We thank Dyar et al for their comments and questions. We appreciate the opportunity to respond and to discuss the issues raised in more detail. The correct unit when indexing body surface area (BSA) is indeed m^2.76. The published units of m^2.6 was a typographical error that was unfortunately not recognized prior to final publication.
The second issue raised regarding the fit of the model across all BSA is an important one and merits a more detailed response. We appreciate that heteroscedasticity (nonconstant variance) is a problem one faces when examining the relation between body size (growth) and cardiovascular structure size. Sluysmans and Colan convincingly showed that left ventricular (LV) volume should be indexed to the BSA^1.38 power. Our goal was to report a normative dataset for subxiphoid bullet LV end-diastolic volume for clinical use that utilized this previously validated indexing method. Our hypothesis was simply that indexing LV end-diastolic volume (LVEDV) to BSA^1.38 would result in less residual dependence on BSA, than indexing to BSA^1.0 alone. This is unequivocally true as evidenced in figure 3 of our publication. We did not set out to examine which regression method “best fit” the data or to correct for any residual nonconstant variance that remained. As pointed out by Sluysmans and Colan, studies examining vascular structures consistently show more data spread at larger BSA, which is improved, but not fully eliminated when correct indexing methods (such as BSA^1.38) are employed.
The above issues aside, we did take the opportunity to reexamine our data applying the method utilized in the recent publication by Dallaire F, et al , as Dyar et al suggested. We believe the findings are informative. Most importantly, our indexed LVEDV data meets two critical criteria for z-score datasets: (a) being normally distributed; and (b) having an intercept close to zero. Our indexed LVEDV (ml/m^2.76) dataset is indeed normally distributed based on an A^2 value of 0.385 and a nonsignificant P value of .39 by the Anderson-Darling test. In addition, the intercept of the LVEDV to BSA^1.38 plot is not significantly different than zero (intercept of 0.2 ml). Furthermore, as we understand Dallaire F et al methods, one could further address the issue of nonconstant variance by altering the derived z-score equation. Our equation is Z= (LVEDVi -μ)/δ ; where μ is the mean value of 70.4 and δ is the standard deviation of 9.1. Dallair F et al , alters this basic equation by estimating the degree that μ and δ change as the independent variable of body size (BSA) increased.
The goal, in their words is, “….to redistribute the weight in the model so that standard error would remain constant as the value of the independent variable increased.” In other words, for a given small interval of BSA one utilizes different values of μ and δ depending on the data variance at the given BSA. With the aid of a statistician, we performed this correction method to our data. The impact of this method of correction was not large, and is as follows: for 77/100 data points the z-score change was < 0.5; for 19/100 data points the change was between (0.5 and 1.0); and for only 4/100 data points the z-score change was >1.0. Additionally, only 2/100 data points had z-scores that changed from “normal” (between -2.0 and +2.0) to outside of “normal” – one changed from +1.60 to +2.48 and one from -1.47 to -2.30.
Although we agree that this methodology is sound statistically, the impact when applied to our data as demonstrated above does not appear to be large. This is especially true when one considers the other inherent error in estimating LV size in infants. First, there is error in the estimation of BSA in infants which is not correctable. Secondly, we reported an interobserver measurement error of 4.7-5.9%. Using a practical example, if one observer measures an LVEDV of 20 ml in an infant who is 0.40 m^2, the resulting z-score is +.05; while a second observer measures 21.5 ml (observer error of 5-6%), the resulting z-score is +0.65. Clinically, when dealing with small structures as we do in pediatric cardiology, z-scores are probably best interpreted on a somewhat larger scale -values of +2.0, +3.0, +4.0, etc, rather than smaller intervals. This is how we are utilizing our data clinically and would anticipate that other clinicians would as well.
In conclusion, we regret and take full responsibility for the typographical error. We now more fully appreciate statistical nuances of z-score methodology and are grateful for Dyar et al’s comments and Dallaire et al ’s contribution. Fortunately, when a more rigorous methodology is applied to our data the results and central message of our publication remain valid.