### Description

Cole et al developed curves to describe the change in body mass index (BMI) with age and gender in pediatric patients in the United Kingdom based on 1990 reference data. The SD Score describes the number of standard deviations from the mean (50%) curve for a given BMI result.

body mass index (BMI) for patient =

= (body weight in kilograms) / ((body height in meters)^2) in kilograms per square meter

Age range for patients: from 1 to 22 (although data from 0 to 1 year was available, it changes rapidly and so was excluded to simplify the analysis)

Parameters to determine SD score:

(1) 50% curve for BMI relative to age and gender

(2) L curve (degree of skewness) relative to age and gender

(3) S curve (coefficient of variation) relative to age and gender

Data for mean (50%) BMI curve for age and gender

age in years

boys

girls

1

17.3

17.4

2

16.1

16.4

3

15.7

15.8

4

15.5

15.5

5

15.4

15.4

6

15.5

15.5

7

15.5

15.6

8

15.7

15.9

9

15.9

16.4

10

16.3

16.9

11

16.8

17.4

12

17.4

18.1

13

18.0

18.8

14

18.6

19.4

15

19.3

19.9

16

19.9

20.4

17

20.5

20.7

18

21.1

21.1

19

21.5

21.3

20

22.0

21.5

21

22.4

21.8

22

22.9

21.9

based on Figures 1 and 2, page 27

This data was analyzed in JMP and the following equations were calculated:

Gender

Age Range

Equation

male

1 to 6

(-0.030556 * ((age)^3)) + (0.458333 * ((age)^2)) - (2.253968 * (age)) + 19.1

6 to 22

(0.0001275 * ((age)^4)) - (0.009871 * ((age)^3)) + (0.2651489 * ((age)^2)) - (2.387667 * (age)) + 22.284276

female

1 to 6

(-0.012037 * ((age)^3)) + (0.2603175 * ((age)^2)) - (1.684788 * (age)) + 18.83333

6 to 22

(0.0002778 * ((age)^4)) - (0.018113 * ((age)^3)) + (0.4062743 * ((age)^2)) - (3.211087 * (age)) + 23.7107

L curve data

age in years

boys

girls

1

-1.27

-1.18

2

-1.39

-1.22

3

-1.51

-1.26

4

-1.62

-1.30

5

-1.72

-1.34

6

-1.80

-1.38

7

-1.86

-1.39

8

-1.90

-1.39

9

-1.90

-1.38

10

-1.90

-1.36

11

-1.86

-1.34

12

-1.81

-1.32

13

-1.75

-1.28

14

-1.68

-1.26

15

-1.62

-1.24

16

-1.56

-1.22

17

-1.50

-1.19

18

-1.45

-1.17

19

-1.40

-1.16

20

-1.35

-1.15

21

-1.31

-1.14

22

-1.27

-1.13

based on Figure 3, page 27

This data was analyzed in JMP and the following equations were calculated:

Gender

Age Range

Equation

male

1 to 8

(0.0007744 * ((age)^3)) - (0.003272 * ((age)^2)) - (0.116665 * (age)) - 1.150635

8 to 22

(-0.00033 * ((age)^3)) + (0.0153639 * ((age)^2)) - (0.175489 * (age)) - 1.339173

female

1 to 7

(0.0008333 * ((age)^3)) - (0.008214 * ((age)^2)) - (0.016905 * (age)) - 1.157143

7 to 22

(-0.000142 * ((age)^3)) + (0.0059323 * ((age)^2)) - (0.057339 * (age)) - 1.236155

S curve data (as percent from 0 to 100)

age in years

boys

girls

1

7.4

7.5

1.5

7.2

7.4

2

7.1

7.5

3

7.1

7.8

4

7.2

8.4

5

7.5

9.1

6

8.2

9.9

7

9.0

10.8

8

9.8

11.6

9

10.4

12.2

10

10.9

12.6

11

11.3

12.8

12

11.6

13.0

13

11.7

12.9

14

11.8

12.9

15

11.8

12.8

16

11.7

12.8

17

11.7

12.7

18

11.6

12.6

19

11.6

12.5

20

11.5

12.4

21

11.5

12.4

22

11.4

12.3

based on Figure 4, page 27

This data was analyzed in JMP and the following equations were calculated:

Gender

Age Range

Equation

male

1 to 3

(-0.03333 * ((age)^3)) + (0.35 * ((age)^2)) - (1.116667 * (age)) + 8.2

3 to 8

(0.0982143 * ((age)^3)) - (0.520357 * ((age)^2)) + ( * (age)) + 7.7378571

8 to 22

(0.0026018 * ((age)^3)) - (0.141185 * ((age)^2)) + (2.4706286 * (age)) - 2.270756

female

1 to 3

(-0.16667 * ((age)^3)) + (1.15 * ((age)^2)) - (2.28333 * (age)) + 8.8

3 to 9

(0.008333 * ((age)^2)) + (0.6607 * (age)) + 5.6738

9 to 22

(0.0022179 * ((age)^3)) - (0.115906 * ((age)^2)) + (1.907926 * (age)) + 2.857789

SD score for patient BMI relative to mean value for age and gender =

= ((((BMI value for patient) / (mean value for age and gender)^(L curve value))) - 1) / ((L curve value) * (S curve value) / 100)

where:

• The 100 in the denominator converts S value from a percent to a decimal fraction.