Saturday, November 1, 2008

Echo Z-Scores and Percentiles

I recently revisited the idea of calculating percentiles in addition to z-scores for the pediatric echo z-score calculators.

The cumulative percent is shown along with the z-score in the following image:

 

Since the relationship between z-score and percentile is constant, it seemed to me of no great benefit to add the percentile information. However, I now feel that percentiles convey information that some find more meaningful. For instance, the commonly accepted limits of normal for z-scores is -2 to +2 (the middle 95% of values). This range corresponds to percentiles of 2.3 and 97.7. But maybe a more realistic range of normal is

  • 5th - 95th percentiles: z-scores of ± 1.65
  • 10th - 90th percentiles: z-scores of ± 1.3

Using percentiles might encourage us to draw a more conservative boundary for the range of normal, which, in my opinion, will help us interpret otherwise "borderline" z-scores. Accepting the normal range of ±2, a z-score of -2.3 doesn't seem that far off. However, -2.3 is the 1st percentile- clearly nowhere near "normal".


Initially, I had thought that maybe I'd find a z-score/percentile table,  and simply incorporate a lookup routine, percentilesTable

but I like the idea of calculating the percentile better. However, the calculation (or rather, estimation) is hardly straightforward.

After some searching and trial and error, I finally found something that I could adapt. I admit I don't really understand how the polynomial approximation works, but hey, it does work, and it's in the public domain.

The first z-score calculator to receive the percentiles "upgrade" is the Aortic Root Z-Score Calculator. I hope to add the functionality to the others as well, as time permits.

Wednesday, October 22, 2008

Designing a Pediatric Echo Database

Having trolled the literature in an effort to consume and digest what has already been published in the name of "Pediatric Echo Normal Values" and "Pediatric Echo Reference Values" I have come to the conclusion that what I really wanted was this: a common collection of normative data, from which we could all draw our own conclusions.

That doesn't exist.

Yet.

There now appears to be growing and international interest in the matter of a common source of reference data for pediatric echo. An editorial (ePub ahead of print) in the  European Journal of Echocardiography now is calling for:

immediate discussions of a universal standard...
a concerted and collaborative international approach...
a single study to allow z-score computation...
a robust set of normal values, derived from a large number of individuals...

I hope the European Society of Echo plans on discussing this similar matter with the American Society of Echo (or vice-versa) before things get too far along...

While it is looking like this project is in much more capable hands than my own (thankfully!), had I to do it myself it was going to be guided by one thing: data transparency.

Show me the data

After having read some of the literature, I would occasionally find myself wondering "What if they had used a different BSA equation?", or "what if they had used height instead?" or used a different regression model, etc. For myself, I would love to see some of the studies re-done, but just slightly different.

Of course, nobody is going to do that— re-calculate their regressions— just because I, or you, want to see it done with our own particular and fanciful bias. And that is the point of a full disclosure database: DIY if you don't like this flavor. And, increasingly, I think that people will want to do just that. As an example, there is a preponderance of evidence that BSA, height, and weight are all inadequate for the purpose of scaling:

The cardiovascular system has evolved for effective distribution of metabolic substrates to tissue with high metabolic potential (Circ. 2008)

Cardiovascular structures scale with cardiac output and lean body mass.

In a very practical sense, there is no way to measure lean body mass (LBM) in the echo lab so the need for a good surrogate remains. Foster et. al., have already hinted at the concept of re-combining height and weight to better estimate lean body mass:

The combination of height and weight may provide a better surrogate for lean body mass than height alone, which could result in a superior prediction... This approach differs from normalization for body surface area; although body surface area equations include both height and weight, the particular combination of height and weight is lost once the surface area calculation is done.

Without providing open access to collected variables, like height and weight, any future data collection/analysis risks becoming irrelevant as our understanding of scaling cardiovascular structures evolves.

Show me more data

One of the biggest problems (IMHO) with the current approach to reference values is related to the matter of prediction. Different authors have proposed various methods of trying to predict the mean value of a given structure for a given body size, and these authors have similarly varied approaches to predicting the standard deviations. Understanding the relationship of the structure to body size is profound- and obviously important- but it is a different matter to determine if your measurement is normal- or not. For the purposes of reference values, the precise relationship of cardiac structure to body size doesn't matter.

At its essence, a z-score has nothing to do with regression equations. Whenever we make an echocardiographic measurement, and consider its "normality" all we are really asking is "how does this measurement compare to the same measurement of normal subjects with similar size ?" That is, what is the mean and standard deviation of the same structure measured in a large group of similar-sized normal subjects?

The exact relationship and regression doesn't matter- as long as we have a collection of enough data on similar-sized subjects. What is required, though is... an awful lot of data, grouped in a meaningful way. The number of required subjects is daunting: grouped the way they did in their study (by height), an LV Mass reference database modeled after Foster et al., should probably have tens of thousands of subjects: 145 groups (47 to 191 cm, in 1 cm increments) x 100-200 subjects in each group (although, I would think the increment could safely be increased to 2 cm, thereby cutting the number of groups in half). This is why there is so much in the way of prediction: you need fewer patients. In spite of the huge numbers required, the study by Foster et al., is, or probably should be, the model for the future of echocardiographic reference values.

Even More Data

In the same way that our understanding of scaling of cardiovascular structures is evolving (height vs. BSA vs. LBM) , so too is our ability to measure these cardiovascular structures. Similar databases of reference values for the various Doppler modalities and 3D echo measures should be taken into consideration.

The architecture of this database could have long lasting effects. Designing a large database of common reference measurements for data transparency will allow us to continually make the most intelligent use of the tremendous effort required to collect this data.


Normalization of echocardiographically derived paediatric cardiac dimensions to body surface area: time for a standardized approach.
Kaski JP, Daubeney PE.
Eur J Echocardiogr. 2008 Sep 30. [Epub ahead of print]
Does size matter? Clinical applications of scaling cardiac size and function for body size.
Dewey FE, Rosenthal D, Murphy DJ Jr, Froelicher VF, Ashley EA.
Circulation. 2008 Apr 29;117(17):2279-87. Review.
A novel method of expressing left ventricular mass relative to body size in children.
Foster BJ, Mackie AS, Mitsnefes M, Ali H, Mamber S, Colan SD.
Circulation. 2008 May 27;117(21):2769-75. Epub 2008 May 19.
Interpretation of echocardiographic measurements: a call for standardization.
Vasan RS, Levy D, Larson MG, Benjamin EJ.
Am Heart J. 2000 Mar;139(3):412-22.

Friday, October 3, 2008

Aortic Stenosis: Discriminant Score

Based on work from Boston Children's Hospital, this calculator determines the aortic valve z-score and the discriminant score — for "predicting which neonates with AS are suitable for biventricular repair and which are better served by single ventricle management."

Discriminant Score Calculator

 
Results
   
 

Analysis:

"If EFE is omitted from the analysis (owing to high interobserver variability in grading), the most accurate model for predicting survival with a biventricular circulation is: 12.16 (BSA) + 0.59 (aortic valve annulus z-score) + 5.73 (LAR) - 7.02 with a discriminant cutoff of -0.46 accurately predicting 91% of survivors and 80% of events (87% overall)."

References:

Validation and Re-Evaluation of a Discriminant Model Predicting Anatomic Suitability for Biventricular Repair in Neonates With Aortic Stenosis
Steven D. Colan, MD*, Doff B. McElhinney, MD, Elizabeth C. Crawford, RDCS, John F. Keane, MD and James E. Lock, MD
J Am Coll Cardiol, 2006; 47:1858-1865, doi:10.1016/j.jacc.2006.02.020 (Published online 11 April 2006).

 

(Since I dropped this calculator from the ParameterZ.com remodel, I had to find a new home for it... here.)

Thursday, September 25, 2008

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.

Wednesday, July 23, 2008

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:

AVAPressRecov

PressRecovFormula

Aortic Stenosis Valve Area and Pressure Recovery Calculator


(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.