||Application of Principal Component Analysis and Artificial Neural Network on Ultrasonographic Parameters for Fetal Weight Estimation
||Department of BioMedical Engineering
Principle components analysis
Artificial Neural Network
two-step cluster analysis
Fetal Weight Estimation
本研究方法，首先收集2,127位單胞胎新生兒其產前三天內胎兒的超音波參數值(雙頂骨間徑、枕額徑、腹圍、頭圍、股骨長度等) 及出生之新生兒真實體重，以上參數值經由(1)常態分析(Kolmogorov-Smirnov test)檢定資料分佈形態及項目分析(item analysis)篩檢出具有鑑別力的參數；(2)相關性分析(correlation analysis)及逐步迴歸法(stepwise regression)選取與胎兒體重最具貢獻度的超音波參數作為分組依據再利用K平均演算法 (K-means analysis) 進行胎兒分組之分析；(3)主成份分析(Principle components analysis)量化胎兒體型特徵值作為分組依據在利用兩階段法(two-step cluster analysis) 進行胎兒體型分組之分析；(4)建立及訓練分組倒傳遞類神經網路模式(back propagation network algorithm)，並求得各組最佳預估胎兒體重輸出值；(5)以赤池信息量準則(Akaike information criterion)及最小均方誤差法(Minimum mean squared error)建立系統及參數的誤差補償模式。以胎兒體型作為網路分組之架構，將個案資料隨機分配為二組，其中1,489位作為建立及訓練倒傳遞類神經網路(比例共軛梯度演算法)學習模組，另外638位則作為驗證模組。預測準確度的評估是採用Friedman test 統計分析法。
本研究結果以胎兒體型分組為基礎之倒傳遞網路，驗證胎兒體重預估的準確度為 (n = 638，MAPE = 4.9 ± 3.5％，MAE = 149.4 ± 110.2g) 與台灣 (1) Hsieh formula 1B迴歸分析(n = 638，MAPE = 6.0 ± 4.6％，MAE = 173.2 ± 120.3g, p＜0.01)；(2) Hsieh formula 2B迴歸分析(n = 638，MAPE = 6.5 ± 7.2％，MAE = 175.1 ± 120.4g, p＜0.01)；(3)美國Hadlock 迴歸分析(n = 638，MAPE = 7.4 ± 5.3％，MAE = 224.6 ± 169.0g, p＜0.01) 及 (4)以胎兒腹圍分組為基礎之倒傳遞網路(n = 638，MAPE = 5.3 ± 4.1％，MAE = 157.9 ± 119.9g, p＜0.01)比較後，均有顯著的改善。
For obstetrics, prenatal assessment of fetal weight and growth is paramount. Accurate estimated fetal weight (EFW) is the principal way to measure and monitor fetal growth in utero, and thereby assist the management of delivery. EFW is an important and reliable method for predicting fetal growth disorders which can result in serious antenatal, perinatal, and postnatal complications. Clinicians rely on EFW for determining appropriate delivery mode, timing, and suitable delivery procedure to reduce maternal-fetal risk and medical cost. Accurate estimation of fetal weight lowers the risk of the normal spontaneous delivery (NSD). On the other hand, clinicians may encourage parents to proceed with NSD when a safe outcome is foreseeable and reduce medical costs. Currently, ultrasound (US) is the major tool for EFW. EFW methods, such as multiple regression model, are commonly used in clinical Obstetrics. Combinations of US fetal growth parameters, such as biparietal diameter (BPD), abdominal circumference (AC) and femur length (FL), along with Hsieh’s reported equations, are the major methods for the estimation of fetal weight in Taiwan. Although Hsieh’s regression methods are commonly accepted, estimation errors increase when birth weight is greater than 4000g or less than 2000g. Estimation errors are a common problem in daily practice for obstetricians so there is room for improvement of fetal weight estimation accuracy. Extreme body variations among fetal US parameters, such as macrosomia or low birth weight result in increasing error of EFW via regressive analysis. With the assistance of real-time high-resolution US and principal component analysis (PCA) along with artificial neural network (ANN), a better EFW model can be achieved.
The purpose of this research project was to design and develop an automated feature-based classification method. We attempted (1) to identify fetal characteristics through ultrasound parameters (USP) sets for classifying fetuses (2) in order to develop an artificial neural network (ANN). Our hypothesis is that using PCA and ANN can improve the accuracy of EFW. This research accomplishes the following procedures: (1) collect USP data for analysis; (2) apply PCA to extract the characteristic parameters of fetal groupings; (3) apply two-step cluster analysis for the classification of fetal groupings; (4) establish a back-propagation ANN model of the classified groups for fetal weight estimation; (5) Apply Akaike information criteria (AIC) and Minimum-mean-square-error (MMSE) compensation methods to USP data; (6) compare the clinical efficacy of our proposed ANN models and other conventional regression models of EFW.
The research was divided into five stages: (1) Collection of US measurements of fetal biometric parameters and preliminary parameters analysis; (2) Calculation of correlation analysis, stepwise regression and K-means with one parameter for fetal size classification; (3) Apply PCA and two-step cluster algorithm with multiple parameters for fetal size classification; (4) Use AIC and MMSE model to compensate for US errors; (5) Use ANN modeling on the classified groups for EFW. The dataset used in this study came from 2,127 singleton fetuses examined within 3 days prior to delivery. The cases were randomly divided into a training set with 1,489 samples and a testing set with 638 samples. The Friedman test was used for comparing the performance of the proposed ANN model with the regression-based EFW formulas.
Our experimental results showed the accuracy of EFW from our PCA-based ANN model was significantly better than the results generated by the Taiwanese conventional regression analysis equations (i.e. Hsieh’s formula 1B, or Hsieh’s formula 2B), and even better the results using the Western conventional regression equations (all p < 0.01). The mean absolute percent error (MAPE) and the mean absolute error (MAE) was 4.9 ± 3.5% and 149.4 ± 110.2 g for our proposed PCA-based ANN model, 6.0 ± 4.6% and 173.2 ± 120.3 g for the Hsieh 1B model, 6.5 ± 7.2% and 175.1 ± 120.4 g for the Hsieh 2B model, 7.4 ± 5.3% and 224.6 ± 169.0 g for the Hadlock model , and 5.3 ± 4.1% and 157.9 ± 119.9 g for our AC-based ANN model, respectively (all p <0.01).
Our study proves that statistical selection of US parameters for grouping, together with different ANN models, can improve EFW accuracy, even in fetuses with weight at range extremities. This study also shows the following are crucial to improve EFW accuracy: (1) considering and controlling the heterogeneity using statistics among the high variability and broad ranged US parameters, and (2) using extracted parameters to classify fetuses into suitable group for each ANN model. Establishment of standardized criteria for group classification is indispensable for the subsequent cluster methods. We believe our more accurate EFW models can decrease the risks of NSD and lower medical costs by contributing to better clinical decision-making, and reduce maternal-fetal morbidity and mortality.
TABLE OF CONTENTS IX
LIST OF TABLES XII
LIST OF FIGURES XIV
Chapter 1 Introduction 1
1.1 Estimation of Fetal Weight 3
1.1.1 Fetal Ultrasound Biometry for Evaluating Fetal Weight 3
1.1.2 Regression Model 8
1.1.3 Artificial Neural Network Model 11
1.2 Principal Component Analysis 13
1.3 K-means Method 14
1.4 Back-propagation Networks 17
1.5 Motivation and Objectives 19
1.5.1 Purpose and Specific Aims 19
1.5.2 Research Hypothesis 21
1.5.3 Significance 21
Chapter 2 Materials and Methods 22
2.1 Data Collection 24
2.1.1 Ultrasonographic Measurement of Fetal Biometric Parameters 25
2.1.2 Descriptive Statistics and Item Analysis 29
2.2 Ultrasonographic Parameters (USPs) Analysis 30
2.2.1 AC-based Group Analysis 30
2.2.2 PCA-based Group Analysis 32
2.3 ANN Development for Fetal Weight Estimation 35
2.3.1 AC-based ANN Model 35
2.3.2 PCA-based ANN Model 39
2.4 Minimum Mean Squared Error Framework for Compensating USPs 43
2.4.1 AIC Database Partition and Subset Number Determination 45
2.4.2 Minimum Mean Squared Error (MMSE) Compensation 47
2.5 Accuracy Comparison and Performance Evaluation 48
Chapter 3 Results 51
3.1 Data Description 51
3.1.1 Descriptive Statistics 51
3.1.2 Strong Correlation between USP and BW 53
3.2 Results of AC-based Grouping 56
3.3 Results of Principal Component Analysis 57
3.4 Performance of AC-based ANN Model 60
3.5 Performance of PCA-based ANN Model 66
3.6 Performance of MMSE Model Combined with AIC 74
Chapter 4 Discussion 79
4.1 Characteristics of the AC-based Grouping 80
4.2 Effects on the PCA-based Transformation 81
4.3 Comparison and Efficacy Evaluation of Model-based Approaches 83
4.3.1 Effects of AC-based ANN Model for EFW 83
4.3.2 Effects on PCA-based ANN Model in EFW 84
4.3.3 Effects on MMSE Model Combined with AIC in EFW 86
Chapter 5 Conclusions and Recommendations 88
D.D. McIntire, S.L. Bloom, B.M. Casey, and K.J. Leveno, “Birth weight in relation to morbidity and mortality among newborn infants,” N Engl J Med, vol.340, no. 16, pp.1234-8, Apr, 1999.
E. Merz, “Ultrasound in Obstetrics and Gynecology,” New York, Thieme, chap. 14, pp. 164, 2005.
F.J. Hsieh, F.M. Chang, and H.C. Huang, “Computer-assisted analysis for prediction of fetal weight by ultrasound-comparison of biparietal diameter, abdominal circumference and femur length,” J Formosan Med Assoc, vol.86, pp.957-64, 1987.
F.M. Chang, H.C. Ko, Y.S. Lin, B.L. Yao, C.H. Wu, P.L. Kuo and C.H. Liu, “Clinical validation of two equation in antenatal prediction of Chinese fetal weight by ultrasonography,” J Formosan Med Assoc, vol.90,pp.1086-92, 1991.
I.M. Usta, S. Hayek, F. Yahya, A.Abu-Musa, and A.H. Nassar, “Shoulder dystocia: what is the risk of recurrence?,” Acta Obstet Gynecol Scand, vol. 87, no. 10, pp.992-7, 2008.
F.G. Cunningham, K.J. Leveno, S.L. Bloom, J.C. Hauth, L. Gilstrap III, and K.D. Wenstrom, “Williams Obstetrics twenty-second edition,” New York, McGraw-Hill, chap.20,pp.514, 2005.
K.H. Hsu, P.J. Liao, and C.J.Hwang, “Factors affecting Taiwanese women's choice of cesarean section,” Soc Sci Med, vol.66, no.1, pp.201-9, Jan, 2008.
World Health Organization, “Appropriate technology for birth,” Lancet vol.2, no.8452, pp.436-7,1985.
S. Campbell, and D. Wilkin, “Ultrasonic measurement of the fetal abdominal circumference in the estimation of fetal weight,” Br J Obstet Gynaecol, vol. 82, no. 9, pp. 689–697, Sep, 1975.
S. L. Warsof, P. Gohari, R. L. Berkowitz, and J. C. Hobbins , “The estimation of fetal weight by computer-assisted analysis,” Am J Obstet Gynecol, vol. 128, no. 8, pp. 881–892, Aug. 1977.
M. J. Shepard, V. A. Richards, R. L. Berkowitz, S. L. Warsof, and J. C. Hobbins, “An evaluation of two equations for predicting fetal weight by ultrasound,” Am J Obstet Gynecol, vol. 142, no. 1, pp. 47–54, Jan. 1982.
C. P. Weiner, R. E. Sabbagha, N. Vaisrub, and M. L. Socol, “Ultrasonic fetal weight prediction: role of head circumference and femur length,” Obstet Gynecol, vol. 65, no. 6, pp. 812–817, Jun. 1985.
F. P. Hadlock, R. B. Harrist, R. S. Sharman, R. L. Deter, and S. K. Park, “Estimation of fetal weight with the use of head, body and femur measurements--a prospective study,” Am J Obstet Gynecol, vol. 151, no. 3, pp. 333-7, Feb. 1985.
B.R. Benacerraf, R. Gelman, and F.D. Jr. Frigoletto, “Sonographically estimated fetal weights: accuracy and limitation,” Am J Obstet Gynecol, vol.159, no.5, pp.1118-21, Nov, 1988.
N. J. Dudley, “A systematic review of the ultrasound estimation of fetal weight,” Ultrasound Obstet Gynecol, vol. 25, no. 1, pp. 80–89, Jan. 2005.
N. C. Hart, A. Hilbert, B. Meurer, M. Schrauder, M. Schmid, J. Siemer, M. Voigt, and R. L. Schild, “Macrosomia: a new formula for optimized fetal weight estimation,” Ultrasound Obstet Gynecol, vol. 35, no. 1, pp. 42-7, Jan. 2010.
J. Gardosi, M. Mongelli, M. Wilcox, and A. Chang, “An adjustable fetal weight standard,” Ultrasound Obstet Gynecol, vol. 6, no.3, pp. 168-74, Sep. 1995.
R. E. Sabbagha, J. Minogue, R. K. Tamura, and S. A. Hungerford, “Estimation of birth weight by use of ultrasonographic formulas targeted to large-, appropriate-, and small-for-gestational-age fetuses,” Am J Obstet Gynecol, vol. 160, no. 4, pp. 854-62, Apr. 1989.
J.S. Woo, C.W. Wan, and K.M. Cho, “Computer-assisted evaluation of ultrasonic fetal weight prediction using multiple regression equations with and without the fetal femur length,” J Ultrasound Med, vol.4, no.2, pp.65-7, Feb, 1985.
Bureau of Health Promotion, Department of Health, R.O.C. (Taiwan) http://www.bhp.doh.gov.tw/BHPNet/Web/HealthTopic/TopicArticle.aspx?id=201109200013&parentid=201109200006.
J.A. Martin, B.E. Hamilton, S.J.Ventura, M.J.K. Osterman, E.C. Wilson, and T.J. Mathews, “Births: final data for 2010,” Natl Vital Stat Rep, vol.61, no.1, pp.1-72, Aug, 2012.
K. Marsál, P.H. Persson, T. Larsen, H. Lilja, A. Selbing, and B. Sultan,“ Intrauterine growth curves based on ultrasonically estimated foetal weights,” Acta Paediatr, vol.85, no.7, pp.843-8, Jul, 1996.
D.S. Sahota, T.Y. Leung, T.N. Leung, O.K. Chan, and T.K. Lau, “Fetal crown-rump length and estimation of gestational age in an ethnic Chinese population,” Ultrasound Obstet Gynecol, vol. 33, no.2, pp.157-160, Feb, 2009.
H.P. Robinson, “Sonar measurement of fetal crown-rump length as means of assessing maturity in first trimester of pregnancy,” Br Med J, vol. 4, no.5883, pp. 28-31, Oct, 1973.
H.P. Robinson, and J.E. Fleming, “A critical evaluation of sonar “crown-rump length” measurements,” Br J Obstet Gynecol. Vol. 82, no.9, pp.702-10, Sep, 1975.
A. J. Parker, P. Davies, and J. R. Newton, “Assessment of gestational age of the Asian fetus by the sonar measurement of crown-rump length and biparietal diameter,” British Journal of Obstetrics & Gynaecology, vol. 89, no. 10, pp. 836-8, Oct. 1982.
R.E. Sabbagha, and M. Hughey, “Standardization of sonar cephalometry and gestational age,” Obstet Gynecol, vol. 52, no. 4, pp.402-6, Oct, 1978.
S. Campbell, and A. Thoms, “Ultrasound measurement of the fetal head to abdomen circumference ratio in the assessment of growth retardation,” Br J Obstet Gynaecol, vol. 84, no.3 pp.165-74, Mar, 1977.
F.P. Hadlock, R.L. Deter, R.J. Carpenter, and S.K. Park, “Estimating fetal age: effect of head shape on BPD,” AJR, vol.137, no. 1, pp.83-5, Jul, 1981.
F. P. Hadlock, R. L. Deter , R. B. Harrist, and S. K. Park, “Fetal biparietal diameter: a critical re-evaluation of the relation to menstrual age using real-time ultrasound,” J Ultrasound Med, vol. 1, no. 3, pp. 97–104, Apr. 1982.
F.P. Hadlock, R.L. Deter, R.B. Harrist, and S.K. Park, “Computer Assisted analysis of fetal age in the third trimester using multiple fetal growth parameters,” J Clin Ultrasound, vol.11, no.6, pp.313-6, Aug, 1983.
F.P. Hadlock, R.L. Deter, R.B Harrist, and S.K. Park, “Estimating fetal age: computer assisted analysis of multiple fetal growth parameters,” Radiology, vol.152, no.2, pp.497-501, 1984.
R.G. Law, and K.D. MacRae, “Head circumference as an index of fetal age,” J Ultrasound Med, vol.1, no. 7, pp.281-8, Sep, 1982.
W.J. Ott, “The use of ultrasonic fetal head circumference for predicting expected date of confinement,” J Clin Ultrasound, vol.12, no. 7, pp.411-5, Sep, 1984.
C.B. Kasby, and V. Poll, “The breech head and its ultrasound significance,” Br J Obstet Gynecol, vol.89, no. 2, pp.106-10, Feb, 1982.
F.P. Hadlock, R.L. Deter, R.B. Harrist, and S.K. Park, “Fetal abdominal circumference as a predictor of menstrual age,” AJR Am J Roentqenol, vol.139, no. 2, pp.367-70, Aug, 1982.
A.B. Kurtz, R.J. Wapner, and R.J. Kurtz, “Analysis of biparietal diameter as an accurate indicator of gestational age,” J Clin Ultrasound, vol.8, no. 4, pp.319-26, Aug, 1980.
P. H. Persson and B. M. Weldner, “Reliability of ultrasound fetometry in estimating gestational age in the second trimester,” Acta Obstet Gynecol Scand, vol. 65, no. 5, pp. 481-3, 1986.
F.A. Chervenak, D.W. Skupski, R. Romero, M.K. Myers, M. Smith-Levitin, Z. Rosenwaks, and H.T. Thaler, “How accurate is fetal biometry in the assessment of fetal age?,” Am J Obstet Gynecol, vol.178, no.4, pp.678-87, Apr, 1998.
T.N. Leung, M.W. Pang, S.S. Daljit, T.Y. Leung, C.F. Poon, S.M. Wong, and T.K. Lau, “Fetal biometry in ethnic Chinese: biparietal diameter, head circumference, abdominal circumference and femur length,” Ultrasound Obstet Gynecol, vol.31, no.3, pp.321-7, Mar, 2008.
D.L. Gray, G.S. Songster, C.A. Parvin, and J.P. Crane, “Cephalic index: a gestational age-dependent biometric parameter,” Obstet Gynecol, vol.74, no.4, pp.600-3, Oct, 1989.
P. Taipale, and V. Hiilesmaa, “Predicting delivery date by ultrasound and last menstrual period in early gestation,” Obstet Gynecol, vol.97, no.2, pp.189-94, Feb, 2001.
D.A. Guidetti, M.Y. Divon, J.J. Braverman, O. Langer, and I.R. Merkatz, “Sonographic estimates of fetal weight in the intrauterine growth retardation population,” Am J Perinatol, vol.7, no.1, pp.5-7, Jan, 1990.
G. Jacobsen, “Detection of intrauterine growth deviation. A comparison between symphysis-fundus height and ultrasonic measurements,” Int J Technol Assess Health Care, vol.8, pp.170-5, 1992.
F.P. Hadlock, R.B. Harrist, R.J. Carpenter, R.L. Deter, and S.K. Park, “Sonographic estimation of fetal weight. The value of femur length in addition to head and abdomen measurements,” Radiology, vol.150, no.2, pp.535-40, Feb, 1984.
F.M. Chang, R.I. Liang, H.C. Ko, B.L. Yao, C.H. Chang, and C.H. Yu, “Three-dimensional ultrasound-assessed fetal thigh volumetry in predicting birth weight,” Obstet Gynecol, vol.90, no.3, pp.331-9, Sep, 1997.
R.L. Schild, R. Fimmers, and M. Hansmann, “Fetal weight estimation by three-dimensional ultrasound,” Ultrasound Obstet Gynecol, vol.16, no.5, pp.445-52, Oct, 2000.
R. M. Farmer, A. L. Medearis, G. I. Hirata, and L. D. Platt, “The use of a neural network for the ultrasound estimation of fetal weight in the macrosomic fetus,” Am J Obstet Gynecol, vol. 166, no.5, pp. 1467-72, May, 1992.
L. Chuang, J. Y. Hwang, C. H. Chang, C. H. Yu, and F. M. Chang, “Ultrasound estimation of fetal weight with the use of computerized artificial neural network model,” Ultrasound Med Biol vol. 28, no. 8, pp. 991-6, Aug, 2002.
Richard A. Johnson and Dean W. Wichern, “Applied Multivariate Statistical Analysis sixth edition,” U.S.A., Pearson Prentice Hill, 2007,chap.8,pp.430.
S.R. Veena, G.V. Krishnaveni, A.K. Wills, J.C. Hill, and C.H. Fall, “A principal components approach to parent-to-newborn body composition associations in South India,” BMC Pediatr, vol.24, no.9:16, pp.1-11, Feb, 2009.
J. B. MacQueen, “Some Methods for classification and Analysis of Multivariate Observations,” in Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, vol.1, pp. 281-97, 1967.
L. Zhang, G.W. Small, A.S. Haka, L.H. Kidder, and E.N. Lewis, “Classification of Fourier transform infrared microscopic imaging data of human breast cells by cluster analysis and artificial neural networks,” Appl Spectrosc, vol.57, no.1, pp.14-22, Jan, 2003.
E. Salamalekis, P. Thomopoulos, D. Giannaris, I. Salloum, G. Vasios, A. Prentza, and D. Koutsouris, “Computerised intrapartum diagnosis of fetal hypoxia based on fetal heart rate monitoring and fetal pulse oximetry recordings utilising wavelet analysis and neural networks,” BJOG, vol.109, no.10, pp.1137-42, Oct, 2002.
L. Fausett, “Fundamentals of Neural Networks: an architectures, algorithms, and applications,” Prentice Hall ,1994.
I. Etikan, and M.K.Caglar, “Prediction methods for babies' birth weight using linear and nonlinear regression analysis,” Technol Health Care, vol.13, no.2, pp.131-5, 2005.
S. Kol, I. Thaler, N. Paz, and O. Shmueli, “Interpretation of nonstress tests by an artificial neural network,” Am J Obstet Gynecol, vol.172, no. 5, pp.1372-9, May, 1995.
J.M. Miller,G.A. Kissling, H.L. Brown, and H.A. Gabert, “Estimated fetal weight: applicability to small- and large-for-gestational-age fetus,” J Clin Ultrasound,vol.16, no.2, pp.95-7, Feb, 1988.
Y.C. Cheng, G.L. Yan, Y.H. Chiu, F.M. Chang, C.H. Chang, K.C. Chung, “Efficient fetal size classification combined with artificial neural network for estimation of fetal weight,” Taiwan J Obstet Gynecol, vol.51, no.4, pp.545-53, Dec, 2012.
F.P. Hadlock, R.L. Deter, R.B. Harrist, and S.K. Park, “Fetal biparietal diameter: rational choice of plane of section for sonographic measurement,” AJR Am J Roentgenol, vol.138, no.5, pp.871-4, May, 1982.
S. Campbell, “An improved method of fetal cephalometry by ultrasound,” J Obstet Gynaecol Br Commonw, vol.75, no.5, pp.568-76, May, 1968.
C. B. Benson and P. M. Doubilet, “Sonographic prediction of gestational age: accuracy of second- and third-trimester fetal measurements,” AJR Am J Roentgenol, vol.157, no.6, pp.1275-7, Dec, 1991.
F.P. Hadlock, R.B. Harrist, Y.P. Shah, D.E. King, S.K. Park, and R.S. Sharman, “Estimating fetal age using multiple parameters: a prospective evaluation in a racially mixed population,” Am J Obstet Gynecol, vol.156, no.4, pp.955-7, Apr, 1987.
K.A. Ruvolo, R.A. Filly, and P.W. Callen, “Evaluation of fetal femur length for prediction of gestational age in a racially mixed obstetric population,” J Ultrasound Med, vol.6, no.8, pp.417-9, Aug, 1987.
N. Melamed, A. Ben-Haroush, I. Meizner, R. Mashiach, M. Glezerman, and Y. Yogev, “Accuracy of sonographic weight estimation as a function of fetal sex,” Ultrasound Obstet Gynecol, vol. 38, no. 1, pp. 67-73, Jul. 2011.
N. Melamed, A. Ben-Haroush, I. Meizner, R. Mashiach, Y. Yogev, and J. Pardo, “Accuracy of sonographic fetal weight estimation: a matter of presentation,” Ultrasound Obstet Gynecol, vol.38, no. 4, pp.418-24, Oct, 2011.
M. Wilcox, J. Gardosi, M. Mongelli, C. Ray, and I. Johnson, “Birth weight from pregnancies dated by ultrasonography in a multicultural British population,” BMJ, vol. 307, no. 6904, pp. 588-91, Sep, 1993.
R. L. Gorsuch, “Exploratory factor analysis: its role in item analysis,” Journal of Personality Assessment, vol. 68, no. 3, pp. 532-60, Jun, 1997.
P. W. Lei, S. B. Dunbar, and M. J. Kolen, “A Comparison of parametric and nonparametric approaches to item analysis for multiple-choice tests,” Educational and Psychological Measurement”, vol. 64, no. 4, pp. 565-87, Aug, 2004.
J. A. Hartigan, and M. A. Wang, “A K-means clustering algorithm,” Applied Statistics, vol. 28, pp. 100-8, 1979.
 D. S. Modha, and W. S. Spangler, “Feature Weighting in k-Means Clustering,” Machine Learning, vol. 52, no. 3, pp. 217-37, 2003.
S. A. Billings, and W. S. F. Voon, “A prediction-error and stepwise-regression estimation algorithm for non-linear systems,” Int J Control, vol. 44, no. 3, pp. 803-22, 1986.
D. A. Henderson, and D. R. Denison, “Stepwise regression in social and psychological research,” Psychological Reports, vol. 64, pp. 251-7, 1989.
R.R. Castro, M. Magini, S. Pedrosa, A.R. Sales, and A.C. Nóbrega, “ Principal components analysis to evaluate ventilatory variability: comparison of athletes and sedentary men,” Med Biol Eng Comput, vol.49, no.3, pp.305-11, Mar, 2011.
D. Rosenberg, A. Handler, and S. Furner, “A new method for classifying patterns of prenatal care utilization using cluster analysis,” Matern Child Health J, vol.8, no.1, pp.19-30, Mar, 2004.
P. S. La Rosa, A. Nehorai, H. Eswaran, C. L. Lowery, and H. Preissl, “Detection of uterine MMG contractions using a multiple change point estimator and the K-means cluster algorithm,” IEEE Trans Biomed Eng, vol. 55, no. 2, pp. 453-67, Feb, 2008.
W. G. Baxt, “Application of artificial neural networks to clinical medicine,” Lancet, vol. 346, no. 8983, pp. 1135-8, 1995.
H. Akaike, “A new look at the statistical model identification,” IEEE Transactions on Automatic Control, vol. 19, pp.716-23, 1974.
K.P. Burnham, and D.R. Anderson, “Multimodel inference: understanding AIC and BIC in Model Selection,” Sociological Methods and Research, vol.33, no.2, pp.261-304, 2004.
J. Bibby, H. Toutenburg, “Prediction and Improved Estimation in Linear Models,” John Wiley & Sons Inc, 1978.
S. S. Cross, R. F. Harrison, and R. L. Kennedy, “Introduction to neural networks,” Lancet, vol. 346, no.8982, pp. 1075-9, Oct, 1995.
C. P. Chen, F. M. Chang, C. H. Chang, Y. S. Lin, C. Y. Chou , and H. C. Ko, “Prediction of fetal macrosomia by single ultrasonic fetal biometry,” J Formosan Med Assoc, vol. 92, no. 1, pp. 24-8, Jan, 1993.
S. P. Chauhan, E. F. Magann, R. W. 3rd Naef, J. N. Jr Martin, J. C. Morrison , “Sonographic assessment of birth weight among breech presentations,” Ultrasound Obstet Gynecol, vol. 6, no.1, pp. 54-7, Jul,1995.
R. O. Davis, G. R. Cutter, R. L. Goldenberg, H. J. Hoffman, S. P. Cliver , and C. G. Brumfield, “Fetal biparietal diameter, head circumference, abdominal circumference and femur length. A comparison by race and sex,” J Reprod Med, vol. 38, no. 3, pp. 201-6, Mar, 1993.
J. Siemer, A. Hilbert, T. Wolf, N. Hart, A. Müller, and R. L. Schild, “ Gender-specific weight estimation of fetuses between 2,501 and 3,999 g--new regression formulae,” Fetal Diagn Ther, vol. 24, no. 3, pp. 304-9, Oct, 2008.
R. L. Schild, C. Sachs, R. Fimmers, U. Gembruch and M. Hansmann, “ Sex-specific fetal weight prediction by ultrasound,” Ultrasound Obstet Gynecol, vol. 23, no. 1, pp. 30-5, Jan, 2004.
C.P. Chen, “ Prenatal sonographic features of fetuses in trisomy 13 pregnancies (I),” Taiwan J Obstet Gynecol, vol.48, pp.210-7, 2009.
C.P. Chen, “Prenatal sonographic features of fetuses in trisomy 13 pregnancies (II),” Taiwan J Obstet Gynecol, vol.48, pp.218-24, 2009.
C.P. Chen, “Prenatal sonographic features of fetuses in trisomy 13 pregnancies (III),” Taiwan J Obstet Gynecol, vol.48, pp.342-9, 2009.
C.P. Chen, “Prenatal sonographic features of fetuses in trisomy 13 pregnancies (IV),” Taiwan J Obstet Gynecol, vol. 49, pp. 3-12, 2010.
C.P. Chen, “Prenatal diagnosis and genetic counseling for mosaic trisomy 13,” Taiwan J Obstet Gynecol, vol. 49, pp.13-22, 2010.
C.P. Chen, “Prenatal diagnosis, fetal surgery, recurrence risk and differential diagnosis of neural tube defects,” Taiwan J Obstet Gynecol, vol.47, pp.283-90, 2008.
S.C. Lu, C.H. Chang, C.H. Yu, L. Kang, P.Y. Tsai, and F.M. Chang, “Reappraisal of fetal abdominal circumference in an Asian population: analysis of 50,131 records,” Taiwan J Obstet Gynecol, vol.47, pp.49-56, 2008.