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A Review and Critique of the Statistical MethodsUsed to Generate Reference Values

in Pediatric Echocardiography

Wadi Mawad, MD, Christian Drolet, MD, BSc, Nagib Dahdah, MD, and Frederic Dallaire, MD, PhD,

Quebec, Montreal, and Sherbrooke, Quebec, Canada

Several articles have proposed echocardiographic reference values in normal pediatric subjects, but ade-quate validation is often lacking and has not been reviewed. The aim of this study was to review published ref-erence values in pediatric two-dimensional and M-mode echocardiography with a specific focus on theadequacy of the statistical and mathematical methods used to normalize echocardiographic measurements.

All articles proposing reference values for transthoracic pediatric echocardiography were reviewed. The typesof measurements, the methods of normalization, the regression models used, and the methods used to detectpotential bias in proposed reference values were abstracted. The detection of residual associations, residualheteroscedasticity, and departures from the normal distribution theory predictions were specifically analyzed.

Fifty-two studies met the inclusion criteria. Most authors (87%) used parametric normalization to account forbody size, but their approaches were very heterogeneous. Linear regression and indexing were the most com-mon models. Heteroscedasticity was often present but was mentioned in only 27% of studies. The absence ofresidual heteroscedasticity and residual associations between the normalized measurements and the inde-pendent variables were mentioned in only 9% and 22% of the studies, respectively. Only 14% of studies docu-mented that thedistribution of theresidual values was appropriate forZscore calculation or that the proportionof subjects falling outside the reference range was appropriate. Statistical suitability of the proposed referenceranges wasoften incompletely documented. This review underlines thegreat need for better standardization inechocardiographic measurement normalization. (J Am Soc Echocardiogr 2013;26:29-37.)

Keywords: Echocardiography, Reference values, Pediatric, Normalization, Zscores

Echocardiography is a reliable, noninvasive tool to evaluate heartstructure and function in children and adults. Many important clinical

decisions are routinely based on the absolute sizes of cardiac struc-

tures.1 Evaluation is highly dependent on the quality of the measure-

ments but also on the quality of the reference values with which

these measurements are compared. The American Society of

Echocardiography Pediatric and Congenital Heart Disease Council re-

cently published recommendations for quantification methods during

the performance of pediatric echocardiography.2 However, reference

values for the proposed methods often lack adequate validation.

Unbiased reference values require appropriate normal subjects,

standardized reproducible measurements, and appropriate sample

sizes.3 In children, reference values are also highly dependent on

accurate adjustment for body size.1 Although nonparametric ap-proaches have sometimes been used, parametric methods, such as

Z scores, are now becoming the standard for body size adjustment

in pediatric echocardiography.2,4,5 However, parametric methods

rely on an appropriate distribution of the data, on the absence of

residual associations, and on constant variance of the normalized

measurements throughout the entire sample. These important

requirements have not always received the attention they deserve.

A recent review by Cantinotti et al.6 underlined several limitations

of the available reference values in pediatric echocardiography, in-

cluding a lack of standardization in data acquisition, a limited number

of healthy subjects, and heterogeneous methods of normalizing and

reporting reference values. However, their review did not specifically

address the statistical methods used or the potential pitfalls of para-metric normalization. In this article, we present a systematic review

of available reference values in two-dimensional (2D) and M-mode

echocardiography in infants, children, and adolescents with a focus

on thestatistical validity of themethods usedto generate theproposed

reference ranges. For each reviewed article, we analyzed how the ref-

erence values were estimated, what type of normalization was used,

and how the authors documented the detection of potential bias.

METHODS

Literature Search Strategy

A search of the National Library of Medicines PubMed database

was performed using the Medical Subject Headings controlled

From the Division of Pediatric and Congenital Cardiology, Department of

Pediatrics, Laval University Hospital, Faculty of Medicine, Laval University,

Quebec City, Quebec, Canada (W.M., C.D., F.D.); the Division of Pediatric

Cardiology, Sainte-Justine University Hospital, University of Montreal, Montreal,

Quebec, Canada (N.D.); and the Division of Pediatric Cardiology, University

Hospital of Sherbrooke, University of Sherbrooke, Sherbrooke, Quebec, Canada

(F.D.).

Reprint requests: Frederic Dallaire, MD, PhD, Division of Pediatric Cardiology, De-

partment of Pediatrics, Faculty of Medicine, University of Sherbrooke, 3001, 12e

Avenue Nord, Sherbrooke, QC J1H 5N4, Canada (E-mail: frederic.a.dallaire@

usherbrooke.ca).

0894-7317/$36.00

Copyright 2013 by the American Society of Echocardiography.

http://dx.doi.org/10.1016/j.echo.2012.09.021

29
mailto:[email protected]:[email protected]://dx.doi.org/10.1016/j.echo.2012.09.021http://dx.doi.org/10.1016/j.echo.2012.09.021mailto:[email protected]:[email protected]


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vocabulary from the National

Library of Medicine. The

search strategy was built to re-

trieve all articles containing

the Medical Subject Headings

terms echocardiography and

reference values or their equivalents: (reference values OR bi-ometry OR anthropometry OR regression analysis) AND {echo-

cardiography OR [ultrasonography AND (heart OR

cardiovascular system)]}. We limited the search results to articles

whose subjects were


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Table 1 Summary of 2D studies published after 1990

Study n Age Structures

Model and type

of normalization

Was the detection

Testing for

heteroscedasticity

Testing

resid

associa

Lytrivi et al. (2011)28 100 0 to 3 y LVEDV (bullet shape

formulas)

Indexed to BSA1.38 (allometric

model)

No Yes

Dallaire and Dahdah(2011)8

1,033 2 mo to 18 y Coronary arteries Linear with square root of BSA Yes Yes

Gautier et al. (2010)14 353 Mean,12 6 4.5 y

AoV, sinus, STJ,AscAo

Log-log with BSA No No

Olivieri et al. (2009)37 432 0 to 20 y Coronary arteries Log-log model with BSA Yes No

Neilan et al. (2009)33 4,109 1 to 17 y LA Log-log model with BSA or weight Yes YesPettersen et al. (2008)41 782 0 to 18 y 14 structures by 2D

imaging, 7 structuresby M-mode imaging

Third-order polynomial withlog-transformed dependentvariable

Unclear No

Kaldararova et al. (2007)24 702 0 to 20 y AoV, aortic sinus, STJ Nonparametric NA NASuleymanoglu et al.

(2007)50213 0 to 15 y RV volume Nonparametric normalization;

authors report 5th and 95th

percentiles for severalindependent variables

NA NA

Poutanen et al. (2006)43 168 2 to 27 y Mitral and aortic area Linear with BSA (range presentedas 5th and 95th percentiles)

NA No

Zilberman et al. (2005)58 748 0 to 18 y AoV, PV, TV, MV annuli Log-log model with BSA No No

Makan et al. (2005)29 250 controls,900 eliteathletes

14 to 18 y LV dimensions andmass, LA, aortic root

No normalization, mean 6 2SDsaccording to age

No NA

Poutanen et al. (2003)42 168 2 to 27 y AoV, sinus of Valsalva,STJ, aortic arch

Linear with BSA (range presentedas 5th and 95th percentiles)

NA No

Tan et al. (2003)53 390 2 mo to 8 y Coronary arteries Linear (results presented with 5different independent variables

No No

Joyce et al. (2001)22 44 0 to 17 y RV free wall mass Indexed to BSA No No

Tan et al. (2001)52 62 Preterm

infants

AoV, PV, PAs Linear with weight No No

Tacy et al. (1995)51 70 0 to 10 d AoV, PV, MV, TV Linear with weight No No

Sheil et al. (1995)47 48 0 to 23 y LVOT, AoV, sinus of Valsalva, STJ, AscAo

Linear with height and indexedto AoV

No No

Nidorfet al. (1992)34 196 6 d to 18 y AoV, LA, LVEDD, LVlength

Indexed to height No Yes

Domanski et al. (1991)12 10 4 to 12 y LVEDD, LA Indexed to LVOT dimension No YesPearlman et al. (1990)39 196 children,

72 adults6 d to 18 y

(children)LA Power model with BSA Yes No

AoV, Aortic valve; AscAo, ascending aorta; LA, left atrium; LV, left ventricular; LVEDD, left ventricular end-diastolic diameter; LVEDV, left ventriventricular outflow tract; MV, mitral valve; NA, not available; PA, pulmonary artery; PV, pulmonary valve; RV, right ventricular; STJ, sinotubular jun


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Table 2 Summary of M-mode studies published after 1990

Study n Age Structures Type of normalization

Was the detection

Testing for

heteroscedasticity

Test

for res

associ

Nagasawa (2010)31 243 0 to 12 mo LVEDD Linear with height (with 2 inflexionpoints)

No No

Foster et al. (2008)13 440 0 to 21 y LVM Nonparametric. lambda-mu-sigmamethod

NA NA

Bonatto et al. (2006)7 595 1 mo to 12 y 8 structures by M-modeimaging and LVM

Nonparametric (centile curves withBSA)

NA NA

Overbeek et al.(2006)38

747 0 to 18 y Left ventriculardimensions

Log-log model with weight Yes Ye

Kervancioglu et al.(2006)25

229 0 to 15 y Aortic sinus Nonparametric NA NA

Huicho et al (2005)18 321 (subjects

living at highaltitude)

2 mo to 19 y 10 structures Linear with BSA No No

Joyce et al. (2004)23 45 0 to 4 mo Left and r ight ventr icularvolumes, masses, wallthicknesses

No normalization, mean 6 SDaccording to age

NA NA

Skelton et al. (1998)48 79 Newbornsincludingpreterminfants

LV, Ao, LA Nonparametric, mean and SDfor strata of GA and BW

NA NA

Nagasawa et al.(1996)32

437 1 mo to 17 y LVEDD Linear with height No No

Daniels et al. (1995)9 192 6 to 17 y LV Indexed to height3 (allometric model) No Ye

Huwez et al. (1994)19 127 7 mo to 19 y LV, aortic root, LA, RV Linear with age and linear with BSA No NoMalcolm et al. (1993)30 904 6 to 16 y LVM Multiple regression with height, age,

and height

age interaction

No No

de Simone et al.(1992)11

444 4 mo to 23 y LVM Indexed to height2.7 (allometric model) No Ye

Gupta and Jain(1991)15

183 3 to 12 y LV Indexed to height No No

Ao, Aorta; AoV, aortic valve; BW, birth weight; GA, gestational age; LA, left atrium; LV, left ventricle; LVEDD, left ventricular end-diastolic diametavailable; RV, right ventricle.


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parametric normalization tested one regression model only. Of

them, eight articles reported linear regression only, six reported

indexing (including two using allometric indexing), two reported

power or logarithmic models only, and three used multivariate

regression but tested only one model. In the remaining reports,

two or more models were assessed, usually linear, polynomial,

power, and log-log models. Pearsons correlation coefficient (R2

)was often used to assess the goodness of fit of the regressions.

Various mathematical transformations of both the dependent and

the independent variables were commonly used to deal with the

nonlinearity of most echocardiographic measurements with growth

parameters. Logarithmic transformation of either the dependent or

the independent variable, or both, was the most common strategy

to adjust for nonlinearity, followed by the square and cube roots

of the independent variable.

Unequal Variance and Heteroscedasticity

Heteroscedasticity is defined as the inconstant variance of the

dependent variable across the entire range of the independent

variable. In parametric normalization, one uses the magnitude ofdispersion around the mean to establish reference ranges. Such

ranges are thus dependent on any variation of that dispersion.

Heteroscedasticity was mentioned in the text of 12 of the 45 studies

in which some form of parametric normalization was done.

However, there were four studies in which heterogeneous variance

seemed to have been taken into account, although we could not

find any mention of it in the text. The most common methods to

account for increasing variance were logarithmic transformation of

the dependent variables (seven studies) and weighted regression

models (seven studies).

Types of Reference Values

The reference values proposed by the selected studies were ex-

pressed in a variety of ways.Zscore equations were suggested in eight

studies. The remaining studies proposed graphs (14 studies), tables

(two studies), equations to derive the upper and lower ranges of nor-

mal (12 studies), indexes (10 studies), means and standard deviations

(four studies), or other methods (two studies).

Evaluation of Bias

Only 14 studies using parametric normalization mentioned any type

of further evaluation of the proposed reference values. The authors of

10 studies assessed if residual associations between the normalized

measurements and the chosen independent variables were still pres-

ent. The authors of six studies stated that the distribution of the de-pendent variable was appropriate for Z score calculation or that the

proportion of subjects falling outside the reference range was appro-

priate. Testing for absence of residual heteroscedasticity was men-

tioned in only four studies. Finally, intraobserver and interobserver

variability was evaluated in 13 and 19 studies, respectively.

DISCUSSION

In pediatric and congenital cardiology, many clinical, interventional,

and surgical decisions are based on the sizes of cardiac structures.

Moreover, follow-upof children with repaired andunrepaired cardiac

defects often depends on the identification of structural growth that

deviates from expected. The development of reliable and validated

reference values in transthoracic echocardiography is thus of great im-

portance, because a biased or inaccurate cardiac growth curve could

lead to inappropriate clinical and surgical management.

In this review, we identified multiple articles recommending refer-

ence ranges for most cardiac structures. However, information on the

detection of potential biases was absent from more than half of them,

and few authors seemed to have gone beyond the goodness of fit oftheir regressions to assess the quality and validity of the reference

ranges they proposed.8,11,13,33,38,40,59 Furthermore, although most

cardiac structures displayed clear nonlinearity with weight, height,

BSA, or age, many authors put forward simple linear models or

indexes.

Nonparametric methods do not assume that the response variable

adopts a given distribution and are therefore less prone to bias.

However, because echocardiographic reference ranges change as

the body grows, if one wants to define precise reference ranges across

growth using nonparametric methods, one must compute percentiles

for several growth strata of the studied population. Because each stra-

tum must include a sufficient number of subjects to estimate reliable

percentiles,60 and because of the large number of strata needed to

generate precise percentile curves from birth to early adulthood, non-

parametric methods are rarely used in pediatric echocardiography.

Bonatto et al.7 used this approach, and although their study included

almost 600subjects, some strata had only 20 subjects to compute ref-

erence ranges. Consequently, most of the reviewed studies relied on

parametric normalization to define reference ranges.

In parametric normalization, one uses the known distribution pa-

rameters of a population to estimate reference values according to

one or more independent growth variables. The response variable

is modeled mathematically on the independent variable, and the

results of that regression yield the predicted mean of the response

variable according to the independent variable. Several regression

approaches exist. It has been advocated that the choice of a regres-

sion model should be in accordance with whatis expected physiolog-ically.61 For example, Sluysmans and Colan59 estimated the optimal

vessel dimensions that would minimize flow-mediated energy loss

and then showed that cardiac structure size predictions were in

agreement with their theoretical model. Whereas a regression ap-

proach that is in accordance to what is predicted by physiologic

principles is likely to be superior to an empirical model, several steps

are needed to ensure that no important biases were introduced by

the modeling of the response variable, regardless of the regression

approach used.

First, the regression model should be chosen so that the fit is

adequate across the entire population. A significant lack of fit could

result in a predicted mean value higher or lower than the true

mean for certain strata of the population. Figure 1 provides anexample of two different models from a sample of sinus of Valsalva

diameters in children (see the legend for details on the method). In

Figure 1A, a poorly fitted linear model for sinus of Valsalva diameter

against BSA is shown. Figure 1B shows a visually more adequate fit

using a gamma function model (Y = aBSAbexp[lBSA]) proposed

by Nevill et al.61 The quality of the fit should be evaluated statistically

but should also be carefully inspected visually using plots of the de-

pendent on the independent variables and plots of the residual values

(or Z scores) on the independent variable. Adequate fit should result

in no significant residual associations between the residual values and

the independent variable. Figure 2 shows the Z scores according to

BSA for the two models from Figure 1. Note the strong residual asso-

ciation in Figure 2A (red curve) and the absence of a residual associ-

ation in Figure 2B. The current review identified only 12 studies that

Journal of the American Society of Echocardiography

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Mawad et al 33


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documented assessment of the residual association. It should be

noted that having a good R2 value does not rule out residual

association. In our example, the linear model had an R2 value of

0.80, which could be considered adequate, although visually it was

obviously poorly fitted.

Second, the distribution of the residual values should be inspected.

WhenZscores are computed, or when the standard deviation is used

to estimate percentiles, residual values must be normally distributed.Importantly, they must be so across the entire range of the indepen-

dent variable. To better detect departure from the normal distribution,

it was previously suggested that the residual values should be divided

into at least three equal groups according to the independent vari-

able.62 The distribution of each of these groups should then be as-

sessed. Any departure from the normal distribution in any stratum

of the population studied could lead to biased reference values.

Moreover, when Z scores are computed, each stratum must adopt

a normal distribution with a mean of 0 and a standard deviation of

1. In Figure 2A, small children in the first tertile of BSA had Z scores

with a distribution close to normal, but the mean was significantly

smaller than zero, which indicates a high likelihood ofZ score under-

estimation. This review identified only four studies documenting as-sessment of response variable distribution.

Third, heteroscedasticity should be assessed, and when it is pres-

ent, a model taking it into account should be used. In the example

from Figure 1, clear heteroscedasticity was present. A weighted

model was used only in Figure 1B, and the reader can appreciate

that the distance between the Z = 2 and Z = 2 limits increases

with B SA (represented by the blue lines). Adequate heteroscedastic-

ity management should result in no significant residual heterosce-

dasticity, which should also be verified thoroughly. Although no

consensus exists on how to detect residual heteroscedasticity, the

presence of a statistically significant slope between the absolute

residual values and the dependent variable and a statistical test

aimed at the detection of heteroscedasticity (the White test or the

Breusch-Pagan test) yielding a low P value both indicate that resid-

ual heteroscedasticity is likely present. Residual heteroscedasticity

could lead to underestimated or overestimated variance for some

strata of the population, which in turn could bias the reference

values or Z scores. Clear residual heteroscedasticity was present

in Figure 2A. Although the authors of nearly half of the studies

recognized and corrected for unequal variance, only four studies

documented assessment of residual heteroscedasticity.

Logarithmic transformation of the dependent variable was usedby many authors to adjust for nonlinearity and heteroscedasticity.

When logarithmic transformation of the dependent variable is

used, the assumption is usually that the dependent variable has

a log-normal distribution so that the regression of the log-

transformed value will produce residual values with a normal distri-

bution.63 It should also be noted that logarithmic transformation may

mask potentially strong outliers.63 Although logarithmic transforma-

tion was used by the authors of 13 studies, assessment of adequate

distribution of the residual values was noted in only two studies.

Our previous observations led to the conclusion that many echocar-

diographic measurements were normally distributed at any given

stratum of growth, and when logarithmic transformation was used,

parametric normalization failed to produce normally distributed re-sidual values, which could introduce bias (unpublished results and

Dallaire and Dahdah8).

Finally, whatever the method used to estimate reference values

with parametric methods on the basis of the normal distribution,

one should always ensure that the proportion of individuals falling

outside the reference range does not deviate from what is predicted

by the normal distribution theory. For example, in a normal popula-

tion, 2.28% of the population will have Z scores $ 2.0. A significant

difference between the predicted and observed proportions (i.e., Z

score > 2 in >2.28% of the subjects) in any stratum of the population

studied is a strong indicator that bias is present. Such verification was

described in very few of the reviewed studies. In our example, the

proportion of small patients falling below Z = 2 in the linear model

(Figure 2A) was 9.7%, well above the predicted 2.28%.

Figure 1 Sinus of Valsalva diameter according to BSA. The dashed curves represent the predicted mean and the solid curves theZ= +2 and Z = 2 limits. (A) Linear model. The predicted mean is poorly fitted, especially for smaller patients. The parallel Z scoreboundaries do not capture the clear heteroscedasticity. (B) Gamma function weighted model. The predicted mean displays a more

adequate fit, and the weighted model allowsZscore limits to follow the increasing variance with body surface area. The sinus of Val-salva diameters were extracted from the Sainte-Justine University Hospital database (Montreal, QC, Canada). Studies were per-formed on children ranging from 1 day to 17 years of age who were referred for murmurs, syncope, or chest pain from May 2001to May 2003. Patients above or below 2 standard deviations from the mean body mass index for age were excluded.

34 Mawad et al Journal of the American Society of EchocardiographyJanuary 2013


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In its recent recommendations, the American Society of

Echocardiography advocated that when parametric normalization is

done, reference values should be expressed as Z scores.2 Z scores

are superior to dichotomous normal values because they allow cli-

nicians to appreciate the magnitude of abnormality. Z score esti-

mates are now part of the daily decision making in clinical and

surgical management in pediatric cardiology.64,65 When adequately

validated Z score equations are available, their inclusion in simple

computer software renders the interpretation of cardiac structure

size and growth simple and intuitive. An ascending aorta with a Z

score diameter increasing from 1.8 to +1.8, although within the

normal range, is not following its expected normal growth curve.

This can be easily appreciated by a clinician without having to referto cumbersome normal value tables. Furthermore, although the Z

score is used to estimate percentiles, extreme Z scores are easier to

interpret than percentiles; for example, a Z score of 3 corresponds

to the 99.865th percentile, while a Z score of 4 corresponds to the

99.997th percentile.

Nine studies proposed indexes as a way to normalize measure-

ments. Likely because of their simplicity, indexes have often been

used to normalize echocardiographic and hemodynamic measure-

ments. This simplicity comes at a significant cost. Indexes are prone

to the same biases as any other parametric normalization. To be

valid, they also need to meet very stringent criteria: perfect linear

correlation, a zero intercept, and absence of heteroscedasticity.

These criteria are almost never present in pediatric echocardio-graphic measurements, and previous studies have repeatedly shown

that simple linear indexing introduces bias.8,13,33,66 In our opinion,

such a method for normalization in pediatric echocardiography

should be abandoned.

In structurally normal hearts, the sizes of cardiac structures are

a function of the cardiac output. The linear relationship between

BSA and cardiac output has been widely recognized and has led

many authors to use BSA to normalize echocardiographic measure-

ments.67 Surprisingly, the vast majority used the formula of Du Bois

and Du Bois68 to estimate BSA, although it has been shown to under-

estimate BSA in young children.69,70 None of the available equations

for calculating BSA are perfect, and it is likely that the sizes of cardiac

structures are a function of both weight and height and that each of

them affects cardiac output in different proportions as children

develop and grow. Indeed, it has previously been shown that the

relationship between cardiac output and growth parameters

changes as children grow.71 Several articles reviewed in this study

showed relatively linear relationships between cardiac structure sizes

and various transformations of BSA. However, because BSA does not

capture differences in body composition (fat/muscle proportion), it

remains an imperfect surrogate of cardiac output. Normalization

across a wide range of body sizes has many practical benefits, but

more subtle effects in the extremes of the pediatric ages could be

masked by the search of a single model to describe the complex

mechanisms of heart growth. The extremes of the pediatric age range,

particularly newborns and infants, should be studied separately to en-

sure adequately validated reference ranges, especially because manycrucial interventional andsurgical decisions are made very early in life.

Other factors also complicate the anthropometric equations such as

gender, obesity, and physical fitness.

In 2001, Lipshultz et al.72 showed that systematic biases among lab-

oratories existed for some measurements of left ventricular dimen-

sion. Such biases are likely present for other structures as well, and

their magnitudes probably relate to the technical difficulty of the mea-

surement. Systematic error, whether among laboratories or among

observers, will greatly affect reference values. This should be kept in

mind when a laboratory uses reference ranges derived at another

institution. The change in Z score over time for a specific measure-

ment in a given individual will, however, be less affected by systematic

bias. There is a great need for adequately validated multicenter refer-ence values derived from large populations of healthy children.

However, we recommend that validation be performed on local

controls to ensure that a systemic bias does not lead to an underesti-

mation or overestimation of the normalized measurements.

CONCLUSIONS

Choice of population, technical standardization of echocardiographic

measurements, and detailed strategies for model selection were out-

side the scope of this review, as they were recently addressed else-

where.6,59,61 The recent recommendations of the American Society

of Echocardiography on quantification methods in pediatric

echocardiography concluded that standardizing quantification

Figure 2 Relation between Zscores and BSA computed with the models from Figure 1. (A)Zscores computed with the unweightedlinear model. (B)Zscorescomputed with the gamma function weighted model. Dashed curvesrepresent residual association with the

Zscores and BSA. AdequateZscores should be evenly distributed around 0, with 95.4% of the population within the red boundariesfor all BSA strata.


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Mawad et al 35


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methods is the first step in the task of generating a normative database

that encompasses the range of body sizes and ages encountered in the

pediatric population.2 This review underlines that there is also a great

need for a more thorough approach in the detection of bias in para-

metric normalization. Of course, incomplete validation does not nec-

essarily mean that a given set of reference values is biased.However, if

any set of reference values is expected to be used routinely with con-fidence, its authors must provide to readers and clinicians adequate

proof that significant bias is not present.

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