# Dependent variable_ by hcj

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```									                              SUPPLEMENTARY MATERIAL

Detailed methods

A. Dependent variables

For each patient, kidney length (mm), kidney thickness (mm), serum creatinine (mg/dl), serum

BUN (mg/dl), SBP (mmHg), DBP (mmHg) and age (years) were recorded.

"Kidney size" (KS) was defined by calculating the weighted mean between kidney length (KL) and

that kidney thickness (KT) correlated best with height, weight, age and gender (see below). The

result of this analysis generated the following formula:

KS = 0.58 (right KL + left KL) + 0.42 (right KT + left KT)               [equation 1]

B. Variable transformation

Non-linear transformation was applied to express all dependent variables as a function of height,

weight, age and gender. Age was used up to a maximal value that was calculated using a best

fitting approach. The value for gender was set as +1 for males and -1 for females. After testing

several models, a third degree logistic model was selected for continuous variables. The following

equations were used in the order indicated below:

ƒ(H) = (aH + bH2 + cH3 + d)·z                                            [equation 2]

ƒ(H,W) = ƒ(H) + (aW + bW 2 + cW 3 + d)·z                                 [equation 3]

ƒ(H,W,A) = ƒ(H,W) + (aA + bA2 + cA3 + d)·z                               [equation 4]

ƒ(H,W,A,G) = ƒ(H,W,A)·(1+aG)                                             [equation 5]

(H=height in cm, W=weight in Kg, A=age in years, G= gender)

These equations were looped in sequence until the model was stable and reached a maximal

correlation value between the dependent value and ƒ(H,W,A,G). Values for coefficients a, b, c, d,

and z are reported in supplementary table 1.
Pearson correlation coefficients before data normalization, between each dependent variables and

growth parameters are reported in supplementary table 2. Also listed is the correlation coefficient

after data transformation (ƒ(H,W,A,G)). All correlations were statistically significant. All five

dependent variables correlated best with height. After data transformation, the gain in correlation

was marginal for KS, creatinine, SBP and DBP and more significant for BUN. Nonetheless, this

method allowed to normalize data for all growth- and gender-related variables and to express them

as a function of the same independent variables.

C. Data normalization

Regression curves were used to perform asymmetrical analysis of residuals and to correct for

heteroscedasticity by non-linear regression. This allowed to expressed data as SDS. Normal

distribution was checked graphically and with the Shapiro-Wilk and Kolmogorov–Smirnov test.

This process is illustrated in figure 1. Panels A and D shows data dispersion for KS and serum

creatinine after data transformation (see above); panels B and E confirm a normal distribution of

data points after correction for heteroscedasticity, which is further confirmed by plotting data

expressed as SDS as function of height, weight, age and gender in panels C and F.

To confirm data normalization, correlation tests were repeated using data expressed as SDS. As

indicated in table 1, all Pearson correlation coefficients had a value close to zero, indicating that

SDS data were independent of height, weight, age and gender. None retained statistical

significance.

D. Validation of the cohort

The final step of the preliminary data elaboration process involved comparison of SDS between the

four population sub-groups. Data are reported in table 2. As shown, the mean SDS was similar in

all subgroups. The ANOVA analysis showed small, but statistically significant differences only for

the DBP SDS. No differences were observed in KS, serum creatinine, BUN and SBP between the

four groups.
Supplementary table 1. Coefficients used in the equations for data normalization

Kidney Size              Equation 2          Equation 3          Equation 4        Equation 5
-3
a                           1.000              1.599               1.955           6.592·10
-3
b                        -2.660·10             -0.023              -0.421
-6                  -4
c                         7.601·10           1.256·10              0.021
-6                  -3
d                         1.563·10           5.818·10             23.285
z                           1.225              0.819               0.823
Age max Males                                                       11.0
Age max Females                                                     15.3

Creatinine               Equation 2          Equation 3          Equation 4        Equation 5
a                          69.338               0.555             11.214             0.012
-3
b                          -0.513            3.805·10              -1.135
-3                   -5
c                        1.891·10            -5.581·10             0.052
-3
d                          -0.631            6.123·10              0.182
z                           0.027               0.882              0.760
Age max Males                                                       17.3
Age max Females                                                     13.2

BUN                      Equation 2          Equation 3          Equation 4        Equation 5
-3
a                         1.046158             -0.895              2.018           9.054·10
-3
b                        -6.996·10              0.018              -0.381
-5                   -4
c                         1.478·10           -1.005·10             0.018
-10                 -9                  -6
d                       -6.292·10            5.425·10            1.346·10
z                           2.323               1.100              0.983
Age max Males                                                       16.0
Age max Females                                                     10.1

SBP                      Equation 2          Equation 3          Equation 4        Equation 5
-3
a                           1.001              3.836               9.242           -1.656·10
-3
b                        -6.725·10             -0.045              -1.343
-5                  -4
c                         1.787·10           2.301·10              0.063
-5
d                         3.175·10             0.024               -0.014
z                           2.146              0.632               0.865
Age max Males                                                       13.7
Age max Females                                                      8.7

DBP                      Equation 2          Equation 3          Equation 4        Equation 5
-3
a                           1.002               3.248             10.434           -1.302·10
-3
b                        -5.164·10             -0.043              -1.178
-5                  -4
c                         1.103·10           2.161·10              0.047
-6                   -3
d                         2.778·10           -2.014·10             -0.013
z                           1.819               0.686              0.815
Age max Males                                                       15.3
Age max Females                                                     14.1
Supplementary table 2. Pearson correlation coefficients
Correlation coefficients before and after data normalization for height, for weight, for age or as a
function of height, weight, age and gender (ƒ(HWAG)).

Height            Weight              Age            ƒ(H,W,A,G)           p

Before data normalization
Kidney size          0.93**            0.86**            0.89**            0.94**

Creatinine           0.76**            0.74**            0.76**            0.78**
(**) <0.001
BUN                  0.14*             0.10*              0.11*            0.29**
(*) <0.01
SBP                  0.75**            0.72**            0.72**            0.77**

DBP                  0.72**            0.66**            0.69**            0.73**

After data normalization
Kidney size          0.00               0.01              0.00              0.01

Creatinine           -0.01              0.05              0.04              0.03
n.s.
BUN                  0.00              -0.02              -0.01             0.01

SBP                  -0.01              0.04              0.03              0.03

DBP                  0.00              -0.03              -0.04             -0.03

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