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J Am Soc Echocardiogr. 2016 Aug;29(8):794-801.e29. doi: 10.1016/j.echo.2016.03.017. Epub 2016 Jun 7.

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

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Division of Clinical Research Planning, Department of Development Strategy, Center for Clinical Research and Development, National Center for Child Health and Development, Tokyo, Japan; Department of Pediatrics, Gunma University Graduate School of Medicine, Maebashi, Japan.
Department of Pediatrics, NTT East Japan Sapporo Hospital, Sapporo, Japan.
Department of Clinical Investigation and Research Unit, Gunma University Hospital, Maebashi, Japan.
Division of Biostatistics, Department of Data Management, Center for Clinical Research and Development, National Center for Child Health and Development, Tokyo, Japan.
Department of Pediatrics, Nippon Medical School, Tokyo, Japan.
Department of Pediatric Cardiology and Nephrology, Kyoto Prefectural University of Medicine Graduate School of Medical Science, Kyoto, Japan.
Department of Pediatrics, Kurashiki Central Hospital, Okayama, Japan.
Department of Pediatrics, Kanazawa Medical University School of Medicine, Kahoku, Japan.
Department of Pediatrics, Gifu Prefectural General Medical Center, Gifu, Japan.
Department of Pediatrics, Nagoya University Graduate School of Medicine, Nagoya, Japan.
Department of Pediatrics, Chiba Kaihin Municipal Hospital, Chiba, Japan.
Department of Pediatrics, Hamamatsu University School of Medicine, Hamamatsu, Japan.
Department of Pediatrics, Kobe City Medical Center General Hospital, Kobe, Japan.
Department of Pediatrics, Saitama Red Cross Hospital, Saitama, Japan.
Department of Cardiology, Gunma Children's Medical Center, Shibukawa, Japan.
Department of Pediatrics, St. Marianna University School of Medicine, Kawasaki, Japan.
Department of Pediatrics, Niigata City General Hospital, Niigata, Japan.
First Department of Pediatrics, Toho University Omori Medical Center, Tokyo, Japan. Electronic address:



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.


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.


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 (


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.


Coronary artery abnormality; Kawasaki disease; Lambda-mu-sigma method; Pediatric; Z score

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