The future of Z

While I am not going to rush out to get the first web-enabled washing machine, I am keen on Google's vision of the future, and commonality of scientific data:

Scientific measurements and experimental results will be blogged and automatically entered into common data archives to facilitate the distribution, sharing and reproduction of experimental results.

I have not yet given up on the idea of the common database of reference values for pediatric echo...

I hope to have a working mock-up soon. On second thought, maybe I will wait a bit.

It seems that the "Pediatric Measurements Writing Group of the American Society of Echocardiography and Congenital Heart Disease Council" is indeed making headway. According to the council's Fall 2008 Newsletter:

The current plan is to have a first draft of the document available for review at the American Heart Association meeting in November.

Members of the writing group include SD Colan and T Geva from Boston Children's Hospital... So this should be the definitive "how-to" for pediatric echo z-scores.

Aortic Stenosis: Calculating Valve Area and Pressure Recovery

The January 2008 issue of JASE includes the article:

Routine Adjustment of Doppler Echocardiographically Derived Aortic Valve Area Using a Previously Derived Equation to Account for the Effect of Pressure Recovery (source)

Wherein the matter of cath vs. echo discrepancies in evaluating aortic stenosis is addressed. While this article focuses on the matter of the aortic valve area, prior work has directed attention to the differences in gradients:

Comparison of simultaneous invasive and noninvasive measurements of pressure gradients in congenital aortic valve stenosis (source)

Combining the concepts of the two articles, this calculator considers both pressure recovered valve area and gradient estimations, as given by the formulae in the aforementioned articles:

Aortic Stenosis Valve Area and Pressure Recovery Calculator

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(I originally busted this out back in January; it has been updated to run as a JavaScript calculator so as to be compatible here in it's new home on Blogger)

update, Nov. 2014:

The calculator on this site is broken :-| .

So I moved it: www.parameterz.com/tools/aortic-valve-area-and-pressure-recovery.

Aortic Valve Z-Score Smackdown

After overcoming my perplexity about the distribution of left atrial scores, I thought it might be interesting to look a little closer at how other normative data is predicted.

For the sake of simplicity and to illustrate the point, the estimation of BSA from height and weight has been omitted and the Cincinnati z-score calculation is limited to "boys".

Aortic Valve Z-Score Comparison

What's The Difference?

In part: Skewness.

That is to say, the Cincinnati, Michigan, and Wessex data are all modeled as having positive skew, whereas the Boston data demonstrates a normal distribution about the mean:

Their difference is perhaps most apparent as an overlay (_B=Boston):

Fortunately, most of the predictions perform well when evaluating for hypoplasia. The "big" question is how do you want to deal with dilation? Compared to the Boston predictions, the Cincinnati predictions will call an abnormal, dilated aortic valve "normal" (a false negative). Conversely, The Boston data will call an abnormal on what would otherwise be considered normal in Cincinnati (a false positive).

Which type of error are you willing- or unwilling- to make?

LV Mass Z-Scores

"...these could easily be included in echocardiography software, which would allow automated generation of an LV mass-for-height z score and percentile for each child undergoing echocardiography."

A Novel Method of Expressing Left Ventricular Mass Relative to Body Size in Children [link]

Bethany J. Foster, MD, MSCE; Andrew S. Mackie, MD, SM; Mark Mitsnefes, MD; Huma Ali;
Silvia Mamber, MD; Steven D. Colan, MD

Circulation. 2008;117:2769-2775 Published online before print May 19, 2008

Apart from debunking the practice of simply indexing LV mass by dividing mass by height, the "novel method" is the LMS (lambda, mu, sigma) method of analysis. While I couldn't paint my way out of a Box-Cox transformation, I get the idea: the lambda (power transformation to deal with skew), mu (mean), and sigma (coefficient of variation) are determined for each of many groups, elegantly- and deliberately- addressing the matters of skewness and heteroscedasticity.

Lots to read up on with this technique:

• The LMS method for constructing normalized growth standards [link]
• Smoothing reference centile curves: the LMS method and penalized likelihood [link]
• download LMS chart-making software from Tim Cole's website

The authors acknowledge that their data should not be taken to represent the definitive model of LV mass reference values, only that they are proposing the LMS technique as an alternate, superior, method.

Note: LV Mass was estimated from m-mode using the Devereux equation.

LV Mass Z-Score Calculator

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 ?"