A new nonlinear multivariate regression method called the LMSR method is proposed, by which a multidimensional understanding for the development process of human fetuses can be provided. Statistically important quantities such as median, skewness, coefficient of variation, and correlation of underlying structure can be described by corresponding smooth curves. Those curves can be obtained by a fine combination of a multivariate power transformation of data and penalized likelihood. It will be shown that the LMSR method and some associated tools are clearly efficient in analyzing development process of human fetuses.
PappZFeketeT. The evolving role of ultrasound in obstetrics/gynecology practice. Int J Gynaecol Obstetr2003; 82: 339–346.
2.
ChandrasekaranNThilaganathanB. The diagnostic and therapeutic role of ultrasound in obstetrics. Obstetr Gynaecol Reprod Med2012; 22: 321–326.
3.
BensonCBDoubiletPM. The history of imaging in obstetrics. Radiology2014; 273: S92–110.
4.
GongQYRobertsNGardenASet al.Fetal and fetal brain volume estimation in the third trimester of human pregnancy using gradient echo MR imaging. Magn Reson Imaging1998; 16: 235–240.
5.
RasmussenSKiserudTAlbrechtsenS. Foetal size and body proportion at 17–19 weeks of gestation and neonatal size, proportion, and outcome. Early Hum Dev2006; 82: 683–690.
6.
HasegawaTKamataSImuraKet al.Use of lung-thorax transverse area ratio in the antenatal evaluation of lung hypoplasia in congenital diaphragmatic hernia. J Clin Ultrasound1990; 18: 705–709.
7.
SokolJShimizuNBohnDet al.Fetal pulmonary artery diameter measurements as a predictor of morbidity in antenatally diagnosed congenital diaphragmatic hernia: a prospective study. Am J Obstetr Gynecol2006; 195: 470–477.
8.
TanakaO. Variabilities in prenatal development of orofacial system. Anat Anz1991; 172: 97–107.
9.
TongsongTWanapirakCSirichotiyakulSet al.Sonographic markers of hemoglobin bart disease at midpregnancy. J Ultrasound Med2004; 23: 49–55.
10.
NaitoKUdagawaJOtaniH. Multidimensional standard curve for the development process of human fetuses. Stat Med2010; 29: 2235–2245.
11.
WandMPJonesMC. Vol. 60 of Monographs on statistics and applied probability. Kernel smoothing, London: Chapman and Hall, 1995.
12.
EubankRL. Nonparametric regression and spline smoothing, 2nd ed. New York: Marcel Dekker, 1999.
13.
VidakovicB. Statistical modeling by wavelets, New York: Wiley-Interscience, 1999.
14.
ColeTJ. The LMS method for constructing normalized growth standards. Eur J Clin Nutr1990; 44: 45–60.
15.
ColeTJGreenPJ. Smoothing reference centile curves: the LMS method and penalized likelihood. Stat Med1992; 11: 1305–1319.
16.
HamasakiTGotoM. On inferences of parameters in the bivariate power-normal distribution. Jpn J Behaviormetr2002; 29: 199–222. in Japanese.
17.
GreenPJSilvermanBW. Vol. 58 of Monographs on statistics and applied probability. Nonparametric regression and generalized linear models: a roughness penalty approach, London: Chapman and Hall, 1994.
ColeTJFreemanJVPreeceMA. British 1990 growth reference centiles for weight, height, body mass index and head circumference fitted by maximum penalized likelihood. Stat Med1998; 17: 407–429.
20.
TanakaO. Time of the appearance of cartilage centers on human embryos with special reference to its individual difference. Okajimas Folia Anat Jpn1976; 53: 173–198.
21.
NishimuraHTakanoKTanimuraTet al.Normal and abnormal development of human embryos: first report of the analysis of 1213 intact embryos. Teratology1968; 1: 281–290.
22.
NishimuraHPrenatal versus postnatal malformations based of the Japanese experience on induced abortions in the human being. In: BlandauRJBaselSKargerAG (eds). Aging gametes1975, pp. 349–368.
23.
ShiotaK. Development and intrauterine fate of normal and abnormal human conceptuses. Congen Anom1991; 31: 67–80.
24.
YamadaSHamanishiJTanadaSet al.Embryogenesis of fused umbilical arteries in human embryos. Am J Obstetr Gynecol2005; 193: 1709–1715.
25.
OtaniHUdagawaJLundhTet al.Morphometric study on the characteristic external features of normal and abnormal human embryos. Congen Anom2008; 48: 18–28.
26.
Kawai N. Taiban no Keitai (Tokuni Kekkann wo Chusin tosite). In: Sakamoto S, Taki I and Murooka H (eds) Taiji·Taiban-kei no Kiso to Rinshou, Sanfujinka Mook 17. Kanehara-Shuppan, Tokyo, 1981, pp.16–19 (in Japanese).
27.
Iwasaki H. Taiji·Taiban-kei no Aging. In: Sakamoto S, Taki I and Murooka H (eds) Taiji·Taiban-kei no Kiso to Rinshou, Sanfujinka Mook 17. Kanehara-Shuppan, Tokyo, 1981, pp.40–45 (in Japanese).
28.
NishimuraH. Atlas of human prenatal histology, Tokyo: Igaku-Shoin, 1983.
29.
ArchieJGCollinsJSLebelRR. Quantitative standards for fetal and neonatal autopsy. Am J Clin Pathol2006; 126: 256–265.
30.
HansenKSungCJHuangCet al.Reference values for second trimester fetal and neonatal organ weights and measurements. Pediatr Dev Pathol2003; 6: 160–167.
31.
MammenEMarronJSTurlachBAet al.A general projection framework for constrained smoothing. Stat Sci2001; 16: 232–248.
32.
MagnusJRNeudeckerH. Matrix differential calculus with applications to statistics and econometrics, Chichester: Wiley, 1999.
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
