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.
- Attachments
- Attachment
Submitted filename: Response to Reviewers.docx
http://orcid.org/0000-0003-4567-1433
