Skew in Echocardiographic Reference Data

some offhand observations about the treatment of skewness in pediatric echo reference data.

Skewness:

1. asymmetry in a frequency distribution.

2. a measure of such asymmetry.

Underlying the use of z-scores is an assumption about the symmetric nature of the distribution: the use of "Z" is because the normal distribution is also known as the "Z distribution". However, as noted elsewhere[1, 2], cardiac growth data are skewed to the right. Here are a few examples that I find remarkable.

Left Atrial Diameter

Neilan et al.[3] examined the nature of the relationship of body size to cardiac structures using the left atrial diameter as measured in over 15,000 normal patients. Their plot of LA diameter against body weight—and the underlying rightward skew—can be examined here: left atrial diameter vs. body weight. Although the chart is presented in the source article with logarithmic axes, "back transforming" the axes into natural units reveals the magnitude and direction of the skew.

Left Ventricular Mass

Using the LMS technique to deliberately account for skew (and non-constant variance), Foster et al.[4] provide the data used to construct the following curves: left ventricular mass vs. height (I used ±1.65 for the upper and lower bounds). Interestingly, while the LMS method handles the skew and variance in a discrete (although smoothed) fashion, applying a log transformation appears to control both phenomenon as well.

Fetal Data

Comparing the recently published[5] fetal echo z-score data with the earlier reference[6] reveals one obvious difference: the Boston data is modeled as having a normal distribution, with no obvious skew. What, I wonder, happens if the underlying data really does have rightward skew, but is modeled as a normal distribution? Hmm...

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References

1. Sluysmans T and Colan SD (2009). Structural Measurements and Adjustment for Growth. In Wyman Lai [et al.] (Eds.), Echocardiography in Pediatric and Congenital Heart Disease: From Fetus to Adult . Oxford: Wiley-Blackwell
2. Abbott RD, Gutgesell HP. Effects of heteroscedasticity and skewness on prediction in regression: modeling growth of the human heart.
3. Neilan TG, Pradhan AD, Weyman AE. Derivation of a size-independent variable for scaling of cardiac dimensions in a normal adult population.
4. Foster BJ, Mackie AS, Mitsnefes M, Ali H, Mamber S, Colan SD. A novel method of expressing left ventricular mass relative to body size in children.
5. McElhinney DB, Marshall AC, Wilkins-Haug LE, Brown DW, Benson CB, Silva V, Marx GR, Mizrahi-Arnaud A, Lock JE, Tworetzky W. Predictors of technical success and postnatal biventricular outcome after in utero aortic valvuloplasty for aortic stenosis with evolving hypoplastic left heart syndrome.
6. Schneider C, McCrindle BW, Carvalho JS, Hornberger LK, McCarthy KP, Daubeney PE. Development of Z-scores for fetal cardiac dimensions from echocardiography.

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More Fetal Echo Reference Values

Seems like I spent most of the month of October thinking about fetal echos in one form or another. Apart from the earlier release of the Fetal Echo Z-Scores: Femur Length calculator, I also developed a couple of "helper" routines:

• A calculator to cross-check the femur length against the EGA derived from dates. Also Gives reference values for fetal thoracic circumference:

  Fetal Biometry

• A remake of the CHOP calculator- useful for describing the hemodynamic status of the recipient twin in twin-twin transfusion syndrome (TTTS). Good stuff for reminding me about the various manners in which heart failure can be categorized by fetal echo:

  CHOP Fetal CV Profile Score

• A calculator for fetal LV/RV/IVS wall thicknesses. In the absence of any published z-score equations, these two sources (one uses autopsy data) seem to be our only recourse:

  Fetal Ventricular Wall Thickness Reference Values

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Additionally, the October 13 issue of Circulation brought a new fetal echo z-score reference:

Predictors of technical success and postnatal biventricular outcome after in utero aortic valvuloplasty for aortic stenosis with evolving hypoplastic left heart syndrome.
McElhinney DB, Marshall AC, Wilkins-Haug LE, Brown DW, Benson CB, Silva V, Marx GR, Mizrahi-Arnaud A, Lock JE, Tworetzky W.
Circulation. 2009
Oct 13;120(15):1482-90. Epub 2009 Sep 28.

• Z-Score equations for fetal mitral valve, left ventricle, aortic valve, ascending aorta, and right ventricle are included. The ParameterZ.com z-score calculator is here:

  Fetal Echo Z-Scores: Boston Data

• The Smackdown, pitting the established equations from London against these 'new' equations, is here:

  Fetal Echo Z-Score Smackdown: Boston vs. Royal Brompton

I won't attempt an analysis beyond the smackdown itself because, as the authors reveal, these new z-score equations are based on

unpublished fetal norms…

Still, it is interesting (to me) to see the data published at all, and I think the smackdown sheds some interesting light on the two groups of equations.

Fetal Echo Z-Score Calculator: Updated

Cardiac valve, chamber, and arch z-scores based on femur length; predicted LMP/EDD/EGA; LV/RV size discrepancy ratios.

This update provides the following functionality:

Fetal cardiac z-scores calculated from femur length

According to the source article, each of the independent variables (EGA, FL, BPD) had similar performance, with the regressions based on femur length being slightly superior. I have not yet compared the z scores across the two calculations- it is likely that minor differences exist between z-scores based on femur length, and those based on the derived EGA.

Femur length estimates of EGA, EDD, and LMP

Since the ICAEL guidelines require reporting of the EGA (and manner of determination), this is estimated according to this common citation: New charts for ultrasound dating of pregnancy. Without getting wrapped up in the subtleties of another field entirely, this reference seemed suitable . From the looks of it though, EGA predictions by femur length alone are open to some criticism.

Size discrepancy ratios

A common referral for fetal echocardiography is the discovery on routine ultrasound of a "size discrepancy" between the left and right ventricles. The authors of this new article Left Ventricle to Right Ventricle Size Discrepancy in the Fetus: The Presence of Critical Congenital Heart Disease Can Be Reliably Predicted suggest the use of easily calculated ratios as a simple manner for stratifying the various underlying lesions. Ratios of 0.6 for each of the sites (MV/TV, LV/RV, AoV/PV) appear to have good predictive value- particularly when used in combination with the transverse arch measurement and descriptions of the flow across the atrial septum.

The topic of z-scores is touched upon briefly with reference to the transverse arch. Although the data presented suggests that the arch z-scores were significantly different between groups (intervention vs. not), no cutoff values for the z-score are suggested. It is interesting (to me) that the stated z-scores in the intervention vs. non groups is –4.7 vs. –3.2 (or, the difference between the 0.0001 percentile and the 0.0687 percentile !!). If one uses the normal boundaries of the 5th and 95th cumulative percentiles (z-scores of ±1.65), or the more liberal 2.3-97.3 percentiles (z scores of ±2), even the non-intervention group seems way out there.

It is also interesting to me that the chamber size and valve z-scores weren't discussed- at all. Many of the referrals for 'size discrepancy' seem more imagined than real, and z-scores of the left heart structures ought to provide evidence of normality, even if things appear discrepant. Along those lines, I am looking forward to the manuscript to follow this abstract: Fetal Cardiac Growth: New Z-Score Ranges From 3,000 Normal Pregnancies.

You can find the updated z-score calculator here:

ParameterZ.com Fetal Echo Z-Score Calculator

Pediatric Echo Z-Score Calculator: Children's Mercy Hospital

Calculate z-scores and normal ranges for 80+ echocardiographic measures including m-mode, 2D, and Doppler; generate z-score graphs.

While browsing, I more-or-less stumbled upon a great website put together by the good folks at Children's Mercy Hospital (Kansas City, MO). The depth and breadth of measurements is astonishing, as is the number of observations from which the reference values are generated.

I understand an article is forthcoming— destined to be the largest and most encompassing work to date on normative values for pediatric echocardiography.

CMH Pediatric Echo Z-Score Calculator

Also worth reading, their newsletter announcement: Creating New Growth Charts

 

Congratulations (and thanks!) to Dr. Drake and his staff for creating an incredible resource and service.

LV Mass Reference Values: Smackdown

I am starting to think I should change the tagline for this blog to:

more questions than answers

I am in the midst of building another smackdown calculator:



I hope that it use is self-explanatory and that it requires no introduction- because I am now out of time (heading out to the ASE meeting!).
This is still a 'work in progress' (I seem to have lots of these). Upon my return from the nation's capitol, I plan to add additional functionality:

• tips on measurement technique
• input validation
• automatically detecting discrepancies between references
• allowing users the opportunity to provide feedback in the cases where there are discrepancies

I think this is going to be very interesting ...