlents were heavier, and perhaps taller, than the controls for most of thelr chlldhoad and adolescence. VeIoclty curves Indlcatedthat the ex-patlents had hlgher pre-adolescent peak Increments than the controls and a generally longer growth spurt of reduced magnltude. Two posslble expianatlons ace discussed: (1) Garrow and Plke's theory that chlldren wlth kwashlorkor have a genetic potential for greater physical growth, and (2) a socloeconomlc crtsls occurring wlthln a famlly affects the youngest Chlld, who subsequently requires a longer tlme to recover than do slbllngs wlthln an Improvlng socloeconomlc sltuatlon (J PEOIATR1986;109:548-555) N. C a m e r o n , Ph.D., P. R. M. Jones, Ph.D., Aileen Moodle, A I M S W , Jeanette Mitchell, MSc., M. D. Bowie, M.D,, M, D. M a n n , M . D L Ph.D,, a n d J. D. L. Hansen, M.D. From the Departments of Anatomy and Paediatrics,Medical School, Universityof the Witwatersrand,Johannesburg,and the Department of Paecliatrics,Red CrossWar Memorial Hospital,Cape Town, South Africa
Little is known of the long-term consequences of kwashiorkor. Although several animal experiments have been carSupported by a research grant from the Richard Ward Endowment Fund, by USPHS Grant AMO-3995, and by the South African Medical Research Council. Dr. Jones on study leave from Human Biology Laboratory, Department of Human Sciences, University of Technology, Loughborough, Leicestershire, England. Submitted for publication Jan. 28, 1986; accepted March 28, 1986. Reprint requests: N. Cameron, Ph.D., Department of Anatomy, Medical School, University of the Witwatersrand, Johannesburg, South Africa.
548
ried out, 1-7 the effects of malnutrition vary from species to
species and may therefore not be extrapolated to humans. Such work, however, has led to a general consensus that the earlier in life a severe nutritional insult occurs, the greater and more protracted the retardation 5,8,9 and the less likelihood of reaching full genetic potential) Several longitudinal and follow-up studies of kwashiorkor have been made in an effort to elucidate the long-term effects of malnutrition. Catch-up growth j~ has been apparent in the years immediately following treatment, but conflicting evidence exists of the long-term effects. Some studies have found ex-paticnts to be stunted in relation to "local" unaffected children) ,"~3 Cabak and Najdanvic 14
Volume 109 Number 3
found their ex-patients to have normal physiques, but subnormal mental capacities, 5 to 12 years after having had malnutrition, and Garrow and Pike Is reported no evidence of growth stunting 2 to 8 years after treatment for severe malnutrition. Although their ex-patients were small by American standards, many had outgrown their unaffected siblings in height and weight. Graham 16 concluded that severe and continuous malnutrition in the first year of life is likely to cause permanent retardation, although a single episode of protein deficiency is less likely to have such consequences. In South Africa, Suckling and CampbelP 7 conducted a 5-year follow-up study of 27 Coloured children treated for kwashiorkor; despite the fact that the children returned to. their previous, deprived environment after discharge, they usually made a "good recovery." Moodie et al.lS. 19reported that prolonged malnutrition rather than an acute episode affects health and retards growth; half of these children eventually reached internationally accepted standards of weight and height, demonstrating a capacity for full physical recovery,s~ Subsequently, the 15-year follow-up examination of the ex-patients found that no significant difference existed between the ex-patients and the controls, but together they showed a general pattern of retarded growth and development. One of the problems of interpretation is that control groups may not have significantly better nourishment than patients but simply have not been identified as having clinical malnutrition. Another problem is that most of the follow-up and longitudinal studies have been analyzed using cross-sectional techniques; data at each age point have been analyzed independently without regard to the fact that the same children may be present in the age groups either side of the one being analyzed. No allowance has been made for the subjects who miss examinations within a series and are thus present in some but not all of the age group analyses. The height and weight data from the Cape Town 15-year longitudinal study were made available to us, and have been analyzed using newer longitudinal techniques to determine individual differences in growth patterns, particularly with regard to the timing and magnitude of the adolescent growth spurt in height and weight. We hoped to provide estimates of adolescent growth that more closely relate to individual growth rates than those presently available. METHODS The ex-patients and controls have been described in detail by Keet et al. 2~ Briefly, 116 patients between the ages of 5 months and @f2 years received treatment for kwashiorkor and then were observed for 15 years. Eighty-
Kwashiorkor and growth
549
Table I. Selection of study groups n
15-Year follow-up study (Bowie et al.28) Ex-patients Siblings Present study After level 1 selection Ex-patients Males Females Siblings Males Females After level 2 selection Ex-patients Males Females Siblings Males Females
Height
Weight
53 23 30 30 15 15
47 21 26 26 13 13
l 16 89 72 32 40 41 20 21
nine children, most of whom were siblings of the patients, were measured on a regular basis as controls. Sampling. To carry out a true longitudinal analysis of these data, a two-level selection procedure was conducted. Level 1 involved the application of three criteria: (1) adult puberty ratings at the last examination, (2) height velocity of <2 cm/yr during the final year of study, and (3) complete anthropometric data, that is, each subject had to have been measured at least once each year during the first 5 years and the last 5 years of the 15-year period. From 5 to 10 years no measurements were made, but social data were obtained. 2~These stringent criteria were necessary to ensure that values for final dimensions were indeed adult and not pubertal. The sample selected by these criteria consisted of 72 ex-patients and 41 controls (Table I). Level 2 was applied during the analysis of data for individuals selected from level 1. This involved the goodness of fit of the growth function used for analysis and is discussed under Longitudinal analysis. Anthropometrie variables. The variables chosen for analysis were height and weight. These dimensions were measured by "accepted international techniques, ''2~ although the original authors have neither described the instrumentation nor the reliability of the observers. In the first 5 years of the study, height was measured to the nearest one-eighth inch, and weight to the nearest ounce. After that, height was measured to the nearest millimeter, and weight to the nearest one-tenth kilogram. Longitudinal analysis. The Preece-Baincs model 1 growth function 2~ was fitted to the height data of the 72 ex-patients (40 females) and 41 controls (21 females)
550
Cameron et aI.
The Journal of Pediatrics September 1986
T a b l e II. Height distance and velocity Females
Males
P1 (Adult height) Mean SD Age at take-off Mean SD Velocity at take-off Mean SD Height at take-off Mean SD Age at PHV Mean SD Velocity at PHV Mean SD Height at PHV Mean SD Height increase to PHV Mean SD Velocity increase to PHV Mean SD Percent adult at take-off Mean SD Percent adult at PHV Mean SD
Patients (n = 30)
Controls (n : t5)
NS
156.70 7.59
10.48 1.38
NS
4.72 0.50
4.16 0.61
129.10 10.20
Patients (n : 23)
Controls (n = t5)
171.00 10.09
165.70 6.74
10.27 1.16
P
Males vs females P
Patients
Controls
155.70 4.78
NS
0.001
0.001
8.58 0.90
9.34 1.57
NS
0.001
0.05
0.01
4.84 0.69
4.60 0.58
NS
NS
NS
125.00 9.93
NS
116.60 11.58
120.90 8.50
NS
0.001
NS
14.25 1.34
14.48 0.86
NS
12.19 0.70
12.65 1.40
NS
0.001
0,001
7,85 1.10
8.90 1.47
0.01
7.98 1,31
8.18 1.81
NS
NS
NS
152.80 9.44
148.70 6.39
NS
139.00 7.06
140.70 5.61
NS
0.001
0.001
23,69 3,66
23.65 5.90
NS
22.40 6.10
19.80 4.45
NS
NS
NS
3,13 1,21
4.74 1.65
0.01
3.14 1.60
3.59 2.06
NS
NS
NS
75.48 3.63
75.48 5.90
NS
74.47 6.92
77.69 4.72
NS
NS
NS
89,35 1.63
89.72 2.55
NS
88.75 3.21
90.39 1.97
NS
NS
NS
NS, not significant;PHV, peak height velocity. using the Statistical Analysis System Non-Linear Routine. 22 This routine fits the function to time series data by nonlinear least squares, using the maximum neighborhood algorithm according to Marquardt? 3 An arbitrary value of 2.0 cm was chosen for the limit of acceptance of the residual mean square following the fitting procedure. Nineteen ex-patients and 11 controls were excluded after the fitting of height, and a further six ex-patients and four controls after the fitting of weight, making 40 exclusions in all. Reasons for exclusion were (1) no convergence because of an unusual growth pattern (eight males, four females), (2) residual SD >2.0 cm (six males, 13 females), (3) no asymptotic final height values (four males, four females), (4) missing early adolescent data (one female ). The final sample was thus 53 ex-patients and 30 controls for height and 47 ex-patients and 26 controls for weight. Of the 47 ex-patients fitted for both height and weight, 16 had
siblings in the study; of the 26 controls fitted for both dimensions, 11 had siblings in the study. The exclusion of siblings does not represent unusual or abnormal growth but simply lack of reasonable long-term data. Statistical atudysis. The Preece-Baines model 1 growth function provided a series of model parameters and biologic variables for analysis3 ~ Briefly, using height as an example, the model parameters relate to adult height (PI), height at peak height velocity (P2), height velocity at the take-off point for the adolescent growth spurt (P3), height velocity at peak adolescent velocity (P4), and age at peak height velocity (P5). The biologic variables are landmarks during adolescent growth (e.g., take-off age, take-off velocity, peak velocity age, and peak velocity). Such variables provide a detailed description of adolescent growth and have been used in a number of studies for comparison between samples? ~,24.2s The significance of the
Volume 109 Number 3
Kwashiorkor and growth
190
190 -
Ex- Patients Controls S
..........
170
.
170-
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|176
o Age (years)
Mean constant curves of height and height velocity for male ex-patients and controls (A) and female ex-patients and controls (B) compared with British 50th centile. Fig. 1.
differences between mean values for ex-patients and controls within and between sexes was tested by small-sample t tests, after testing for homogeneity of variance using the variance ratio. Mean constant curves were determined for each sample and plotted against the British longitudinal standards) 6 These longitudinal results were also compared with the cross-sectional results from the previous analyses of the same data. The original analyses were not available, and thus the significance of any differences could not be tested. RESULTS H e i g h t . There were no significant differences between the absolute heights of male ex-patients and controls. Analysis of the biologic factors related to velocity show the ex-patients to have had significantly greater take-off velocities (P <0.01) and significantly smaller peak velocities (P <0.01) (Table II). Thus, although the age at which adolescent events took place was similar for ex-patients and controls, the ex-patients had a flattened adolescent growth spurt with less deceleration to take-off and less acceleration to peak velocity (Fig. 1, A). Female ex-patient and control height distance and velocity curves were virtually identical, with no significant differences between them (Fig. 1, B). W e i g h t . Male ex-patients were significantly heavier as adults (P <0.05), had a greater weight at peak velocity (P <0.05), and showed a significantly greater take-off velocity (P <0.001) than did controls (Table III). The greater
adult weight can thus be attributed to a greater growth rate prior to peak weight velocity, rather than to an adolescent growth spurt of increased magnitude (Fig. 2, A). Female ex-patients and controls had no significant differences in weight growth (Fig. 2, B). Sexual dimorphism Height. Male and female ex-patients and controls were significantly different within both groups for the model parameters P1, P2, P3, and P5 but not for the rate constant P4, indicating a similarity in the rate of change toward the end of the adolescent growth spurt. Ages at take-off and peak were significantly different between male and female ex-patients (P <0.001) and male and female controls, but although a 2-year difference in age existed between the ex-patients at take-off, only about a 1-year difference existed between controls. At peak height velocity the female controls had established the normal 2-year difference, thus going through the period from take-off to peak more quickly than the males (Table II). Weight. Male and female ex-patients were more divergent than controls, having significant differences for adult weight P1, P2, and P5, whereas male and female controls were only significantly different for P5. In addition, weight velocity and distance at take-off were significantly greater for male than female ex-patients, whereas the controls showed no difference. The ages at take-off were not significantly different between the sexes either for expatients or controls, but by peak velocity males were significantly older than females. Male controls had greater increases in velocity from take-off to peak than females
552
Table
Cameron et al.
The Journal of Pediatrics September 1986
III. Weight distance and velocity Males
P1 (adult weight) Mean SD Age at take-off Mean SD Velocity at take-off Mean SD Weight at take-off Mean SD Age at PWV Mean SD Velocity at PWV Mean SD Weight at PWV Mean SD Weight increase to PWV Mean SD Velocity increase to PWV Mean SD Percent adult at take-off Mean SD Percent adult at PWV Mean SD
Females Patients (n = 26)
Controls (n = 13)
0.05
56.60 7.70
7.96 2.24
NS
1.81 0.26
1.45 0.31
20.60 4.43
Patients (n = 21)
Controls (n = 43)
63.60 9.25
57.50 7.22
7.35 1.92
P
Patients
Controls
54.50 7,09
NS
0.01
NS
6.47 1.49
6.37 2.53
NS
NS
NS
0.001
1.64 0.28
1.52 0.31
NS
0.05
NS
19.80 4.20
NS
18.10 3.44
18.50 5.22
NS
0.05
NS
14.60 1.28
14.82 0.85
NS
13.43 0.84
13.68 1.35
NS
0.001
0.05
7,02 1.54
7.45 1.66
NS
6.76 1.31
6.26 1.10
NS
NS
0.05
45.60 5.48
41.50 4.39
0.05
40.50 4.85
39.30 2.65
NS
0.001
NS
25.00 6,17
21.70 5.13
NS
22.40 4.71
20.90 6.74
NS
NS
NS
5.20 1.53
5.99 1.69
NS
5.12
4.74
NS
NS
0.05
1.29
1.20
33,09 8,07
35.13 8.97
NS
32.45 7.08
35.40 14.09
NS
NS
NS
72.02 3.43
72.45 3.77
NS
71.65 3.06
72,81 6.11
NS
NS
NS
P
NS, not significant;PWV,peakweight velocity. had, and a greater magnitude of peak weight velocity (Table III). DISCUSSION This longitudinal analysis used nonlinear curve-fitting techniques to study the adolescent growth and development of patients who had had kwashiorkor, and control subjects. (The authors will supply details of the curvefitting techniques on request.) The two-level selection procedure isolated a group of ex-patients who had normal patterns of growth after their initial nutritional insult. They presumably did not experience any further insult of a magnitude sufficient to alter growth pattern more than would be expected from simple measurement error. In addition, the original study was undertaken entirely for purposes of observation and did not include food supplementation or medical care.
Little difference was observed between ex-patients and controls for the distance curves of both height and weight in both sexes. Subjectively, however, female distance curves were more similar than male curves. This subjective impression was reinforced by the velocity analysis, which demonstrated significant differences between male, as opposed to female, ex-patients and controls. Females are generally more canalized than males,27 and a particular insult must be of a relatively greater magnitude to affect their growth patterns. In both sexes, weight demonstrated clearer patterns of change than did height. In terms of sexual dimorphism, the male and female ex-patients were significantly different for adult weights, whereas the controls were not. Sexual dimorphism in the adolescent growth spurt appeared to occur after take-off, in marked contrast to other populations that exhibit sexual dimorphism at take-off. Male controls did not appear to gain
Volume 109 Number 3
Kwashiorkor and growth
801
553
80.......
Ex-Patients .........
7O
Controls
. . . . . . . . . .
70-
Ex-Potients Controls
5O 60-
.i
5O
50-
50-
# v
8
8c 40-
40-
C5
0
30-
30-
/.i.-'..-'" ..,:,,
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.
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l
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i:~ ,;
3
2
B
o
0
IB
Age (years)
I ' ,
2
4
A
(~
6
Age (years)
,8
0
Fig. 2. Mean constant curves of weight and weight velocity for male ex-patients adn controls (A) and female ex-patients and controls (B) compared with British 50th centile. from the longer prepubertal phase of growth common to other populations, which causes greater male adult weight. Comparison with previous cross-sectionul results. The cross-sectional analysis reported by Bowie et al. 28 gave height and weight distance values at only four age points: 2, 7, 12, and 17 years. It was therefore only possible to make a nonstatistical comparison of the distance data at these age points. Our longitudinal analysis shows our sample of ex-patients to be taller than those from the previous analysis, but male controls were shorter for the pre-adolescent age points of 7 and 12 years. Female ex-patients and controls were generally shorter throughout, except for ex-patients at 17 years. The comparison of weight data was not substantially different9 Data relating to velocities demonstrate the effectiveness of a longitudinal analysis in smoothing growth curves and allowing more precise definitions of peak magnitudes and ages. No cross-sectional data were available for take-off, but the longitudinally analyzed data showed greater peak velocities at roughly similar ages as those reported for their cross-sectional counterparts. Female ex-patients and controls had younger peak-weight velocity ages than those from the cross-sectional analysis9 Inspection of the velocity graph illustrated (Fig. 3) reveals the unstable nature of the cross-sectionally derived "velocity of the mean. ''28 Indeed, it is virtually impossible either to determine when an adolescent growth spurt is occurring or the value of the landmarks within it.
1312III0(D 98E 76fo 50 432I0 0
Male Ex-Patients Male Controls Bowie etal (1980) %.
.,,'~ "-X%, -
V
_
"~-.'-.: /~,
'I" .,\ --
./,
~, \',
\.
\\ ',,x,
Age (years) Fig. 3. Mean constant curves of height velocity for male expatients and controls compared with cross-sectional determined velocity of mean.
Comparison with internationalstandards. Both male and female ex-patients and controls started below or just on the 3rd centile of the British standards 26 and followed it fairly closely until adolescence. At this time all four groups accelerated through the centiles, but the ex-patients more so, to finish on or near the 25th centile. Male ex-patients are significantly heavier than male controls and female ex-patients at adulthood, but no significant adult differences occur within the female ex-patients and controls or between male and female controls. Differences between
554
Cameron et al.
the sexes for adult height are highly significant for both ex-patients and controls. In summary, our analysis clarifies the pattern, timing, and magnitude of adolescent growth following early kwashiorkor in Cape Coloured children. The findings suggest that boys who experience this single acute insult may eventually end up heavier, and perhaps taller, than nonaffected children from the same geographic and socioeconomic circumstances. At first sight this would appear to be incongruous, but two explanations are available. Garrow and Pike ~5reported similar findings in a study in Jamaica. They postulated that although all children in a family experience a similar nutritional environment, not all have acute malnutrition. Affected children may have a genetic potential for greater weight and height and thus require a greater quantity or quality of food to maintain normal growth velocity and avoid clinical malnutrition. Once refed, such children may catch up and revert to their genetically determined growth channel, ending up taller and heavier than their siblings. However, in the socially deprived periurban populations of the Third World, where marasmic kwashiorkor typically occurs, growth failure increases from the time of weaning as malnutrition interacts with infection. If a child survives kwashiorkor and returns to the old environment, his or her future growth depends on the balance struck. There will be the advantage of hospital care and feeding, followed possibly by convalescence or closer clinical supervision. The child will also have been cleared of intercurrent infections. Indeed, this increased medical care might have produced the differences observed between the ex-patients and controls. It would be impossible to show, however, that a sibling control who subsequently grew less well would not have developed kwashiorkor had he or she received precisely similar nutritional deprivation and infection at precisely the same stage of development. The second explanation results from the characteristics of the subjects of this particular study. At the start of the study 82% of the families were below the poverty datum line, and only 4% above the effective minimum standard. Fifteen years later, only 16% of the families remained below the poverty level, and 57% were above the minimum standard? s Thus most families had experienced improving socioeconomic conditions during the 15 years. Hansen (personal communication) suggests that because expatients were younger than controls, they returned home after treatment to experience these improving conditions longer than their older siblings. The older siblings had also spent more time in a poorer socioeconomic environment than had the ex-patients. Thus the ex-patients grew better because they grew in better socioeconomic conditions than
The Journal of Pediatrics September 1986
their siblings. However, measurements of household income are only a general criterion of family circumstances and give no indication of how the money is spent or distributed and how much nutriment actually reaches each member. Moreover, for family income to be above the effective minimum standard is by no means a measure of affluence. Finally, we cannot determine the effect on family attitudes and on the underprivileged child of his or her being the focus of interest to one observer over a period of 15 years. All in all, there are too many variables in the lives of such children to permit acceptance of a single reason for their subsequent growth achievement. Explanations must therefore remain speculative until longitudinal studies incorporating fine control of both environmental and genetic factors are available for analysis. The difficult logistics of this type of study, particularly in a Third World environment, militate against large sample sizes with their increased statistical strength. We thank Professor J. M. Tanner, Professor of Child Health and Growth, Institute of Child Health, University of London, for helpful comments.
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1. Chow BF, Lee C. Effect of dietary restriction of pregnant rats on body weight gain of the offspring. J Nutr 1964;82:10-18. 2. Barnes RH, Reid IM, Pond WG, Moore AU. The use of experimental animals in studying behaviour abnormalities following recovery from early malnutrition. In McCance RA, Widdowson EM, eds. Calorie deficiencies and protein deficiencies. London: J & A Churchill, 1968:277-286. 3. MeCance RA. The effect of calorie deficiencies and protein deficiencies on final weight and stature. In McCance RA, Widdowson EM, eds. Calorie deficiencies and protein deficiencies. London: J & A Churchill, 1968:319-328. 4. Platt BS. Experimental protein-calorie deficiency. In McCance RA, Widdowson EM, eds. Calorie deficiencies and protein deficiencies. London: J • A Churchill, 1968:237248. 5. Widdowson EM. The place of experimental animals in the study of human malnutrition. In McCance RA, Widdowson EM, eds. Calorie deficiencies and protein deficiencies. London: J & A Churchill, 1968:225-236. 6. Lister D, McCance RA. The effect of two diets on the growth, reproduction and ultimate size of guinea-pigs. Br J Nutr 1965;19:311-319. 7. Ramalingaswami V, Deo MG. Experimental protein-calorie malnutrition in the Rhesus monkey. In McCancc RA, Widdowson EM, eds. Calorie deficiencies and protein deficiencies. London: J & A Churchill, 1968:265-275. 8. Garrow JS. Treatment of malnutrition. Lancet 1969;2:324325. 9. Krueger RH. Some long-term effects of severe malnutrition in early life. Lancet 1969;2:514-517. 10. Prader A, Tanner JM, yon Harnack GA. Catch-up growth
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following illness or starvation: an example of developmental canalization in man. J PEDIATR 1963;62:646-659. MacWilliam KM, Dean RFA. The growth of malnourished childrenafter hospital treatment. E Aft Med J 1965;42:297304. Giok LT, Rose CS, Gyorgy P. Influence of early malnutrition on some aspects of the health of school-age children. Am J Clin Nutr 1967;20(12):1280-1289. Chase HP, Martin HP. Undernutrition and child development. N Engl J Med 1970;282(17):933-939. Cabak V, Najdanvic R. Effects of undernutrition in early life on physical and mental development. Arch Dis Child 1965;40:532-534. Garrow JS, Pike MC. The long-term prognosis of severe infantile malnutrition. Lancet 1967;1:1-4. Graham GG. The later growth of malnourished infants: effects of age, severity, and subsequent diet. In McCance RA, Widdowson EM, eds. Calorie deficiencies and protein deficiencies. London: J & A Churchill, 1968:301-316. Suckling PV, Campbell JAH. A five-year follow-up of Coloured children with kwashiorkor in Cape Town. J Trop Pediatr 1956;2:173-180. Moodie A. Kwashiorkor in Cape Town: the background of patients and their progress after discharge. J PEDIATR 1961; 58:392-403. Moodie AD, Wittmann W, Bowie MD, Hansen JDL. Kwashiorkor in Cape Town: five-year follow-up study. S Air Med j 1967;41:1253.
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20. Keet MP, Moodie AD, Wittmann W, Hansen JDL. Kwashiorkor: a prospective ten-year follow-up study. S Aft Med J 1971;45:1427-1449. 21. Preece MA, Baines MJ. A new family of mathematical models describing the human growth curve. Ann Hum Biol 1978;5:1-24. 22. Ray AA, Sail JP, eds. SAS user's guide: Statistics. Cary, N.C. SAS Institute, 1982:15-38. 23. Marquardt DW. An algorithm for least squares estimation of non-linear parameters. J Soc Industr Appl Math 1963; 11:431-441. 24. Hauspie RC, Das SR, Preex~ MA, Tanner JM. A longitudinal study of the growth in height of boys and girls of West Bengal (India) aged six months to 20 years. Ann Hum Biol 1980;7:429=441. 25. Mirwald RL, Bailey DA, Cameron N, Rasmussen R. Longitudinal comparison of maximal oxygen uptake in active and inactive boys aged seven to 17 years. Ann Hum Biol 1981;8:405-414. 26. Tanner JM, Whitehouse RH. Clinical longitudinal standards for height, weight, height velocity, weight velocity and the stages of puberty. Arch Dis Child 1976;5t:170-179. 27. Tanner JM. Growth at adolescence. Oxford, England: Blackwell Scientific, 1962. 28. Bowie MD, Moodie AD, Mann MD, Hansen JDL. A prospective 1S-year follow-up study of kwashiorkor patients. I. Physical growth and development. S Afr Med J 1980;58:674676.