Echo Z-Score Suggested Reading

 

Lots of people have asked me something like:

We are finding discrepancies in Z scores calculated by your method and the Z scores calculated by software provided by Boston...
WHY ?

I usually feel obligated to first set the record straight: these are not my z-score calculations. They are calculators based upon published literature, and I cite the source literature on the same page as the calculator... In some cases it is clear that this misconception is a language barrier issue, and I must apologize for that. English is the only language I know (well, apart from some Spanish, but most of that I can't repeat in polite company).

To really answer the question I have to admit: I don't really have all the words, or even some of the right words, and I am basically incapable of organizing them in a meaningful order.

Fortunately, the lucid discussion about reference values for pediatric echo, the matters of predicting echo normal values, and the general application of z-scores towards pediatric cardiology has already been done– and by people far brighter and more eloquent than me. I have read and (mostly) understand, and I therefore highly recommend, the following:

• the invited editorial Establishing norms for echocardiographic measurements of cardiovascular structures and function in children
• the original article Theoretical and empirical derivation of cardiovascular allometric relationships in children
• the excellent chapter in Nadas' Pediatric Cardiology: Methodological Issues in Clinical Research
• the recent work, A Novel Method of Expressing Left Ventricular Mass Relative to Body Size in Children

Why are your z-scores different? I don't know for sure, but I can take some guesses. Certainly, I recognize that there are differences.

The inevitable, and, possibly, better question is "Which one is most correct ?"

Universal Z-Score Calculations

According to the Spring issue of the ASE's Pediatric and Congenital Heart Disease Council News, interesting things are afoot:

The council has developed a Normative Database working group... to develop consensus methods for standardization of measures acquired during the pediatric echocardiogram with a long-term goal of creating a normative database of universally available standardized z-score calculations for the pediatric and young adult population.

I have toyed around a bit with making a few z-score calculators for pediatric echo universally available, and in the process one thing became clear: we are a long way from a consensus on z-scores. And, while enormously useful, the z-score calculators by themselves seem to only scratch the surface of what is now possible.

What is truly fascinating to me is the idea of a universal normative database. While I have yet to implement such a design through ParameterZ.com, what I have learned is: technology is not a barrier to creating an online pediatric echo reference values database.

What would be really cool is to marry the reference values with something that would...

... allow participants to create and generate web-based, secure echo reports that are standardized and complete.

(That is the ASE's promised echo toolbox reporting tool).

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I have been contemplating the concept of web based pediatric echo z-scores and standardized echo reports for some time.

I have to say that I am excited and eager to see what more and greater minds come up with.

Fetal Ventricular Wall Dimensions

Reference values for fetal ventricular wall thickness are not easy to come by. This gadget is based on one of few available references.

Evaluation of Fetal Heart Dimensions from 12 Weeks to Term
Cora Firpo, MD, Julien I.E. Hoffman, MD, and Norman H. Silverman, MD
Am J Cardiol 2001 [link]

Measurements of the ventricular walls and septum were made from the "4-chamber" views, below the coapted AV valve leaflets, in diastole.

Children's Hospital of Michigan: Z-Scores of Cardiac Structures

This article is/will be absolutely huge for many pediatric echo labs:

J Am Soc Echocardiogr. 2008 Apr 10 [Epub ahead of print] (PubMed link)
Regression Equations for Calculation of Z Scores of Cardiac Structures in a Large Cohort of Healthy Infants, Children, and Adolescents: An Echocardiographic Study.
Pettersen MD, Du W, Skeens ME, Humes RA.

Carman and Ann Adams Department of Pediatrics, Wayne State University School of Medicine, Detroit, Michigan(M.D.P., W.D., R.A.H.).

Prediction equations (nonlinear regression analysis against BSA) are published for 21 M-mode and 2D echo measurements:

1. RVDd
2. IVSd
3. IVSs
4. LVPWd
5. LVPWs
6. LVIDd
7. LVIDs
8. Aortic valve annulus
9. Sinuses of Valsalva
10. Sinotubular junction
11. Transverse aortic arch
12. Aortic isthmus
13. Distal aortic arch
14. Aorta at diaphragm
15. Pulmonary valve annulus
16. Main pulmonary artery
17. Right pulmonary artery
18. Left pulmonary artery
19. Mitral valve annulus
20. Tricuspid valve annulus
21. Left atrium

That pretty much covers everything from an echo measurement/congenital heart disease angle, so...
WOW.
Without a doubt, a tremendous bit of work on a large data set.

I find a few things about the article to be interesting:

• This data looks to be to be a subset of a Detroit/D.C./Philips superset, presented in abstract form in 2004 (See JASE May 2004, Sable et. al.). Then, they presented data on over 6,000 patients... presented in this article, the authors claim to have analyzed a "large cohort"- which is undeniably true- but it is not as large as it might have been. There remains something proprietary about the superset. 
• Some descriptions about the patient population are notable by their absence: the ranges of age and size, gender and race, and the manner in which the BSA was calculated. All seem to me to be typical required descriptions of the methodology, but are unreported in this presentation.
• The choice of a polynomial/nonlinear regression model is unique, in light of recent work.

It is this last point—the choice of the regression model—that I find most interesting. Recent and prior work has demonstrated suitable models of cardiac growth using: an allometric equation (Neilan, Pradhan, and Weyman), the attractive principles of fluid dynamics and geometric similarity (Sluysmans & Colan), or even an old-school transform both sides (TBS) approach (Abbott & Gutgesell). None of these other models describe the "late deflection" in the relationship that this study's third order polynomial approach does. In my opinion, this may not ideally model the relationship of cardiac structures for larger patients. However, most of the work in pediatric cardiology deals with smaller patients, and the model's performance may be quite suitable for the majority of these patients.

Fascinations with the choice of model aside, this article represents the most comprehensive collection of z-score prediction equations for pediatric echocardiography to date. An online z-score calculator based on these equations can be found, of course, at

ParameterZ.com

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It turns out that there is a considerable limitation of the application of this model to larger pediatric patients (like High School athletes). A large 15 year-old could be pushing 2.5 m² and the model's predicted LVIDd for a patient of that size is an unreasonable 11-17 cm. I have therefore constrained the calculation to z-scores of subjects with BSA < 2.0m²

One Tail or Two? Z-Scores and The More Normal 95 Percent

The question is between two definitions of "95% of normal". On the one hand is the camp, like those describing the Strong Heart Study, that says:

Normal is a z-score of ± 2

Their 95% is the same 95% that is the confidence interval, i.e.: 95% of the population falls within 1.96 standard deviations of the mean- the middle 95%.

We normally round the 1.96 to 2... and that is one way to consider the normal population- the two-tailed approach.

But what if you started at one end of the spectrum, and counted the population going towards the other side? This counts the cumulative distribution, graphically presented here:

(the red curve is the normal distribution)

If you respect your normal population in this manner, as did the investigators of the Framingham Heart Study, you get:

95% of the population is accounted for by a
z-score of 1.645

That is to say, 95% of the population is below a z-score of approximately +1.7- the bottom 95%. That is the one-tailed approach. The difference between one-tailed and two-tailed definitions of normal looks like this:

Interestingly, the Framingham study described five categories:

We classified values of each echocardiographic variable into the following five categories based on sex- and height-specific percentiles (indicating increasing deviation from the reference limits):

• category 0 (reference limits), value <=95th percentile of the reference sample;
• category 1, 95th percentile of reference sample<value<=95th percentile of broad sample;
• category 2, 95th percentile of broad sample<value<=98th percentile of broad sample;
• category 3, 98th percentile of broad sample<value<=99th percentile of broad sample; and
• category 4, value >99th percentile of broad sample.

Their categorization contains one category more than the usual normal-mild-moderate-severe break down... I think I will call z-scores of 1.7 - 2 "borderline".

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All of this depends upon the values having a normal distribution. If the values are not normally distributed, everything goes out the window. This makes me slightly uncomfortable with z-scores and reference values that describe only the "transformed values" as having such a distribution- but maybe that's just me.

What about you?
What considerations do you make about your normal population?