A New Z Score Curve of the Coronary Arterial Internal Diameter Using the Lambda-Mu-Sigma Method in a Pediatric Population

Background Several coronary artery Z score models have been developed. However, a Z score model derived by the lambda-mu-sigma (LMS) method has not been established. Methods Echocardiographic measurements of the proximal right coronary artery, left main coronary artery, proximal left anterior descending coronary artery, and proximal left circumflex artery were prospectively collected in 3,851 healthy children ≤18 years of age and divided into developmental and validation data sets. In the developmental data set, smooth curves were fitted for each coronary artery using linear, logarithmic, square-root, and LMS methods for both sexes. The relative goodness of fit of these models was compared using the Bayesian information criterion. The best-fitting model was tested for reproducibility using the validation data set. The goodness of fit of the selected model was visually compared with that of the previously reported regression models using a Q-Q plot. Results Because the internal diameter of each coronary artery was not similar between sexes, sex-specific Z score models were developed. The LMS model with body surface area as the independent variable showed the best goodness of fit; therefore, the internal diameter of each coronary artery was transformed into a sex-specific Z score on the basis of body surface area using the LMS method. In the validation data set, a Q-Q plot of each model indicated that the distribution of Z scores in the LMS models was closer to the normal distribution compared with previously reported regression models. Finally, the final models for each coronary artery in both sexes were developed using the developmental and validation data sets. A Microsoft Excel–based Z score calculator was also created, which is freely available online (http://raise.umin.jp/zsp/calculator/). Conclusions Novel LMS models with which to estimate the sex-specific Z  score of each internal coronary artery diameter were generated and validated using a large pediatric population.