Abstract

Introduction

Presently, little information is available about evaluation of kidney volume in groups of healthy Latin-American children of different ages. The objective of this work was to develop a predictive model and calculator of renal volume and length in healthy children.

Methods

A selective and representative sample was obtained randomly from two data bases of children considered healthy, living in Resistencia city, Chaco, Argentina: a) the National Health Program for children under 6 years old; b) school children until 18 years old (initial, primary and middle education). Renal dimensions were obtained by ultrasonography by a single operator, at site, schools or primary health care centers. Kidney volume was calculated with Dinkel ´s formulae. A multiple lineal regression model was fitted using potential predictors. The final model was implemented in a web based app freely available.

Results

Among 882 studied children, 600 with normal urinalysis and complete data were used. The data was split in 2 sets (one for train and the other for testing the models). Subjets from the train set (423) were 212 (50%) females, had mean age of 99.95±67.69 months. Mean birth weight, weight, height and gestational age were 3279.95±566.28 g, 32.02±20.86 kg, 1.22±0.35 m, and 38.09±2.34 weeks respectively. Mean renal volume and length were 31.43±16.8 cm3 and 8.24±1.72 cm respectively. Both predictive models significant predictors were: age, height, present and birth weight, and the interaction between age and present weight. Using both final models, predicted renal volume and length were calculated using the test dataset. Root mean square errors were 5.06 cm3 and 0.59 cm respectively.

Discussion

Accurate models for predicting renal volumen and length were developped. An implementation in a Shiny web app can be found in Renal size prediction.

Introduction

Renal volume is proportional to renal mass and therefore this has been used as an in vivo surrogate for the estimation of renal mass and therefore of glomerular number1. This renal volume may be measured by ultrasound in children including in neonates2. Presently, little information is available about evaluation of kidney volume in groups of healthy Latin-american children of different ages, though some studies have found that low birth weight is now a recognized risk factor for later- life hypertension and chronic kidney disease3. Few studies of ultrasonographic renal volume are published with different criteria of sampling, ages, and most of them obtained at ultrasonographic departments of Hospitals4. The objective of this work was to fit predictive model of renal size (volume and length) and develope a web based calculator from data retrieved from in healthy children.

Methods

Statistical analysis

The main objective of this study was to fit prediction models of renal size in a sample of pediatric subjects. Two measurement of renal size were used: average volumen and length. Data from healthy subjects without missing values was used. This dataset was split in a training and test set (70 and 30%). The former was used to fit the prediction models and the latter was only used to evaluate their performance.
Descriptive statistics were calculated. Subjects were classified in 3 age groups to test interaction between renal size and anthropometric measurements.
Multiple linear regression models for renal size measurement (average volume and length) as outcome were fitted using all clinically available predictors. Interaction of predictors with age group were explored. Volume model showed marked heteroscedasticity, so it was rebuilt using a log-transformation of the outcome variable. Finally, an automatic stepwise (both directions) term selection algorithm based on AIC was applied rendering final models.
Prediction models performance was evaluated with the test dataset. Root mean square errors from both measurements were calculated.
Data processing and statistical analysis was performed with R version 3.3.3 (2017-03-06).

Results

The database compromise data from 882 subjects aged between 0.4 and 230.63 months. Among them, 600 had complete data and no signs of renal disease. In order to evaluate the predictors of renal size and develope a prediction model, the database was split in a training (423 subjects) and a testing dataset (177). The latter dataset was only used for evaluating the performance of the final model. The subjects from the training demographic characteristics are summarized in table1.

Table 1

Demographic characteristics from subjets of the training dataset.

n %
Sex (male) 211 49.88
Ethnicity
Hispanic 138 32.62
Native 135 31.91
Other 150 35.46
Age (months)
(0,12] 65 15.37
(12,60] 69 16.31
(60,231] 289 68.32

Figures 1 and 2 illustrate the relationship between renal size (average length and volume) and anthropometric measurements, whereas figure 3 shows the relationship with the weight registered at birth. Table 2 summarize the correlation between these variables by age group, showing that height and weight are correlated. Correlation between renal size and weight at birth and renal size is weak and depends on the age.
No difference in renal size related to the subject gender or ethnicity was detected within age groups.

Figure 1

Average renal size (length and volume) as a function of subject height according to the age.

Figure 2

Average renal size (length and volume) as a function of subject weight according to the age.

Figure 3

Average renal size (length and volume) as a function of subject weight at birth according to the age.

Table 2

Pearson’s correlation between renal measurements and anthrometric measurements by age group. P values are shown inside parentheses.

Measurement Age (months) Height Weight Weight at birth
Volume (0,12] 0.645 (<0.001) 0.708 (<0.001) 0.055 (0.66)
(12,60] 0.747 (<0.001) 0.802 (<0.001) 0.21 (0.084)
(60,231] 0.835 (<0.001) 0.856 (<0.001) 0.091 (0.12)
Length (0,12] 0.745 (<0.001) 0.782 (<0.001) 0.092 (0.47)
(12,60] 0.812 (<0.001) 0.76 (<0.001) 0.235 (0.051)
(60,231] 0.839 (<0.001) 0.794 (<0.001) 0.132 (0.025)

Renal size model fitting

Figure 4 illustrates the relationship between potential predictors. As expected weight and height disclosed a high correlation.
First, multiple regression models for renal size measurement (average volume and length) as outcome were fitted using all clinically available predictors including an interaction term of age group. Volume model showed marked heteroscedasticity, so it was rebuilt using a log-transformation of the outcome variable. Then an automatic stepwise (both directions) term selection algorithm based on AIC was applied rendering final models (table 3).

Figure 4

Correlation plot evaluating the renal volumen (RV) and renal length (RL) with other variables: BW (weight at birth) in kg, weight in kg and height in meters.

Table 3

Multiple regression model predictor coefficients for both renal size measurement. Baseline Age group is < 12 months, Age group 2 is between 12 and 60, and group 3 is \(\geq\) 60 months. Interaction terms are noted as 2 variables names separated by a colon.

Measurement Predictor Coefficient P
Volume Age group 2 0.27 (0.04-0.49) 0.021
Age group 3 0.86 (0.65-1.07) <0.001
Height 0.81 (0.61-1) <0.001
Weight at birth 0 (0-0) 0.040
Weight 0.07 (0.04-0.09) <0.001
Age group 2:Weight -0.03 (-0.05-0) 0.021
Age group 3:Weight -0.06 (-0.08–0.03) <0.001
Length Age group 2 0.14 (0.05-0.22) 0.0011
Age group 3 0.32 (0.24-0.39) <0.001
Height 0.4 (0.33-0.48) <0.001
Weight at birth 0 (0-0) <0.001
Weight 0.02 (0.02-0.03) <0.001
Age group 2:Weight -0.01 (-0.02-0) 0.0031
Age group 3:Weight -0.02 (-0.03–0.02) <0.001

Performance of renal size prediction models

Using both final models, predicted renal volume and length were calculated using the test dataset (figure 5). Root mean square errors were 5.06 cm3 and 0.59 cm respectively.

Figure 5

Predicted versus observed renal size measurements using the test dataset.

These prediction models were used to built a Shiny app available at Renal size prediction.