Left ventricular mass normalization for body size in children based on an allometrically adjusted ratio is as accurate as normalization based on the centile curves method.

BACKGROUND: Normalization for body size is required for reliable left ventricular mass (LVM) evaluation, especially in children due to the large variability of body size. In clinical practice, the allometrically adjusted ratio of LVM to height raised to the power of 2.7 is often used. However, studies presenting normative LVM data for children recommend centile curves as optimal for the development of normative data. This study aimed to assess whether the allometrically adjusted LVM-to-height ratio can reliably reproduce the results of LVM normalization for height based on the centile curves method.
METHODS: Left ventricular mass was computed for 464 boys and 327 girls, 5-18 years old, based on echocardiographic examination. Normalized data representing LVM for height were developed using the centile curves construction method and two variants of the allometrically adjusted ratio method: one variant with the allometric exponents specific to the study groups, and one variant with the universal exponent of 2.7. The agreement between the allometric methods and the centile curves method was analyzed using the concordance correlation coefficient, sensitivity, and specificity.
RESULTS: For both the specific allometric variant and the universal variant, the analysis of concordance has indicated high reproducibility compared to the centile curves method. The respective coefficient values were 0.9917 and 0.9916 for girls, and 0.9886 and 0.9869 for boys. The sensitivity and specificity test has also shown high agreement. However, for girls, the sensitivity was higher for the specific variant (100% vs. 90.9%).
CONCLUSION: The results of the study show that allometric scaling of LVM for height can very reliably reproduce the results of LVM normalization for height based on the centile curves method. However, the analysis of sensitivity and specificity indicates greater agreement for the allometric normalization with the group-specific allometric exponents.

Introduction

Echocardiographic linear heart dimensions and left ventricular mass (LVM), which is calculated based on the linear dimensions of the left ventricle [1,2], are examined in daily clinical practice. The calculation of LVM allows confirmation of the presence of left ventricular hypertrophy (LVH) [2], which is a concern in cardiovascular diseases and a predictor of poor outcome [3,4]. It is also a concern in athletes in whom regular exercise causes physiological changes to the heart, including hypertrophy [5,6,7]. In athletes, a proper LVM assessment and differentiation of physiological LVH from pathological is essential. Normalization is required for reliable LVM evaluation because the size of the heart varies with the size of the body. LVM normalization is of particular importance in children and adolescents due to the large variability of body size in children of similar age.

Normalization of cardiac size for body size is a standard approach in clinical evaluation and recommended by the guidelines [2,8,9,10]. However, there is a discussion about the best body size variable and scaling methodology for cardiac size normalization [11-17].

In a recent study, we showed that among the frequently used body size variables, i.e., body surface area (BSA), lean body mass calculated based on predictive equations, and height, only height provides reliable normalization of LVM [11]. This study is a continuation of our previous work. It addresses the issue of scaling methodology.

The simplest methods of LVM scaling in clinical settings are based on the ratio of LVM to the body size variable (LVM index). The most popular is the simple ratio of LVM and BSA [18], and the ratio of LVM divided by height raised to the power of 2.7 [12]. The latter is an allometrically adjusted ratio and is based on a simple allometric model of a relationship between LVM and height. The value of 2.7 is a commonly used exponent related to the curvilinearity of the relationship (allometric exponent). The LVM index is easy to calculate, and the result can be presented as a numerical value or as a standardized value (z-score). More advanced methods are based on the constructing LVM centile curves for body size, the same as the well-known growth curves of height-for-age, weight-for-age, and weight-for-height used for the pediatric population [19]. A normalized LVM can be presented as a standardized value (z-score) or visualized on a centile chart. It is considered that the centile curves method is more accurate than the ratio methods for normalization of LVM for body size [15-17] and therefore allows for a more reliable diagnosis of LVH. However, the methodology of constructing centile curves, and then computing standardized LVM values, is complicated; that is why this method is not widely used in clinical practice. Additionally, since only a few studies have evaluated an agreement between the ratio method and the centile curves method [15-17], the superiority of the latter method is not confirmed. Should we then strive to replace the ratio method of LVM normalization with the more sophisticated method of centile curves in clinical practice?

We have attempted to provide a substantive basis to answer this question and designed a study to examine the concordance between the centile curves method and the allometrically adjusted ratio method. The study aimed to assess whether the allometrically adjusted LVM-to-height ratio can reliably reproduce the results of LVM normalization for height based on the centile curves method.

Materials and methods

The study group

It was a retrospective study based on data derived during periodic medical evaluation of child and adolescent athletes. All of the studied children were engaged in regular athletic training at the local or national level (mainly soccer, track and field, basketball, swimming, and martial arts). The entire study group consisted of 791 healthy White children (327 girls and 464 boys), aged from 5 to 18 years. All the study participants underwent transthoracic echocardiography as a part of medical evaluation because of innocent heart murmurs or suspicion of abnormal electrocardiographic findings. The athletes in whom echocardiography revealed significant acquired or congenital heart diseases, affecting normal heart size and hemodynamics, were not included in the study. The anthropometric measures, i.e., height and body mass, were measured during the main examination.

Echocardiography

Echocardiographic examinations were performed by two experienced sonographers using a commercially available ultrasound scanner (Toshiba Aplio 400, Toshiba Medical Systems Europe, Zoetermeer, the Netherlands), according to recent guidelines. All measurements were taken in the 2-dimensional parasternal long axis view (PLAX) at end-diastole and included the basic linear cardiac dimensions necessary for LVM computing: left ventricular internal dimension (LVIDd), interventricular septal thickness (IVSd), and posterior wall thickness (PWTd). All measurements were taken from the inner edge to inner edge and reported to within 1 mm. Left ventricular mass was computed according to the formula of Devereux RB et al. [1]:

Ethical considerations

The Ethics Committee of the Medical University of Warsaw approved the study procedure (approval AKBE/75/17). As the study was retrospective, and the data used were collected during routine medical monitoring, neither written nor verbal consent was required for this particular study. However, each subject, or the subject's parent or guardian, had signed the informed consent form for the routine medical monitoring, including a statement of agreement to the use of the results for scientific purposes.

Development of left ventricular mass normative data

Since previous studies about LVM normalization in children and adolescents have indicated that LVM normative data should be sex-specific [15,17,20], all analyses were carried out separately for girls and boys. Thus the entire study group was divided into two sex-specific Study Groups. Three sets of LVM-for-height normative data were developed based on each group’s records, using three different methods of normalization. First, the LMS method was used to construct centile curves [21]. In this method, based on the relationship between LVM and height in the study group, the expected mean LVM (M), coefficient of variation (S), and skewness (L) for each height level are generated. For an individual child, the LVM z-score is then calculated from the L, M, and S values corresponding to the child’s height, according to the equation:

Next, the allometrically adjusted ratio method was used. In this method, the height is raised to the power equal to the exponent from the power law equation (allometric equation) describing the curvilinear relationship of LVM with height [12,22]. Two variants of the method were tested. In the first variant (heightb), allometric equations specific to our Study Groups were fitted for the bivariate relationship of LVM with height, and sex-specific allometric exponents were determined. These equations have the general form LVM = a(body size), where b is the allometric exponent. Logarithmic transformation gives the linearized form of this equation (ln(LVM) = ln(a)+bln(height)), allowing estimation of the allometric coefficients using linear least squares regression modeling [22]. The sex-specific allometric exponents were used to transform height, which is used as a denominator in the ratio method. Then, for each subject, LVM was divided by transformed height. Thus, new variables of indexed LVM were produced, and normative data expressed as a mean and standard deviation of the LVM indexes developed. Next, LVM z-scores were calculated, according to the equation:

In the second variant (height2.7) of the allometrically adjusted ratio method, the universal allometric exponent 2.7 was used to develop normative LVM-for-height data for both sex-specific Study Groups. Like in the first variant, normative data expressed as a mean and standard deviation were produced, and z-scores were calculated with the equation analogous to that in the first variant.

For proper normalization of LVM for body size, it is necessary to eliminate body size information from the normalized LVM [22]. To check whether the body size information had been eliminated in the produced normative data, we tested whether there was a relationship between the calculated LVM z-scores and height. The Pearson correlation coefficient and the slope of the linear regression line for each set of the LVM z-scores were examined, and graphical presentations of the data were inspected.

Comparison of different methods of the LVM normalization

In this part of the study, from each of the sex-specific Study Group, 200 subjects were randomly assigned to corresponding Test Groups, to assess the concordance of different LVM normalization methods. For this comparison, following the aim of this study, we assumed that the LMS method is a reference method for LVM normalization. The z-scores calculated based on the LVM normative data obtained according to the allometrically adjusted ratio methods were compared to those calculated based on the L, M, and S values from the LMS method [21]. This allowed us to evaluate the reproducibility of the allometric methods and to assess their sensitivity and specificity compared to the LMS method.

At first, we examined whether the mean differences between the z-scores calculated based on both allometric LVM normative data and those calculated based on the LMS normative data differ from 0. The paired sample t-test was used. The allometric z-scores were then plotted against the LMS z-scores on scatter graphs. Regression lines were fitted to the data, and equality lines were drawn. For the initial assessment of whether the allometric LVM normalization methods can reproduce the results of the LMS method, the Pearson correlation coefficients and linear regression coefficients, as well as the slopes and y-intercepts, were estimated for the various data sets.

Next, the concordance correlation coefficient (CCC), introduced by Lin LI [23], was used to evaluate the agreement between the normalization methods. The CCC converts the mean squared difference between the paired points of two data sets into a correlation coefficient that measures how far the corresponding data points deviate from the equality line (y = x) in a two-dimensional coordinate system. The CCC is a product of accuracy and precision. The measure of precision is the Pearson correlation coefficient, which measures how far the points deviate from the best-fit line. A measure of accuracy is the coefficient that measures how far the best-fit line deviates from the equality line. This coefficient is considered as the bias correction factor and depends on the location shift and scale shift. A CCC value of 1 represents perfect agreement, a value of minus 1 represents perfect disagreement, and a value of 0 represents no agreement. The equation for calculating the concordance correlation coefficient, as well as equations for the intermediate factors, are presented in the supplementary S1 Table.

Finally, the sensitivity and specificity of the allometric methods, in comparison to the LMS method, were evaluated for the entire study group of 791 children and adolescents. For this analysis, the subjects were classified as having LVH when their z-score > 1.65 [15].

All calculations were performed using R (version 3.5.2, “Eggshell Igloo”; R Foundation, Vienna, Austria, http://www.r-project.org), along with external packages, especially the gamlss package (version 5.0), which contains a function used to fit the LMS curves, and the DescTools package (version 0.99.28), which contains tools used to estimate the concordance correlation coefficients. For all statistical tests, a significance level of α = 0.05 was used.

Results

Subjects characteristics

The characteristics of the entire study group, the sex-specific Study Groups, and the sex-specific Test Groups are presented in Table 1. The sex-specific Study Groups were used for the development of the LVM normative data. The Test Groups, both consisting of subjects randomly selected from the corresponding Study Groups, were used to analyze the agreement between the LVM normalization methods. The entire study group of 791 children and adolescents was used to evaluate the sensitivity and specificity.

Table 1

Characteristics of the entire study group, the sex-specific study groups, and test groups.

	Entire study group	Study Group	Test Group	Study Group	Test Group
		Girls	Girls	Boys	Boys
Number of subjects	791	327	200	464	200
Age [years]	12 (5–18)	12 (5–18)	11 (6–18)	13 (5–18)	13 (6–18)
Height [cm]	157 (111–194)	153 (111–188)	153 (117–181)	162 (112–194)	167 (112–194)
Body mass [kg]	45.4 (18.2–100.0)	41.8 (18.8–86.1)	40.9 (20.0–84.7)	48.9 (18.2–100)	53.5 (18.2–97.6)
LVM [g]	104.50 (38.77–280.47)	93.46 (38.77–213.18)	93.25 (38.77–180.13)	114.13 (45.91–280.47)	122.67 (46.52–263.05)
LVIDd [mm]	44 (31–60)	42 (34–55)	42 (34–54)	45 (31–60)	46 (31–60)
IVSd [mm]	8 (5–13)	8 (5–11)	7 (5–11)	8 (5–13)	8 (5–12)
PWTd [mm]	8 (5–13)	7 (5–10)	7 (5–10)	8 (5–13)	8 (5–12)
Training volume [minutes]	270 (60–630)	240 (60–630)	240 (60–540)	270 (60–630)	300 (60–630)
Resting HR [beats/minute]	71 (45–93)	75 (49–93)	76 (51–93)	68 (45–93)	69 (47–93)
Systolic BP [mmHg]	114 (80–135)	110 (80–135)	109 (80–135)	116 (86–135)	117 (88–135)
Diastolic BP [mmHg]	64 (40–85)	64 (40–85)	63 (40–85)	65 (40–85)	65 (40–85)

Data are expressed as “median (minimum–maximum)”; LVM, left ventricular mass; LVIDd, left ventricular internal dimension; IVSd, interventricular septal thickness; PWTd, posterior wall thickness; training volume is a measure of participation in sports activity and was estimated as the product of the average number of training sessions per week and the average duration of a session; HR, heart rate; BP, blood pressure.

The LVM normative data for the mutual comparison

Two sets of LVM-for-height normative data, separate for girls and boys and generated based on the LMS method, are provided as L, M, and S values in supplementary text files (S1 and S2 Datasets, respectively). The allometric exponents estimated for the sex-specific Study Groups are presented in Table 2. The LVM normative data computed based on the LVM-to-height ratio are expressed as means and standard deviations and also included in Table 2. For the heightb variant, the height is raised to the power of b, where b is equal to the estimated allometric exponent; for the height2.7 variant, the height is raised to the power of 2.7.

Table 2

The LVM normative data for allometrically adjusted LVM-to-height ratios and the parameters used to assess the relationship between the normalized LVM and height for the LMS method and both variants of the allometric method.

	LMS	heightb	height2.7
Girls
Allometric exponent	N/A	2.5848	2.7
LVM to height ratio	N/A	32.0467 (5.1431)	30.5527 (4.9191)
Pearson’s coefficient	0.0015 (ns)	0.0000 (ns)	-0.0719 (ns)
Slope of regression line	0.0001 (ns)	0.0000 (ns)	-0.0048 (ns)
Boys
Allometric exponent	N/A	2.8118	2.7
LVM-to-height ratio	N/A	32.5524 (6.1043)	34.2606 (6.4542)
Pearson’s coefficient	0.0004 (ns)	0.0127 (ns)	0.0864 (ns)
Slope of regression line	0.0000 (ns)	0.0007 (ns)	0.0045 (ns)

Here, “LVM-to-height ratio” refers to the LVM normative data computed based on the allometrically adjusted LVM-to-height ratio and is expressed as “mean (standard deviation).” For heightb, the height is raised to the power of b, where b is equal to the estimated allometric exponent; for height2.7, the height is raised to the power of 2.7. The Pearson correlation coefficient and the slope of the linear regression line both correspond to the relationship between the calculated LVM z-scores and height. “ns” stands for “non-significant” (p ≥ 0.05).

Based on the developed LVM normative data, the LVM z-scores were calculated, according to the LMS method of normalization and according to both variants of the allometric method. Examples of LVM z-score calculations are presented in a supplementary file (S1 Text). The Pearson correlation coefficients and the slopes of the linear regression lines of the relationships between the calculated LVM z-scores and heights are also presented in Table 2. All the coefficients are non-significant. In addition, graphic presentations of the data show point configurations that do not indicate the presence of non-linear relationships (S1 Fig). Thus, both variants of the allometric LVM normalization method, as well as the LMS method, eliminated the height information from the normalized LVM.

The agreement between the LVM normalization methods

For girls, the mean and standard deviation (in parentheses) of LVM z-scores were 0.0791 (1.0122) for the LMS normative data, 0.0748 (1.0121) for allometric LVM normative data produced based on the specific allometric exponent, and 0.0750 (1.0090) for allometric LVM normative data based on the exponent of 2.7. For boys, these were 0.0213 (1.0297), 0.0282 (1.0340), and 0.0378 (1.0344), respectively. The mean differences between the z-scores calculated based on both allometric LVM normative data sets and based on the LMS normative data did not differ from 0, for both female subjects and male subjects.

The heightb and height2.7 allometric LVM z-sores, separate for girls and boys, are plotted against the LMS z-score in Fig 1. These scatter graphs show that, for both variants, data points are congregated along the equality line, and the best fit line overlaps the equality line.

Fig 1

Scatter plots of the LVM z-scores calculated based on the allometric normative data against the LVM z-scores calculated based on the LMS normative data.

On each chart, the regression line is fitted to the data points (solid line), and the equality line is shown (dashed line). The charts on the right correspond to the heightb variant and those on the left to the height2.7 variant. The upper charts are for girls and the lower for boys.

Table 3 presents the results of statistical analyses that test the agreement between the allometric normalization methods and the LMS method. The coefficients of the regression lines indicate that the best-fit lines are very close to the equality line. The y-intercepts of the best-fit lines are close to 0 and are non-significant (the lines pass through the origin). The slopes of the lines are close to 1 and are significant, as are the Pearson correlation coefficients.

Table 3

Evaluation of the agreement between the allometrically adjusted ratio methods of LVM normalization and the LMS method.

	heightb	height2.7
Girls
Mean squared difference	0.0169	0.0231
Slope of regression line	0.9918 (p<0.001)	0.9916 (p<0.001)
Y-intercept of regression line	0.0049 (ns)	0.0047 (ns)
Pearson correlation coefficient	0.9917 (p<0.001)	0.9886 (p<0.001)
Bias correction factor	1.0000	1.0000
Concordance correlation coefficient (CCC)	0.9917	0.9886
Lower one-sided 95% confidence limit for CCC	0.9895	0.9857
Scale shift	1.0001	1.0031
Location shift	0.0043	0.0041
Boys
Mean squared difference	0.0178	0.0279
Slope of regression line	0.9874 (p<0.001)	0.9825 (p<0.001)
Y-intercept of regression line	-0.0066 (ns)	-0.0159 (ns)
Pearson correlation coefficient	0.9916 (p<0.001)	0.9870 (p<0.001)
Bias correction factor	1.0000	0.9999
Concordance correlation coefficient (CCC)	0.9916	0.9869
Lower one-sided 95% confidence limit for CCC	0.9894	0.9834
Scale shift	0.9958	0.9954
Location shift	0.0067	0.0160

heightb and heigh2.7 stand for variants of the allometric normalization method that have been compared with the LMS method. In the heightb variant, sex-specific allometric exponents (represented as b in the allometric equation) were estimated based on the relationship between LVM and height in our Study Groups. In the heigh2.7 variant, a universal allometric exponent 2.7 was used to develop sex-specific normative data for LVM. “ns” means “non-significant” (p ≥ 0.05).

The concordance correlation coefficients reflect the initial evaluation. For the heightb normalization, for both girls and boys, CCC is equal to the Pearson correlation coefficient because the bias correction factor is equal to 1. The situation is similar for the height2.7 normalization. Location shifts and scale shifts are minimal. The lower one-sided 95% confidence limits for all the CCCs are high.

The sensitivity and specificity of the allometric methods, compared to the LMS method, and the distribution of negative and positive LVH classifications according to the allometric normalization methods, compared to the LMS method, are shown in Table 4.

Table 4

Evaluation of sensitivity and specificity of different variants of the allometric method of LVM normalization in comparison to the LMS method.

	heightb	height2.7
Sample size	791	791
Number of true positives	31	30
Number of true negatives	751	751
Number of false positives	9	9
Number of false negatives	0	1
Sensitivity	100.00%	96.77%
95% Confidence Interval for Sensitivity	88.78% - 100.00%	83.30% - 99.92%
Specificity	98.82%	98.82%
95% Confidence Interval for Specificity	97.76% - 99.46%	97.76% - 99.46%

As in Table 3, heightb and heigh2.7 stand for variants of the allometric normalization method that have been compared with the LMS method. The subjects were classified as having LVH when their LVM z-score > 1.65. Confidence intervals for sensitivity and specificity are Clopper-Pearson exact confidence intervals.

Discussion

The results of our study show clearly that the allometrically adjusted LVM-to-height ratio normalization method can very reliably reproduce the results of LVM normalization for height based on the centile curves method. Thus, there is no reason to replace the allometric normalization of LVM with a seemingly-better procedure of centile curves construction like the LMS method.

In this study, we assumed that the LMS method for constructing normalized data, as an advanced statistical method [15-17,21], is the most accurate, and can be regarded as the reference method. We compared standardized results from two variants of the allometric LVM normalization to the results of the LMS method. In the first allometric variant, sex-specific allometric exponents were modeled based on the LVM and height data from our Study Groups of young athletes. In the second variant, we used the universal allometric exponent of 2.7. For both these variants, the normative data development and agreement analyses were performed separately for girls and boys.

It seems that there is not much difference between allometric normalization using a specific allometric exponent as compared to the universal allometric exponent. However, the exact numbers are slightly better for the specific exponents, and analysis of sensitivity and specificity also indicates the allometric normalization with the specific allometric exponents as the preferred method.

Important questions about the cardiac size scaling procedure

An estimation of LVM is necessary for the diagnosis and management of left ventricular hypertrophy [2,6]. Athletic training can be responsible for LVH [24,25], though athleticism does not preclude the influence of pathological factors. Sometimes, it is difficult to differentiate physiological hypertrophy from pathological [5,7].

There is no doubt that proper LVM evaluation, or more generally, cardiac dimensions evaluation, requires normalization for body size [9]. This need is particularly evident in children and adolescents, whose heart size changes with age, in parallel to the size of the body, but also in the youth of the same age, where large variations in body size are observed. In athletes, especially speed and strength athletes, muscle mass significantly increases as a result of a specific exercise regime, with parallel changes in LVM [26,27]. A question thus arises: what body size variable is the best for LVM normalization? In our recent study, we indicated that among commonly used scaling variables, like BSA, LBM computed based on the predictive equation, and height, only height allows for reliable evaluation of LVM in child and adolescents athletes [11]. This is because normalized LVM is underestimated after normalization against BSA or computed LBM in subjects with high body mass, like speed and strength athletes, and overweight and obese subjects.

In this study, we address another question about the best method of LVM normalization, since there is a gap between clinical practice and some recommendations from echocardiographic studies. In clinical practice, the most popular LVM normalization methods are the simple (linear) ratio of LVM divided by BSA and the allometrically adjusted ratio of LVM divided by height raised to the power of 2.7. The guidelines recommend these methods of LVM scaling [8]. In turn, in studies presenting LVM normative data for children and adolescents, the development of LVM normative data is most often based on advanced statistical methods of constructing normalized data, like the LMS method, introduced for the construction of growth curves [15-17]. Some researchers recommend this method as more accurate [15-17,22,28]. Another question then arises: are there significant differences in accuracy and precision between the LVM normalization methods recommended for clinical use by guidelines, and the advanced procedures used in studies developing normalized LVM data?

It can be assumed that the LMS procedure is very accurate for LVM normalization because this method fits data points very well. The echocardiographic studies where the LMS method was used recommended this method for LVH diagnosis, indicating its better performance compared to the ratio methods [15-17]. In these studies, the LMS method was regarded as the reference, and different body size variables were used for LVM normalization of the compared data. It must be noted that because of the lack of a procedure that is able to determine or exclude LV hypertrophy with certainty, any conclusions based on the comparisons between different methods, favoring one method or disqualifying another, are questionable. Furthermore, the different body size variables used for LVM normalization further biased the results of these studies. Our study was the first attempt to directly compare the agreement between the LMS method and the allometric ratio method for LVM normalization, with the same body size variable used as a descriptor. This study has indicated that the allometric LVM normalization provides reproducible results compared to the LMS normalization.

An optimal exponent for allometric LVM normalization for height

Allometry, a term introduced by Julian Huxley and George Tessier in 1936 [29], means “different measures” and refers to the differences in growth rate between parts of the body or between organs and body as a whole during development. This phenomenon is often observed in nature [30]. A comparison of an organ’s size changes with the body’s size changes shows that the course of the changes is nonlinear. However, a specific feature of allometric growth is that, after a bivariate logarithmic transformation, this course of changes becomes linear, and the relationship can be described using a linear equation [22,30]. The slope of the line is a measure of the relative growth of the organ with body size; it is referred to as the allometric coefficient, also known as the allometric exponent. This is because, for original data, the power law equation describes the course of changes.

Cardiac size changes with body size during development, and when one analyzes how LVM changes with body mass, the allometric exponent estimated for different groups is close to 1 [30,31]. Since both the variables are geometrically similar, the relationship is actually linear. For the relationship between LVM and height, the allometric exponent is estimated from about 2.4 to 3.2, depending on the group tested [12,32]. This relationship is allometric, and the estimated values of the exponent are consistent in terms of the dimensions of the two variables because a relationship between a three-dimensional variable and a one-dimensional is modeled.

Allometry is applied to scale LVM to height. Most often, the ratio of LVM to height is used where the height is adjusted with the allometric exponent [12,32,33]. In clinical practice, the allometric exponent of 2.7 is used [8]. This exponent was introduced by de Simone G et al. n 1992 [12] based on a study of two different groups of adults and one group of children and adolescents. In this study, different exponents were computed for different groups, but 2.7 was the exponent estimated for the pooled group.

Our study examines two variants of the allometric method of LVM normalization for height: with the allometric exponent of 2.7 as well as with specific exponents estimated for the sex-specific Study Groups. It was not the aim of our study to question the exponent recommended by de Simone G et al. [12]; therefore, we did not make a direct comparison between those variants. However, since our Study Groups consisted of child and adolescents athletes, we were interested in whether the application of specific allometric exponents would improve the performance of the allometric method when testing against the centile curves method of LVM normalization.

Although the exact estimates of reproducibility indicate slightly better agreement in the case of the specific allometric exponents, the graphs and the concordance coefficients reflect high precision and accuracy, with minimum location shift and scale shift, for both the allometric variants. However, the sensitivity of the specific variant is again slightly better. Thus, a question arises: during the development of LVM normative data with the allometric method, should specific allometric exponents first be estimated, or the universal exponent accepted as reliable?

This universal exponent of 2.7 has been challenged by others [32,33]. For example, 1.7 was recommended as more accurate for LVM quantification based on a study on two large cohorts of middle-aged and older adults of varying ethnicity [32]. In this study, instead of bivariate modeling, multivariate was applied by accounting for sex. As a major drawback of 2.7, researchers have indicated the presence of a significant negative relationship between normalized LVM and height. Additionally, the researchers stated that LVH defined based on the newly recommended ratio "was most consistently associated with cardiovascular events and all-cause death." This latter opinion was disputed by de Simone G and Devereux RB [34].

The problem of a relationship between normalized LVM and height after scaling LVM for height to the power of 2.7 was also raised in a study of 400 White children [33]. The study group consisted of infants, children, and adolescents of both sexes, aged 0–18. Researchers modeled allometric equations specific to sex-specific sub-groups and the pooled group and searched for the ratio adjustment that eliminated this relationship. They stated that a ratio of LVM to height raised to the power of 2.16 with a correction factor of 0.09 (height2.16 + 0.09) has better reliability for diagnosing LVH in children. This variant of allometric scaling looks like a statistical exercise and has not been applied in clinical practice. However, this study, as well as the former, stimulates doubts about a universal exponent for allometric LVM scaling, and its reliability across sexes or age groups. The problem started with the study of de Simone et al. [12] where the biological context of allometry was omitted. The bivariate modeling of LVM against height for a pooled group of children and adults did not consider potential differences in the allometric relationships between these groups; ontogenetic (developmental) allometry vs. static allometry. The next problem is the drive for the universality of the LVM scaling procedure. One allometric exponent for all: males, females, children, adults, and special groups like athletes or infants. Is it necessary? Is it feasible?

To answer those questions was not the aim of our study. For sure, a special consensus is needed in this field. We sought to answer the question of whether the allometric scaling of LVM for height can reliably reproduce the results of the advanced but more complicated normalization based on the centile curves method. However, parallel analysis with two variants of the allometric method, with the universal exponent and with exponents specific to young athletes, has let us estimate the performance of both variants. The specific variant seems to work better, but the universal variant is almost equally effective. Most importantly, in our study, for a group of child and adolescent athletes aged 5–18, we did not find a relationship between normalized LVM and height in the variant with specific exponents, nor in the variant with the universal exponent.

Study limitations

Our study has limitations. We used a group of child and adolescent athletes from 5 to 18 years of age for this analysis; the group was ethnically homogenous. It might be argued that such a characteristic of the group limits the possibility of generalization. We do not question the necessity of further research to confirm the results in younger children, adults, and subjects from different ethnic groups. However, because we call for group-specific exponents in allometric scaling of LVM, the characteristic of the group in this study is consistent with this postulate.

We used height as the normalizing variable for both the allometric method and the centile curves construction method. A question may raise of why we did not use BSA, recommended by the guidelines, or LBM, suggested as the optimal body size variable for LVM normalization. The selection of a normalizing variable is a consequence of our previous study of bias related to body mass, which is introduced to the normalized LVM by BSA or LBM computed based on predictive equations [11]. There, we show that when BSA or equation-based LBM is used for normalization of LVM, the normalized LVM is underestimated in subjects with a high body mass index. The analysis indicates that only the height-based normalization of LVM is free of the BMI bias.

The LVM normative data, generated using both the LMS method and two variants of the allometric procedure, were developed based on the sex-specific Study Groups. Subjects in the Test Groups that were used for the evaluation of the agreement between the methods of LVM normalization were randomly selected from the respective Study Groups. The lack of a distinct group for the assessment of the agreement may be considered a limitation. However, since this research included the development of LVM normative data with different methods, and this procedure requires large samples, all the participants were assigned to the Study Groups. The reproducibility analysis based on the Test Group that consisted of randomly selected subjects from the Study Group is statistically valid. The number of subjects in each Test Group was large enough for this analysis.

The Bland-Altman method is the most commonly used method to measure agreement [35] and a question may arise why we did not use this method. The Bland-Altman plot is not suitable for our data; the plot has a limitation when the outer tails of the compared data distributions are divergent. In our data, the extreme data points of both, the LMS z-scores and the allometric z-scores, contribute to such divergence. As a result, the differences between the z-scores are greater on the outer ends. When this situation occurs, the distribution of the differences is not normal. The Bland-Altman analysis requires normal distribution; the measurement variables need not be normally distributed, yet their differences should be. An additional limitation is the measurement range from negative, through zero, to positive. According to the general idea of Bland-Altman analysis, if the assumption of normality is not met, data may be logarithmically transformed. In the presented case, they cannot, because the z-scores are positive and negative. Besides, an analysis directed to a search for the proportional bias is not practicable. The Bland-Altman plot shows a biphasic configuration of data points and even a parabolic shape. The range of the measurement also limits ratio calculation: there is a risk of dividing by 0. The ratios estimated for z-scores close to 0 might be immense, and may highly influence the calculation, causing misinterpretation of the results.

Conclusions

The results of the study show that in children and adolescents from 5 to 18 years of age, the allometric scaling of LVM for height very accurately reproduces the results of a more advanced centile curves construction procedure represented by the LMS method. Both allometric variants, one with an exponent specific to the tested group, the other with the universal exponent of 2.7, meet the statistical criterion of efficacy: the normalized LVM does not show a linear relationship with the height.

In agreement analysis, the difference between the LVM index with an allometric exponent that is specific to a tested group and the LVM index with the universally used exponent of 2.7 is small, yet the former provides better concordance with the LMS method. Besides, the sensitivity and specificity evaluation, with the LMS procedure as the reference method, indicates a better sensitivity of the LVM index with the specific exponent compared to the universal LVM index; the specificity is similar.

For reliable clinical evaluation of LVM in school-aged children and adolescents, there is no need to replace the allometrically adjusted LVM-to-height ratio with the more sophisticated method of centile curves. However, it seems that group-specific allometric exponents should be used to avoid constraints related to incomplete elimination of body size information from the normalized LVM, and for better performance in daily clinical practice.

The L, M, and S values of the LMS method for girls.

(TXT)

Click here for additional data file.

The L, M, and S values of the LMS method for boys.

(TXT)

Click here for additional data file.

The original dataset.

(TXT)

Click here for additional data file.

Scatter graphs of LVM z-scores against height.

(TIFF)

Click here for additional data file.

The equation for calculating Lin’s concordance correlation coefficient and equations for the intermediate factors.

(DOCX)

Click here for additional data file.

Examples of LVM z-score calculations.

(DOCX)

Click here for additional data file.

13 Aug 2019

PONE-D-19-17289

Left ventricular mass normalization for body size in children based on an allometrically adjusted ratio is as accurate as normalization based on the centile curves method.

PLOS ONE

Dear HUBERT KRYSZTOFIAK

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Additional Editor Comments (if provided):

I have read with great interest the work of Hubert Krysztofiak and collaborators entitled "Left ventricular mass normalization for body size in children based on an allometrically adjusted ratio is as accurate as normalization based on the centile curves method."

The authors clearly present the hypothesis, the objectives and analysis of the data. The writing of the article is clear and correct.

The exact definition of left ventricular hypertrophy in pediatrics is one of the most investigated and still unsolved items. The original contribution of the present study is essential to approximate positions between the different groups that are dedicated to the investigation of this issue.

In my opinion as an editor it is a very interesting study that deserves to be considered for publication in Plos One (MINOR CHANGES).

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Reviewer #1: No

Reviewer #2: Yes

Reviewer #3: Yes

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Reviewer #2: Yes

Reviewer #3: Yes

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Reviewer #3: Yes

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Reviewer #1: I have evaluated with interest the manuscript "Left ventricular mass normalization for body size in children based on an allometrically adjusted ratio is as accurate as normalization based on the centile curves method.

The authors mistakenly use the guidelines developed for adults as a bibliographic reference (Lang 2015) without considering the recommendations for children and adolescents (Lopez 2010, Lopez 2018). It is known that in pediatrics specific percentiles based on sex and age should be used to know the evolution of growth. The authors provide an approach to normalize ventricular mass and avoid standardization based on percentiles but do not fail to show the advantages of this approach.

Reviewer #2: The article addresses a very relevant topic for the area of pediatric medicine (cardiovascular area). The writing is very clear, and the analyzes performed are explained in detail. The authors are clearly aware of the problem analyzed. I have some suggestions and requirements that I believe can increase the quality of the manuscript.

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Page 6: "Three sets of LVM-for-height normative data were developed based on each group’s records, using three different methods of normalization". From which table, database and/or web were the values of LVM (M), coefficient of variation (S), and skewness (L) for each height level obtained, to calculate the z-score for each child ? Please be specific. How were the "expected, normative or reference" mean values and standar deviation levels obtained (calculated), to calculate the z-score by the allometrically adjusted ratio method (two variants)? Considering that PlosOne is a Journal read by professionals from a wide range of disciplines, it would be important to give specific examples of these calculations, indicating where the values used come from (e.g. please consider including this in an Annex).

Page 8: "For proper normalization of LVM for body size, it is necessary to eliminate body size

information from the normalized LVM [20]. To check whether the body size information had

been eliminated in the produced normative data, we tested whether there was a relationship

between the calculated LVM z-scores and height. The Pearson correlation coefficient and the

slope of the linear regression line for each set of the LVM z-scores were examined". Why were only linear models used for this purpose?

Page 8: "Comparison of different methods of the LVM normalization: In this part of the study, from each of the sex-specific Study Group, 200 subjects were randomly assigned to corresponding Test Groups, to compare different LVM normalization methods".Why did you work with a subsample in this part of the analysis? As an example, did you consider using Bootstrapping?

Page 8: "The z-scores calculated based on the LVM normative data obtained according to the allometrically adjusted ratio methods were compared to those calculated based on the L, M, and S values from the LMS method [19]. This allowed us to evaluate the reproducibility of the allometric methods and to assess their sensitivity and specificity compared to the LMS method". Why not also use a Bland and Altman analysis for repeated samples? Do the differences between methods remain the same for any level of body-height (proportional errors)? It would be important to include this (very simple) analysis, which although it has limitations, is widely used to analyze the agreement between tools. Please add it.

Page 9: "For this analysis, the subjects in the Test Groups were classified as having LVH when their z-score>1.65". Add reference

Results (page 10): The authors mentioned in the methodology: " This was a retrospective study based on data derived during periodic medical evaluation of child and adolescent athletes". Table 1. Please include more information on the subjects, in order to know to what extent their values are within "normality" (healthy expeted values). Information on the clinical and / or hemodynamic characteristics (blood pressure, heart rate, other echocardiographic data) of the subjects should be included. In addition, please include the minimum, median and maximum value of each variable. It is important to know the levels of the variables for which the study results are applicable.

Results: The authors mentioned in the methodology: "The athletes in whom echocardiography revealed significant acquired or congenital heart diseases, affecting normal heart size and hemodynamics, were not included in the study". It would be interesting to know the results of a similar analysis performed in this subgroup of children and adolescents. You can do it? In this way it could be known to what extent the methods have similarity in these special cases.

Results: "The Pearson correlation coefficients and the slopes of the linear regression lines of the relationships between the calculated LVM z-scores and heights are also presented in Table 2". Please, can you show these graphics?

Results: Table 5 and Table S2. Only 10 cases (in 200) were "positive" for LVH. Do you consider this "n" appropriate for a sensitivity and specificity analysis? Can you report confidence intervals? Can you present this analysis for "the whole group" (for separate and non-separated sexes).

Discussion (page 16): "It seems that there is not much difference between allometric normalization using a specific allometric exponent as compared to the universal allometric exponent. However, the exact numbers are slightly better for the specific exponents, and analysis of sensitivity and specificity also indicates the allometric normalization with the especific allometric exponents as the preferred method". An important question that arises is: Are children studied similar (in terms of LVM and body height) to children from other places. Could the authors perform an analysis and / or discuss this aspect? It is important for the purpose of understanding how generalizable the results are. Please consider comparing yourself to a population of different latitudes. An example may be the following article:

• Díaz A et al. Reference Intervals and Percentile Curves of Echocardiographic Left Ventricular Mass, Relative Wall Thickness and Ejection Fraction in Healthy Children and Adolescents. Pediatr Cardiol. 2019 Feb;40(2):283-301.

Discussion: An interesting aspect would be to know to what extent the differences (although apparently not significant) between methods, could be explained by other co-factors (e.g. sex, body weight, blood pressure). I understand that it is not the objective of the work, but it could be enriched if the association between the differences in absolute levels and / or z-scores between methods, and the demographic, anthropometric and / or clinical variables of young people were analyzed.

Reviewer #3: The paper addresses a topic of actual relevance and contributes to answer current questions.

The work is clearly written. The methodological approach is adequately explained.

There are some issues, mostly methodological that should be considered and/or addressed.

- Data about characteristics of the studied population is scarce (e.g. information about hemodynamic conditions, cardiovascular risk factors prevalence was not given). What kind of exercise did the subjects practice?

- Why only data from 200 subjects were considered for the comparative analysis?

- Why did the authors choose to compare the approaches using t-tests? Why tools like Bland and Altman tests were not used to assess the agreement between methods? Did the differences between the methods show dependence on the height level (proportional errors)?

- This reviewer considers that it would be of value to analyze the equivalence between the allometric methods themselves and to compare their concordance with the reference methods. The authors state that there would be differences between allometric methods, with the specific allometric exponents as the preferred method. This issue and its significance in clinical practice should be accurately analyzed and discussed.

- Information about cofactors was not given. Were they considered? If so, was their impact on the differences methodological approaches similar? How did the authors defined covariates should not be considered in the analysis?

- How could the characteristics of the practiced sport have an impact on the results obtained and on the possibility of considering them in the usual clinical practice and in other population groups?

- The following sentence should be clarified: It must be noted that, because of a lack of a gold standard procedure, any conclusions based on the comparisons between different methods are limited.

- The tables design should be improved.

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Reviewer #1: No

Reviewer #2: Yes: Daniel Bia

Reviewer #3: Yes: Yanina Zócalo

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25 Sep 2019

Response to reviewers

Reviewer #1: I have evaluated with interest the manuscript "Left ventricular mass normalization for body size in children based on an allometrically adjusted ratio is as accurate as normalization based on the centile curves method.

Q1: The authors mistakenly use the guidelines developed for adults as a bibliographic reference (Lang 2015) without considering the recommendations for children and adolescents (Lopez 2010, Lopez 2018). It is known that in pediatrics specific percentiles based on sex and age should be used to know the evolution of growth. The authors provide an approach to normalize ventricular mass and avoid standardization based on percentiles but do not fail to show the advantages of this approach.

Thank you for reminding us of the 2010 recommendations of Lopez et al. We are familiar with this report and appreciate it. We agree that it should be cited and it will be included as a bibliographic reference. However, we cannot agree that the reference to the 2015 recommendation of Lang et al. is a mistake. Certainly, it depends on the context; we believe that in this case, it was appropriately used. Please note that in both the mentioned works of Lopez et al., the Lang's guideline (the 2005 version) was cited in 1-2 position.

Reviewer #2: The article addresses a very relevant topic for the area of pediatric medicine (cardiovascular area). The writing is very clear, and the analyzes performed are explained in detail. The authors are clearly aware of the problem analyzed. I have some suggestions and requirements that I believe can increase the quality of the manuscript.

Q2: Page 6: "Three sets of LVM-for-height normative data were developed based on each group’s records, using three different methods of normalization". From which table, database and/or web were the values of LVM (M), coefficient of variation (S), and skewness (L) for each height level obtained, to calculate the z-score for each child? Please be specific. How were the "expected, normative or reference" mean values and standar deviation levels obtained (calculated), to calculate the z-score by the allometrically adjusted ratio method (two variants)? Considering that PlosOne is a Journal read by professionals from a wide range of disciplines, it would be important to give specific examples of these calculations, indicating where the values used come from (e.g. please consider including this in an Annex).

Thank you for the comment and recommendation. The cited text is from the Methods section; it refers to the procedure of generating the L, M and S values. However, at the beginning of the sub-section “The LVM normative data for the mutual comparison”, in the Results section, we provide information about supplementary files (S1 and S2 Datasets) with the L, M and S values which were generated based on our data. Quote: “Two sets of LVM-for-height normative data, separate for girls and boys and generated based on the LMS method, are provided as L, M, and S values in supplementary text files (S1 and S2 Datasets, respectively).”

Additionally, in the sub-section “Development of left ventricular mass normative data”, we have added information about the data needed to generate the L, M and S values (quote): “In this method, based on the relationship between LVM and height in the study group, the expected mean LVM (M), coefficient of variation (S), and skewness (L) for each height level are generated. The LVM z-score is then calculated for an individual child, from the L, M, and S values corresponding to the child’s height, according to the equation:”

To add information on how the mean and standard deviation, recognized as the normative data, were obtained, we added text in the aforementioned section (quote): “The sex-specific allometric exponents were used to transform height, which is used as a denominator in the ratio method. Then, for each subject, LVM was divided by transformed height. Thus, new variables of indexed LVM were produced, and normative data expressed as a mean and standard deviation of the LVM indexes developed. Next, LVM z-scores were calculated, according to the equation:”

According to your suggestion, we have prepared a supplementary file with examples of LVM z-score calculations. We added a sentence to the manuscript (quote): “Examples of LVM z-score calculations are presented in a supplementary file (S1 Text)”

In the context of the comments and the queries, it seems important to note that the aim of our study is not a presentation of LVM normative data for a specific group of children and adolescents. It is a continuation of our previous work on improvement to the methodology of LVM scaling. In this study, we wanted to test if there is a significant superiority of the advanced methods (centile curves) over the practical approaches to LVM scaling.

Q3. Page 8: "For proper normalization of LVM for body size, it is necessary to eliminate body size information from the normalized LVM [20]. To check whether the body size information had been eliminated in the produced normative data, we tested whether there was a relationship between the calculated LVM z-scores and height. The Pearson correlation coefficient and the slope of the linear regression line for each set of the LVM z-scores were examined". Why were only linear models used for this purpose?

Good point. The procedure to verify whether normalization eliminates size information from measurement variables was described by Albrecht GH et al. (1993) and is widely accepted. They listed three equivalent criteria:

(1) Statistical - correlation coefficient (R) between the normalized variable and normalizing body size variable is zero or nearly so.

(2) Graphical - the least-squares regression line of the relationship between the normalized variable and normalizing body size variable has a slope of 0 (horizontal line on a scatterplot).

(3) Algebraic - valid for allometric methods only; the expected value of the normalized variable is equal to a constant.

However, it is possible that the correlation coefficient is close to 0, and the slope is 0, too, and there is a strong non-linear relationship. Therefore, Albrecht et al. have recommended inspecting graphical presentation of the data. In our study, the correlation coefficient and slope are both close to 0, and the arrangement of points on the scatterplots does not suggest a non-linear relationship. Of course, we are going to add the graphs to the supplementary data (S1 Figure).

Q4: Page 8: "Comparison of different methods of the LVM normalization: In this part of the study, from each of the sex-specific Study Group, 200 subjects were randomly assigned to corresponding Test Groups, to compare different LVM normalization methods". Why did you work with a subsample in this part of the analysis? As an example, did you consider using Bootstrapping?

For analysis of the agreement between tools or methods, the observations should be collected consecutively or randomly. The LVM z-scores in the Study Group do not meet this requirement. If the LVM z-scores in the Study Group had been calculated for the normative data developed based on the same group, the z-scores thus computed would have had a mean of 0, or very close to 0, and a standard deviation of 1, or very close to 1. Such a sample should be considered distorted.

In the Study Limitations, we admitted that there is a lack of a distinct group for the assessment of the agreement, and that this would be the best option. Therefore, we decided to randomly select observations from the Study Group to develop a sample for the analysis of the reproducibility.

The sample size necessary to perform the analysis significantly exceeds the requirement for such a study, which was estimated at 65 bi-variate measurements. We tripled that number. We did not consider the use of bootstrapping because the adopted procedure was statistically valid and sufficient.

Q5: Page 8: "The z-scores calculated based on the LVM normative data obtained according to the allometrically adjusted ratio methods were compared to those calculated based on the L, M, and S values from the LMS method [19]. This allowed us to evaluate the reproducibility of the allometric methods and to assess their sensitivity and specificity compared to the LMS method". Why not also use a Bland and Altman analysis for repeated samples? Do the differences between methods remain the same for any level of body-height (proportional errors)? It would be important to include this (very simple) analysis, which although it has limitations, is widely used to analyze the agreement between tools. Please add it.

We did not use the Bland-Altman plot because it has a critical limitation when the measurement’s range is from negative values, through zero, to positive values, and the outer tails of the data distributions that are compared are divergent; this is the case with our data.

Please see Figure 1 below. It shows scatterplot of the LMS z-scores (blue) and specific allometric z-scores (red) against height. Estimated quadratic curves are superimposed to illustrate the issue (note: they are not significant.). The curves are divergent on the outer ends. This means that the differences between the z-scores are greater there. Both, the LMS z-scores and the allometric z-scores contribute to the divergence because, for both, extreme data points have a big impact on the outer tails of the distribution.

Figure 1. (figure available in "Response to Reviewers" file attached to the re-submission)

When this situation occurs, the distribution of the differences is not normal (Figure 2). The Bland-Altman analysis requires normal distribution. The measurement variables themselves need not be normally distributed, but their differences should be.

Figure 2. (figure available in "Response to Reviewers" file attached to the re-submission)

According to the general idea of Bland-Altman analysis, if the assumption of a normal distribution is not met, data may be logarithmically transformed. In the presented case, they cannot. This is because the z-scores are positive and negative. Besides, an analysis directed to a search for the proportional error is not practicable. The Bland-Altman plot shows a biphasic configuration of data points and even a parabolic shape. The range of the measurement also limits ratio calculation; there is a risk of dividing by 0. The ratios estimated for z-scores close to 0 might be immense, and may highly influence the calculation, causing misinterpretation of the result.

Please see Figure 3, based on our data, illustrating the problem. Onto the classic Bland-Altman plot prepared for boys (the differences in green), the specific allometric z-scores (red) and the LMS z-scores (blue) have been imposed.

Figure 3. (figure available in "Response to Reviewers" file attached to the re-submission)

The mean difference is 0.0013. The upper and lower limits of agreement are 0.2785 and -0.2759, respectively (densely dashed lines). However, there is a specific, parabolic arrangement of the points with a clear upper border. The differences increase (in absolute value), going down both to the right and to the left of 0, but one cannot work with ratios to assess whether the differences increase proportionally to the magnitude of the measurement. This is because the numbers near 0 give abnormal results and there is a risk of dividing by 0. The slope of the line fitted to the raw data is 0 (solid line).

The results of the agreement analysis performed in our study, using the concordance correlation coefficient, show that the bias correction factors are equal to 1. Scale shifts and location shifts are minimal. There is no systemic and proportional bias.

We added the information about the Bland-Altman method to the Study Limitations: “The Bland-Altman method is the most commonly used method to measure agreement [35] and a question may arise why we did not use this method. The Bland-Altman plot is not suitable for our data; the plot has a limitation when the outer tails of the compared data distributions are divergent. In our data, the extreme data points of both the LMS z-scores and the allometric z-scores contribute to such divergence. As a result, the differences between the z-scores are greater on the outer ends. When this situation occurs, the distribution of the differences is not normal. The Bland-Altman analysis requires normal distribution; the measurement variables need not be normally distributed, yet their differences should be. An additional limitation is the measurement range, from negative, through zero, to positive. According to the general idea of Bland-Altman analysis, if the assumption of normality is not met, data may be logarithmically transformed. In the presented case, they cannot, because the z-scores are positive and negative. Besides, an analysis directed to a search for the proportional bias is not practicable. The Bland-Altman plot shows a biphasic configuration of data points and even a parabolic shape. The range of the measurement also limits ratio calculation: there is a risk of dividing by 0. The ratios estimated for z-scores close to 0 might be immense, and may highly influence the calculation, causing misinterpretation of the results.”

Q6: Page 9: "For this analysis, the subjects in the Test Groups were classified as having LVH when their z-score>1.65". Add reference

Sensitivity and specificity analysis is a test exercise in this study, and the cut-off to define LVH can be arbitrary. However, the z-score of 1.65, which is equivalent to the 95th percentile, has been widely used. As a reference, we will add the original article from 2008 by Bethany Foster et al., in which the authors discuss this issue extensively.

Q7: Results (page 10): The authors mentioned in the methodology: " This was a retrospective study based on data derived during periodic medical evaluation of child and adolescent athletes". Table 1. Please include more information on the subjects, in order to know to what extent their values are within "normality" (healthy expeted values). Information on the clinical and / or hemodynamic characteristics (blood pressure, heart rate, other echocardiographic data) of the subjects should be included. In addition, please include the minimum, median and maximum value of each variable. It is important to know the levels of the variables for which the study results are applicable.

Of course, we will provide additional data. The minimum, median and maximum value of each variable will be presented in Table 1 instead of mean and standard deviation. However, we want to emphasize again that the aim of our study is not a presentation of LVM normative data for a specific group of children and adolescents.

Q8: Results: The authors mentioned in the methodology: "The athletes in whom echocardiography revealed significant acquired or congenital heart diseases, affecting normal heart size and hemodynamics, were not included in the study". It would be interesting to know the results of a similar analysis performed in this subgroup of children and adolescents. You can do it? In this way it could be known to what extent the methods have similarity in these special cases.

We absolutely agree that it would be interesting. However, the vast majority of the youth athletes examined in our Center are healthy girls and boys. The number of excluded athletes is too small to perform such analysis.

Q9: Results: "The Pearson correlation coefficients and the slopes of the linear regression lines of the relationships between the calculated LVM z-scores and heights are also presented in Table 2". Please, can you show these graphics?

Yes; as mentioned, we will attach the graphs to the supplementary data (Figure S1).

Q10: Results: Table 5 and Table S2. Only 10 cases (in 200) were "positive" for LVH. Do you consider this "n" appropriate for a sensitivity and specificity analysis? Can you report confidence intervals? Can you present this analysis for "the whole group" (for separate and non-separated sexes).

Thank you for this question. It forced us to rethink the approach to analyzing sensitivity and specificity in terms of sample size. For expected high sensitivity and specificity, assuming a margin of error of 0.05, and considering the prevalence of LVH, the estimated sample size is about 760. Thus, we will analyze the entire group of 791 children and adolescents and introduce this change to the article. According to your request, we present tables with analysis for the whole group and for the separate sex-specific groups (below).

The whole group heightb height2.7

Sample size 791 791

Number of true positives 31 30

Number of true negatives 751 751

Number of false positives 9 9

Number of false negatives 0 1

Sensitivity 100.00% 96.77%

95% Confidence Interval for Sensitivity 88.78% - 100.00% 83.30% - 99.92%

Specificity 98.82% 98.82 %

95% Confidence Interval for Specificity 97.76% - 99.46% 97.76% - 99.46%

Girls heightb height2.7

Sample size 327 327

Number of true positives 16 15

Number of true negatives 311 311

Number of false positives 0 0

Number of false negatives 0 1

Sensitivity 100% 93.75%

95% Confidence Interval for Sensitivity 79.41% - 100.00% 69.77% - 99.84%

Specificity 100% 100%

95% Confidence Interval for Specificity 98.82% - 100.00% 98.82% - 100.00%

Boys heightb height2.7

Sample size 464 464

Number of true positives 15 15

Number of true negatives 440 440

Number of false positives 9 9

Number of false negatives 0 0

Sensitivity 100% 100%

95% Confidence Interval for Sensitivity 78.20% - 100.00% 78.20% - 100.00%

Specificity 98.00% 98.00%

95% Confidence Interval for Specificity 96.23% - 99.08% 96.23% - 99.08%

Q11: Discussion (page 16): "It seems that there is not much difference between allometric normalization using a specific allometric exponent as compared to the universal allometric exponent. However, the exact numbers are slightly better for the specific exponents, and analysis of sensitivity and specificity also indicates the allometric normalization with the especific allometric exponents as the preferred method". An important question that arises is: Are children studied similar (in terms of LVM and body height) to children from other places. Could the authors perform an analysis and / or discuss this aspect? It is important for the purpose of understanding how generalizable the results are. Please consider comparing yourself to a population of different latitudes. An example may be the following article:

• Díaz A et al. Reference Intervals and Percentile Curves of Echocardiographic Left Ventricular Mass, Relative Wall Thickness and Ejection Fraction in Healthy Children and Adolescents. Pediatr Cardiol. 2019 Feb;40(2):283-301.

Are the children studied similar (in terms of LVM and height) to children from other places? To answer this question reliably we have to say no. Since anthropometric indices of children and adolescents depend on the economic and living conditions of a population, there are differences in height even between neighboring countries, with similar genetic backgrounds. The Dutch are the tallest in the world. Germans are slightly taller than Poles although, during a certain period of development, German boys are shorter than their Polish counterparts.

(Kułaga, Z., Litwin, M., Tkaczyk, M. et al. Polish 2010 growth references for school-aged children and adolescents. Eur J Pediatr (2011) 170: 599. https://doi.org/10.1007/s00431-010-1329-x)

To our knowledge, no study has compared absolute LVM in children from different countries. However, it is proven that malnutrition affects LVM.

(Di Gioia G, Creta A, Fittipaldi M, Giorgino R, Quintarelli F, Satriano U, et al. (2016) Effects of Malnutrition on Left Ventricular Mass in a North-Malagasy Children Population. PLoS ONE 11(5): e0154523. https://doi.org/10.1371/journal.pone.0154523).

What does the specificity of the group mean in the case of our study? The studied children were engaged in regular athletic training. Athletes are our group of interest. Regular exercise causes physiological changes to the heart, including hypertrophy. Therefore, a proper LVM assessment and differentiation of physiological LVH from pathological is important. An essential part of this assessment is reliable normalization of LVM for body size. It is particularly important in children and adolescents due to the large variability of body size in children of similar age.

In our opinion, the group of child and adolescent athletes used in this study is representative of the population of the region. Potential differences in absolute LVM values compared to other regions with a similar economic situation are eliminated after normalization for body size.

In addition, we emphasize that it was not the aim of the present study to introduce LVM normative data for child and adolescent athletes. In previous studies, we presented normative data for child and adolescent athletes and compared them to that presented by others:

Krysztofiak H, Małek ŁA, Młyńczak M, Folga A, Braksator W (2018) Comparison of echocardiographic linear dimensions for male and female child and adolescent athletes with published pediatric normative data. PLoS ONE 13(10): e0205459. https://doi.org/10.1371/journal.pone.0205459

Krysztofiak H, Młyńczak M, Folga A, Braksator W, Małek ŁA. Normal Values for Left Ventricular Mass in Relation to Lean Body Mass in Child and Adolescent Athletes. Pediatr Cardiol (2019) 40: 204. https://doi.org/10.1007/s00246-018-1982-9

The aim of the study was just to verify whether it is necessary to use the sophisticated methodology to develop normative data for LVM. The key question in this study was: should we strive to replace the allometrically adjusted ratio method of LVM normalization with the more sophisticated method of centile curves in clinical practice? In the context of this question, the specificity of the group chosen for analysis does not affect the results. We are convinced that these results are universal and should be considered in clinical practice.

As for the suggestion to compare our group with a population of different latitudes, for example, that studied by Diaz A et al (2019) - since our child and adolescent subjects are athletes, such comparison with the general population has limited rationale. However, we have found the recommended study relevant and will refer to it. It supports our idea of developing sex-specific rather than universal LVM normative data.

Q12: Discussion: An interesting aspect would be to know to what extent the differences (although apparently not significant) between methods, could be explained by other co-factors (e.g. sex, body weight, blood pressure). I understand that it is not the objective of the work, but it could be enriched if the association between the differences in absolute levels and / or z-scores between methods, and the demographic, anthropometric and / or clinical variables of young people were analyzed.

In general, we analyzed the agreement between two diagnostic methods. However, our methods differ from laboratory tests or medical equipment because they are based on the mathematical transformation of the same set of numbers - mathematical analysis of the same bivariate relationship. The final result, a z-score, is computed twice using different equations, but the initial value being transformed, absolute LVM, is the same. Co-factors influence the absolute LVM; they do not impact the equations the mathematical transformations.

There is no significant difference between the computed z-scores. If there was a difference, it would be related not to co-factors, but to an error in the mathematical proceeding. It would be considered then as an error of the method. When trying to analyze the influence of the co-factors on the LVM, we analyze their impact on the absolute value of LVM, even if we test z-scores.

Simply put, co-factors like sex, body weight, and blood pressure affect the cardiac size that can be measured as linear dimensions in echocardiography. From the linear dimensions of the left ventricle, the LVM is calculated - this is the absolute value of LVM. At this point mathematical transformation starts that produces z-scores. In this study, we used three different mathematical transformations to produce z-scores. Co-factors do not impact the mathematical transformation.

This study used the same sample as a previous work, where we thoroughly discussed the effect of body weight on LVM:

Krysztofiak H, Młyńczak M, Małek ŁA, Folga A, Braksator W (2019) Left ventricular mass is underestimated in overweight children because of incorrect body size variable chosen for normalization. PLoS ONE 14(5): e0217637. https://doi.org/10.1371/journal.pone.0217637

As for differences in LVM related to sex, it is a very interesting topic. We will study this in upcoming research.

Reviewer #3: The paper addresses a topic of actual relevance and contributes to answer current questions. The work is clearly written. The methodological approach is adequately explained. There are some issues, mostly methodological that should be considered and/or addressed.

Q13: - Data about characteristics of the studied population is scarce (e.g. information about hemodynamic conditions, cardiovascular risk factors prevalence was not given). What kind of exercise did the subjects practice?

We will provide additional data including information about the volume of physical activity. All of the studied children were engaged in regular athletic training at the local or national level (mainly soccer, track and field, basketball, swimming, and martial arts).

Regarding cardiovascular risk factors, there is no such information because the subjects were healthy children and adolescents without cardiovascular risk factors like hyperlipidemia, diabetes, hypertension, etc. The only potential risk factor that is present in this group, in low prevalence, is overweight or obesity.

In the context of the comments and queries, it seems important to note that the aim of our study is not a presentation of LVM normative data for a specific group of children and adolescents. It is a continuation of our previous work on improvement of the methodology of LVM scaling. In this study, we wanted to test if there is a significant superiority of the advanced methods (centile curves) over the practical approaches to the LVM scaling.

Q14: - Why only data from 200 subjects were considered for the comparative analysis?

For analysis of the agreement between tools or methods, the observations should be collected consecutively or randomly. The LVM z-scores in the Study Group do not meet this requirement. If LVM z-scores in the Study Group had been calculated on the normative data developed based on the same group, the s-score variables thus computed would have had a mean very close to 0, and a standard deviation very close to 1. Such a sample should be considered distorted.

In the Study Limitations, we admitted that there is a lack of a distinct group for the assessment of the agreement, and this would be the best option. Therefore, we decided to randomly select observations from the Study Group to develop a sample for analysis of the reproducibility.

The sample size necessary to perform the analysis significantly exceeds the requirement for such a study, which was estimated at 65 bivariate measurements. We tripled that number.

Q15: - Why did the authors choose to compare the approaches using t-tests? Why tools like Bland and Altman tests were not used to assess the agreement between methods? Did the differences between the methods show dependence on the height level (proportional errors)?

The t-test used was a preliminary analysis. If the differences had been significant, this would have meant that no further study is needed. We would conclude that there is no agreement between the methods.

We did not use the Bland-Altman plot because it has a critical limitation when the measurement’s range is from negative values, through zero, to positive values, and the outer tails of the data distributions that are compared are divergent; this is the case with our data.

Please see Figure 1 below. It shows scatterplot of the LMS z-scores (blue) and specific allometric z-scores (red) against height. Estimated quadratic curves are superimposed, to illustrate the issue (note: they are not significant.). The curves are divergent on the outer ends. This means that the differences between the z-scores are greater there. Both, the LMS z-scores and the allometric z-scores contribute to the divergence because, for both, extreme data points have a big impact on the outer tails of the distribution.

Figure 1. (figure available in "Response to Reviewers" file attached to the re-submission)

When this situation occurs, the distribution of the differences is not normal (Figure 2). The Bland-Altman analysis requires normal distribution. The measurement variables themselves need not be normally distributed, but their differences should be.

Figure 2. (figure available in "Response to Reviewers" file attached to the re-submission)

According to the general idea of Bland-Altman analysis, if the assumption of a normal distribution is not met, data may be logarithmically transformed. In the presented case, they cannot. This is because the z-scores are positive and negative. Besides, an analysis directed to a search for the proportional error is not practicable. The Bland-Altman plot shows a biphasic configuration of data points and even a parabolic shape. The range of the measurement also limits ratio calculation; there is a risk of dividing by 0. The ratios estimated for z-scores close to 0 might be immense, and may highly influence the calculation, causing misinterpretation of the result.

Please see Figure 3, based on our data, illustrating the problem. Onto the classic Bland-Altman plot prepared for boys (the differences in green), the specific allometric z-scores (red) and the LMS z-scores (blue) have been imposed.

Figure 3. (figure available in "Response to Reviewers" file attached to the re-submission)

The mean difference is 0.0013. The upper and lower limits of agreement are 0.2785 and -0.2759, respectively (densely dashed lines). However, there is a specific, parabolic arrangement of the points with a clear upper border. The differences increase (in absolute value), going down both to the right and to the left of 0, but one cannot work with ratios to assess whether the differences increase proportionally to the magnitude of the measurement. This is because the numbers near 0 give abnormal results and there is a risk of dividing by 0. The slope of the line fitted to the raw data is 0 (solid line).

The results of the agreement analysis performed in our study, using the concordance correlation coefficient, show that the bias correction factors are equal to 1. Scale shifts and location shifts are minimal. There is no systemic and proportional bias.

We added the information about the Bland-Altman method to the Study Limitations: “The Bland-Altman method is the most commonly used method to measure agreement [35] and a question may arise why we did not use this method. The Bland-Altman plot is not suitable for our data; the plot has a limitation when the outer tails of the compared data distributions are divergent. In our data, the extreme data points of both the LMS z-scores and the allometric z-scores contribute to such divergence. As a result, the differences between the z-scores are greater on the outer ends. When this situation occurs, the distribution of the differences is not normal. The Bland-Altman analysis requires normal distribution; the measurement variables need not be normally distributed, yet their differences should be. An additional limitation is the measurement range, from negative, through zero, to positive. According to the general idea of Bland-Altman analysis, if the assumption of normality is not met, data may be logarithmically transformed. In the presented case, they cannot, because the z-scores are positive and negative. Besides, an analysis directed to a search for the proportional bias is not practicable. The Bland-Altman plot shows a biphasic configuration of data points and even a parabolic shape. The range of the measurement also limits ratio calculation: there is a risk of dividing by 0. The ratios estimated for z-scores close to 0 might be immense, and may highly influence the calculation, causing misinterpretation of the results.”

Q16: - This reviewer considers that it would be of value to analyze the equivalence between the allometric methods themselves and to compare their concordance with the reference methods. The authors state that there would be differences between allometric methods, with the specific allometric exponents as the preferred method. This issue and its significance in clinical practice should be accurately analyzed and discussed.

As stated in the submitted article, it was not the aim of our study to question the exponent of 2.7, so we did not make a direct comparison between this variant and specific variants. However, since our study group consisted of child and adolescents athletes, we were interested in whether the application of specific allometric exponents would improve the performance of the allometric method when testing against the centile curves method of LVM normalization. Parallel analysis with two variants of the allometric method, with the universal exponent and with exponents specific to young athletes, has let us estimate the performance of both variants.

We did not state that there is a difference between allometric methods. We wrote that the specific variant seems to work better, but that the universal variant is almost equally effective. Although the exact estimates of reproducibility indicate slightly better agreement in the case of the specific allometric exponents, the graphs and the concordance coefficients reflect high precision and accuracy, with minimum location shift and scale shift, for both the allometric variants.

However, because of better sensitivity in our study, we have stated that the analysis of sensitivity and specificity indicates the allometric normalization with the specific allometric exponents as the preferred method. In the discussion, we noted that the universal exponent of 2.7 has been questioned by others. As a major drawback, researchers point to the presence of a relationship between normalized LVM and height. Therefore, we wrote in the conclusion that it seems that group-specific allometric exponents should be used to avoid constraints related to incomplete elimination of body size information from the normalized LVM, and for better performance in daily clinical practice.

Below is a table with concordance correlation coefficients. The rightmost column shows the results of comparing the allometric methods. The results are predictable because we know the reason why the agreement is so close to perfection, yet not perfect: there is a minimal difference between the allometric exponents.

heightb vs. LMS height2.7 vs. LMS heightb vs. height2.7

Girls

Pearson correlation coefficient 0.9917 (p<0.001) 0.9886 (p<0.001) 0.9974 (p<0.001)

Bias correction factor 1.0000 1.0000 1.0000

Concordance correlation coefficient 0.9917 0.9886 0.9974

Lower one-sided 95% CI 0.9895 0.9857 0.9968

Scale shift 1.0001 1.0031 1.0030

Location shift 0.0043 0.0041 0.0002

Boys

Pearson correlation coefficient 0.9916 (p<0.001) 0.9870 (p<0.001) 0.9974 (p<0.001)

Bias correction factor 1.0000 0.9999 1.0000

Concordance correlation coefficient 0.9916 0.9869 0.9974

Lower one-sided 95% CI 0.9894 0.9834 0.9967

Scale shift 0.9958 0.9954 0.9997

Location shift 0.0067 0.0160 0.0092

Q17: - Information about cofactors was not given. Were they considered? If so, was their impact on the differences methodological approaches similar? How did the authors defined covariates should not be considered in the analysis?

In general, we performed an analysis of the agreement between two diagnostic methods. However, our methods differ from laboratory tests or medical equipment because they are based on mathematical transformation of the same set of numbers - mathematical analysis of the same bivariate relationship. The final result, a z-score, is computed twice using different equations, but the initial value being transformed, absolute LVM, is the same. Co-factors influence the absolute LVM, not the equations or the transformation.

There is no significant difference between the computed z-scores. If there was a difference, it would not be related to co-factors, but to an error in the mathematical process. This would be an error of the method. When we are trying to analyze the influence of the co-factors on the LVM, we assess their impact on the absolute value of LVM, even if we test z-scores.

Simply put, co-factors like sex, body weight, and blood pressure affect the cardiac size that can be measured as linear dimensions in echocardiography. From the linear dimensions of the left ventricle, the LVM is calculated - this is the absolute value of LVM. At this point, mathematical transformation starts that produces z-scores; we used three different mathematical transformations to produce z-scores. Co-factors do not impact the mathematical transformation.

Q18: - How could the characteristics of the practiced sport have an impact on the results obtained and on the possibility of considering them in the usual clinical practice and in other population groups?

The key question in this study was: should we strive to replace the allometrically adjusted ratio method of LVM normalization with the more sophisticated method of centile curves in clinical practice? In the context of this question, the specificity of the group, we chose to analyze does not have an impact on the results. Yet there was a secondary question: does a specific population need a specific allometric exponent to develop normative LVM data with an allometrically adjusted ratio? In our case, the population was represented by a group of young athletes. In this part, the results show some difference, thus, the specificity of the group had an impact on the results.

However, you have posed a deeper question about the characteristics of the practiced sport and its impact on the results. We are convinced that the characteristics of the practiced sports in our group did not affect the general results. The results of the study should be considered in clinical practice. The studied children were engaged in regular athletic training at the local or national level, mainly soccer, track and field, basketball, swimming, and martial arts. At this stage of athletic development, training is primarily focused on the systematic development of motor abilities. The profile of the group reflects the population in the context of a practiced sport. In our opinion, the group of child and adolescent athletes used in this study is representative of the population of the region.

Q19: - The following sentence should be clarified: It must be noted that, because of a lack of a gold standard procedure, any conclusions based on the comparisons between different methods are limited.

In our study, we regarded the LMS method as a reference, a current standard, the most accurate procedure available. When we use the term 'gold standard test', we mean a method that is able to determine or exclude disease with certainty. In LVM normalization, this certainty is not possible because this is not a direct measurement and many confounding factors impact the result. Therefore, the best standard should be established after careful consideration of as many limiting factors as possible.

The sentence "It must be noted that, because of a lack of a gold standard procedure, any conclusions based on the comparisons between different methods are limited" is used in a paragraph discussing a comparison of different methods of LVM normalization, with different body size scaling variables. We are trying to draw attention to methodological drawbacks when we arbitrarily assume that one of the methods is the most accurate. We are aware that the LMS method also has some limitations (for example, as stated in the WHO document, extreme data points have a big impact on the outer tails of the distribution) and that we should take them into account when formulating conclusions favoring one method, and disqualifying another.

However, we agree that the sentence should be modified for the sake of clarity. We made the following change (quote): " It must be noted that because of the lack of a procedure that is able to determine or exclude LV hypertrophy with certainty, any conclusions based on the comparisons between different methods, favoring one method or disqualifying another, are questionable."

Q20: - The tables design should be improved.

Thank you, we will improve the design of the tables.

Submitted filename: Response to Reviewers.docx

Click here for additional data file.

1 Nov 2019

Left ventricular mass normalization for body size in children based on an allometrically adjusted ratio is as accurate as normalization based on the centile curves method.

PONE-D-19-17289R1

Dear Dr. Hubert Krysztofiak,

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The answers have been correctly argued

This version can be accepted for publication

12 Nov 2019

PONE-D-19-17289R1

Left ventricular mass normalization for body size in children based on an allometrically adjusted ratio is as accurate as normalization based on the centile curves method.

Dear Dr. Krysztofiak:

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