Experimental Medicine, Vol. 1, Issue 2, Dec  2018, Pages 45-65; DOI: 10.31058/j.em.2018.12004 10.31058/j.em.2018.12004

Fetal Weight Estimation in Case of Missing Data

, Vol. 1, Issue 2, Dec  2018, Pages 45-65.

DOI: 10.31058/j.em.2018.12004

Loc Nguyen 1* , Thu-Hang T. Ho 2

1 Independent Scholar, Loc Nguyen’s Academic Network, An Giang, Vietnam

2 Board of Directors, Vinh Long General Hospital, Vinh Long, Vietnam

Received: 5 July 2018; Accepted: 30 September 2018; Published: 17 December 2018

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Fetal weight estimation before delivery is important in obstetrics, which assists doctors diagnose abnormal or diseased cases. Linear regression based on ultrasound measures such as bi-parietal diameter (bpd), head circumference (hc), abdominal circumference (ac), and fetal length (fl) is common statistical method for weight estimation. There is a demand to retrieve regression model in case of incomplete data because taking ultrasound examinations is a hard task and early weight estimation is necessary in some cases. In this research, we proposed so-called regression expectation maximization (REM) algorithm which is a combination of linear regression method and expectation maximization (EM) method to construct the regression model when both ultrasound measures and fetal weight are missing. The special technique in REM is to build parallelly an entire regression function and many partial inverse regression functions for solving the problem of highly sparse data, in which missing values are fulfilled by expectations relevant to both entire regression function and inverse regression functions. Experimental results proved resistance of REM to incomplete data, in which accuracy of REM decreases insignificantly when data sample is made sparse with loss ratios up to 80%.


Fetal Weight Estimation, Regression Model, Ultrasound Measures, Expectation Maximization Algorithm, Missing Data


© 2017 by the authors. Licensee International Technology and Science Press Limited. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


[1] Nguyen, L.; Ho, T.-H. T. Early Fetal Weight Estimation with Expectation Maximization Algorithm. Experimental Medicine (EM), 2018, 1(1), 12-30, DOI:10.31058/j.em.2018.11002.

[2] Hadlock, F. P.; Harrist, R. B.; Sharman, R. S.; Deter, R. L.; Park, S. K. Estimation of fetal weight with use of head, body and femur measurements: A prospective study. American Journal of Obstetrics and Gynecology, 1st February 1985, 151(3), 333-337, DOI: 10.1016/0002-9378(85)90298-4.

[3] Phan, D. T. Application of Ultrasonography to Diagnose Fetal Age and Weight in Mother Womb. Hanoi Medical University: Hanoi, 1985.

[4] Pham, T.-N. T. Fetal Weight Estimation by Ultrasound Measures. Ho Chi Minh University of Medicine and Pharmacy: Ho Chi Minh, 2000.

[5] Ho, T. H. T. Research on Fetal Age and Weight Estimation by Two-Dimensional and Three-Dimensional Ultrasound Measures. Hanoi Medical University: Hanoi, 2011, DOI: 10.13140/RG.2.2.33184.48645.

[6] Deter, R. L.; Rossavik, I. K.; Harrist, R. B. Development of individual growth curve standards for estimated fetal weight: I. Weight estimation procedure. Journal of Clinical Ultrasound, 1988, 16(4), 215-225. Available online: https://www.ncbi.nlm.nih.gov/pubmed/3152508 (accessed on Day Month Year).

[7] Chien, P. F. W.; Owen, P.; Khan, K. S. Validity of Ultrasound Estimation of Fetal Weight. Obstetrics & Gynecology, 2000, 95(6), 856-860, DOI: 10.1016/S0029-7844(00)00828-0.

[8] Varol, F.; Saltik, A.; Kaplan, P. B.; Kilic, T.; Yardim, T. Evaluation of Gestational Age Based on Ultrasound Fetal Growth Measurements. Yonsei Medical Journal, 2001, 42(3), 299-303, DOI:10.3349/ymj.2001.42.3.299.

[9] Dudley, N. J. A systematic review of the ultrasound estimation of fetal weight. Ultrasound in Obstetrics and Gynecology: The Official Journal of the International Society of Ultrasound in Obstetrics and Gynecology, 2004, 25(1), 80-89, DOI:10.1002/uog.1751.

[10] Salomon, L. J.; Bernard, J. P.; Ville, Y. Estimation of fetal weight: reference range at 20–36 weeks’ gestation and comparison with actual birth-weight reference range. Ultrasound in obstetrics & gynecology, 2007, 29(5), 550-555, DOI: 10.1002/uog.4019.

[11] Akinola, R. A.; Akinola, O. I.; Oyekan, O. O. Sonography in fetal birth weight estimation. Educational Research and Review, 2009, 4(1), 16-20.

[12] Lee, W.; Balasubramaniam, M.; Deter, R. L.; Yeo, L.; Hassan, S. S.; Gotsch, F.; Kusanovic, J. P.; Gonçalves, L. F.; Romero, R. New fetal weight estimation models using fractional limb volume. Ultrasound in Obstetrics & Gynecology, 2009, 34(5), 556-565, DOI: 10.1002/uog.7327.

[13] Bennini, J. R.; Marussi, E. F.; Barini, R.; Faro, C.; Peralta, C. A. F. Birth-weight prediction by two- and three-dimensional ultrasound imaging. Ultrasound in Obstetrics & Gynecology, 2009, 35(4), 426-433, DOI: 10.1002/uog.7518.

[14] Cohen, J. M.; Hutcheon, J. A.; Kramer, M. S.; Joseph, K. S.; Abenhaim, H.; Platt, R. W. Influence of ultrasound-to-delivery interval and maternal–fetal characteristics on validity of estimated fetal weight. Ultrasound in Obstetrics & Gynecology, 2010, 35(4), 434-441, DOI: 10.1002/uog.7506.

[15] Siggelkow, W.; Schmidt, M.; Skala, C.; Boehm, D.; Forstner, S. v.; Koelb, H.; Tresch, A. A new algorithm for improving fetal weight estimation from ultrasound data at term. Archives of gynecology and obstetrics, 2010, 283(3), 469-474, DOI: 10.1007/s00404-010-1390-8.

[16] Wu, M.; Shao, G.; Zhang, F.; Ruan, Z.; Xu, P.; Ding, H. Estimation of fetal weight by ultrasonic examination. International Journal of Clinical and Experimental Medicine, 2015, 8(1), 540-545. Available online: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4358483 (accessed on 11 July 2018).

[17] Pinette, M. G.; Pan, Y.; Pinette, S. G.; Blackstone, J.; Garrett, J.; Cartin, A. Estimation of Fetal Weight: Mean Value from Multiple Formulas. Journal of Ultrasound in Medicine, 1999, 18(12), 813-817. Available online: https://www.ncbi.nlm.nih.gov/pubmed/10591444 (accessed on 11 July 2018).

[18] Hutcheon, J. A.; Platt, R. W. The Missing Data Problem in Birth Weight Percentiles and Thresholds for “Small-for-Gestational-Age. American Journal of Epidemiology, 2008, 167(7), 786-792, DOI: 10.1093/aje/kwm327.

[19] Eberg, M.; Platt, R. W.; Filion, K. B. The Estimation of Gestational Age at Birth in Database Studies. Epidemiology, 2017, 28(6), 854-862, DOI: 10.1097/EDE.0000000000000713.

[20] Kokic, P. The EM Algorithm for a Multivariate Regression Model: including its applications to a non-parametric regression model and a multivariate time series model. Qantaris GmbH, Frankfurt, 2002. Available online: https://www.cs.york.ac.uk/euredit/_temp/The%20Euredit%20Software/NAG%20Prototype%20platform/WorkingPaper4.pdf (accessed on 11 July 2018).

[21] Ghitany, M. E.; Karlis, D.; Al-Mutairi, D. K.; Al-Awadhi, F. An EM Algorithm for Multivariate Mixed Poisson Regression Models and its Application. Applied Mathematical Sciences, 2012, 6(137), 6843-6856. Available online: http://www.m-hikari.com/ams/ams-2012/ams-137-140-2012/ghitanyAMS137-140-2012.pdf (accessed on 11 July 2018).

[22] Anderson, B.; Hardin, M. J. Modified logistic regression using the EM algorithm for reject inference. International Journal of Data Analysis Techniques and Strategies, 2013, 5(4), 359-373, DOI: 10.1504/IJDATS.2013.058582.

[23] Zhang, X.; Deng, J.; Su, R. The EM algorithm for a linear regression model with application to a diabetes data. In Proceedings of the 2016 International Conference on Progress in Informatics and Computing (PIC), Shanghai, China, 2016, DOI: 10.1109/PIC.2016.7949477.

[24] Haitovsky, Y. Missing Data in Regression Analysis. Journal of the Royal Statistical Society: Series B (Methodological), 1968, 30(1), 67-82. Available online: https://www.jstor.org/stable/2984459 (accessed on 11 July 2018).

[25] Robins, J. M.; Rotnitzki, A.; Zhao, L. P. Analysis of Semiparametric Regression Models for Repeated Outcomes in the Presence of Missing Data. Journal of the American Statistical Association, 1995, 90(429), 106-121, DOI: 10.2307/2291134.

[26] Horton, N. J.; Kleinman, K. P. Much ado about nothing: A comparison of missing data methods and software to fit incomplete data regression models. The American Statistician, 2007, 61(1), 79-90, DOI: 10.1198/000313007X172556.

[27] Lindsten, F.; Schön, T. B.; Svensson, A.; Wahlström, N. Probabilistic modeling – linear regression & Gaussian processes. Uppsala University, Uppsala, 2017. Available online: http://www.it.uu.se/edu/course/homepage/sml/literature/probabilistic_modeling_compendium.pdf (accessed on 24 January 2018).

[28] Dempster, A. P.; Laird, N. M.; Rubin, D. B. Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society, Series B (Methodological), 1977, 39(1), 1-38.

[29] Ho, T. H. T.; Phan, D. T. Fetal Weight Estimation from 37 Weeks to 42 Weeks by Two-Dimensional Ultrasound Measures. Journal of Practical Medicine, December, 2011, 12(797), 8-9.

[30] Ho, T. H. T.; Phan, D. T. Fetal Age Estimation by Three-Dimensional Ultrasound Measure of Arm Volume and Other Two-Dimensional Ultrasound Measures. Journal of Practical Medicine, 2011, 12(798), 12-15.

[31] Herlocker, J. L.; Konstan, J. A.; Terveen, L. G.; Riedl, J. T. Evaluating Collaborative Filtering Recommender Systems. ACM Transactions on Information Systems (TOIS), 2004, 22(1), 5-53, DOI: 10.1145/963770.963772.

[32] Montgomery, D. C.; Runger, G. C. Applied Statistics and Probability for Engineers, 5th ed.; John Wiley & Sons: Hoboken, New Jersey, USA, 2010; p. 792. Available online: https://books.google.com.vn/books?id=_f4KrEcNAfEC (accessed on 11 July 2018).

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