The Annals of Applied Statistics

Bayesian analysis of infant’s growth dynamics with in utero exposure to environmental toxicants

Jonggyu Baek, Bin Zhu, and Peter X. K. Song

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Early infancy from at-birth to 3 years is critical for cognitive, emotional and social development of infants. During this period, infant’s developmental tempo and outcomes are potentially impacted by in utero exposure to endocrine disrupting compounds (EDCs), such as bisphenol A (BPA) and phthalates. We investigate effects of ten ubiquitous EDCs on the infant growth dynamics of body mass index (BMI) in a birth cohort study. Modeling growth acceleration is proposed to understand the “force of growth” through a class of semiparametric stochastic velocity models. The great flexibility of such a dynamic model enables us to capture subject-specific dynamics of growth trajectories and to assess effects of the EDCs on potential delay of growth. We adopted a Bayesian method with the Ornstein–Uhlenbeck process as the prior for the growth rate function, in which the World Health Organization global infant’s growth curves were integrated into our analysis. We found that BPA and most of phthalates exposed during the first trimester of pregnancy were inversely associated with BMI growth acceleration, resulting in a delayed achievement of infant BMI peak. Such early growth deficiency has been reported as a profound impact on health outcomes in puberty (e.g., timing of sexual maturation) and adulthood.

Article information

Ann. Appl. Stat., Volume 13, Number 1 (2019), 297-320.

Received: July 2017
Revised: May 2018
First available in Project Euclid: 10 April 2019

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Body mass index Markov chain Monte Carlo (MCMC) Ornstein–Uhlenbeck process prenatal exposure semiparametric stochastic velocity model


Baek, Jonggyu; Zhu, Bin; Song, Peter X. K. Bayesian analysis of infant’s growth dynamics with in utero exposure to environmental toxicants. Ann. Appl. Stat. 13 (2019), no. 1, 297--320. doi:10.1214/18-AOAS1199.

Export citation


  • Afeiche, M., Peterson, K. E., Sanchez, B. N., Cantonwine, D., Lamadrid-Figueroa, H., Schnaas, L., Ettinger, A. S., Hernandez-Avila, M., Hu, H. and Tellez-Rojo, M. M. (2011). Prenatal lead exposure and weight of 0-to 5-year-old children in Mexico city. Environ. Health Perspect. 119 1436–1441.
  • Agarwal, D. K. and Gelfand, A. E. (2005). Slice sampling for simulation based fitting of spatial data models. Stat. Comput. 15 61–69.
  • Baek, J., Zhu, B. and Song, P. X. (2019). Supplement to “Bayesian analysis of infant’s growth dynamics with in utero exposure to environmental toxicants.” DOI:10.1214/18-AOAS1199SUPPA, DOI:10.1214/18-AOAS1199SUPPB.
  • Banister, C. E., Koestler, D. C., Maccani, M. A., Padbury, J. F., Houseman, E. A. and Marsit, C. J. (2011). Infant growth restriction is associated with distinct patterns of DNA methylation in human placentas. Epigenetics 6 920–927.
  • Binkin, N. J., Yip, R., Fleshood, L. and Trowbridge, F. L. (1988). Birth weight and childhood growth. Pediatrics 82 828–834.
  • Botton, J., Heude, B., Maccario, J., Ducimetière, P., Charles, M. A., Basdevant, A., Borys, J. M., Bresson, J. L., Froguel, P., Lommez, A., Oppert, J. M. and Romon, M. (2008). Postnatal weight and height growth velocities at different ages between birth and 5 y and body composition in adolescent boys and girls. Am. J. Clin. Nutr. 87 1760–1768.
  • Braun, J. M., Just, A. C., Williams, P. L., Smith, K. W., Calafat, A. M. and Hauser, R. (2014). Personal care product use and urinary phthalate metabolite and paraben concentrations during pregnancy among women from a fertility clinic. Journal of Exposure Science and Environmental Epidemiology 24 459–466.
  • Casals-Casas, C., Feige, J. N. and Desvergne, B. (2008). Interference of pollutants with PPARs: Endocrine disruption meets metabolism. Int. J. Obes. 32 S53–61.
  • Cole, T. J., Donaldson, M. D. C. and Ben-shlomo, Y. (2010). SITAR-a useful instrument for growth curve analysis. Int. J. Epidemiol. 39 1558–1566.
  • Diamanti-Kandarakis, E., Bourguignon, J.-P., Giudice, L. C., Hauser, R., Prins, G. S., Soto, A. M., Zoeller, R. T. and Gore, A. C. (2009). Endocrine-disrupting chemicals: An endocrine society scientific statement. Endocr. Rev. 30 293–342.
  • Durbán, M., Harezlak, J., Wand, M. P. and Carroll, R. J. (2005). Simple fitting of subject-specific curves for longitudinal data. Stat. Med. 24 1153–1167.
  • González-Cossío, T., Peterson, K. E., Sanín, L. H., Fishbein, E., Palazuelos, E., Aro, A., Hernández-Avila, M. and Hu, H. (1997). Decrease in birth weight in relation to maternal bone-lead burden. Pediatrics 100 856–862.
  • WHO Multicentre Growth Reference Study Group (2006). WHO Child Growth Standards: Length/Height-for-Age, Weight-for-Age, Weight-for-Length, Weight-for-Height and Body Mass Index-for-Age: Methods and Development. World Health Organization, Geneva.
  • Jenns, R. M. and Bayley, N. (1937). A mathematical method for studying growth in children. Hum. Neurobiol. 9 553–556.
  • Jensen, S. M., Ritz, C., Ejlerskov, K. T., Mølgaard, C. and Michaelsen, K. F. (2015). Infant BMI peak, breastfeeding, and body composition at age 3 y. Am. J. Clin. Nutr. 101 319–325.
  • Jones-Smith, J. C., Neufeld, L. M., Laraia, B., Ramakrishnan, U., Garcia-Guerra, A. and Fernald, L. C. H. (2013). Early life growth trajectories and future risk for overweight. Nutr. Diabetes 3 e60.
  • Kobrosly, R. W., Parlett, L. E., Stahlhut, R. W., Barrett, E. S. and Swan, S. H. (2012). Socioeconomic factors and phthalate metabolite concentrations among United States women of reproductive age. Environ. Res. 115 11–17.
  • López-Pintado, S. and McKeague, I. W. (2013). Recovering gradients from sparsely observed functional data. Biometrics 69 396–404.
  • Marie, C., Vendittelli, F. and Sauvant-Rochat, M. P. (2015). Obstetrical outcomes and biomarkers to assess exposure to phthalates: A review. Environ. Int. 83 116–136.
  • Marsee, K., Woodruff, T. J., Axelrad, D. A., Calafat, A. M. and Swan, S. H. (2006). Estimated daily phthalate exposures in a population of mothers of male infants exhibiting reduced anogenital distance. Environ. Health Perspect. 114 805–809.
  • McKeague, I. W., Lopez-Pintado, S., Hallin, M. and Siman, M. (2011). Analyzing growth trajectories. Journal of Developmental Origins of Health and Disease 2 322–329.
  • Neal, R. M. (2003). Slice sampling. Ann. Statist. 31 705–767.
  • Nhanes, I. (2009). Fourth national report on human exposure to environmental chemicals. In Department of Health and Human Services Centers for Disease Control and Prevention, Atlanta, GA.
  • Piaget, J. (2000). Piaget’s theory of cognitive development. In Childhood Cognitive Development: The Essential Readings 33–47.
  • Preece, M. A. and Baines, M. J. (1978). A new family of mathematical models describing the human growth curve. Ann. Hum. Biol. 5 1–24.
  • Rice, J. A. and Wu, C. O. (2001). Nonparametric mixed effects models for unequally sampled noisy curves. Biometrics 57 253–259.
  • Saarni, C. (1999). The Development of Emotional Competence. Guilford, New York.
  • Schettler, T. (2006). Human exposure to phthalates via consumer products. Int. J. Androl. 29 134–139.
  • Silverwood, R., De Stavola, B., Cole, T. and Leon, D. (2005). BMI peak in infancy as a predictor for later BMI in the uppsala family study. Int. J. Obes. 33 929–937.
  • Taylor, R. W., Grant, A. M., Goulding, A. and Williams, S. M. (2005). Early adiposity rebound: Review of papers linking this to subsequent obesity in children and adults. Curr. Opin. Clin. Nutr. Metab. Care 8 607–612.
  • Téllez-Rojo, M. M., Hernández-Avila, M., Lamadrid-Figueroa, H., Smith, D., Hernández-Cadena, L., Mercado, A., Aro, A., Schwartz, J. and Hu, H. (2004). Impact of bone lead and bone resorption on plasma and whole blood lead levels during pregnancy. Am. J. Epidemiol. 160 668–678.
  • Wahba, G. (1978). Improper priors, spline smoothing and the problem of guarding against model errors in regression. J. Roy. Statist. Soc. Ser. B 40 364–372.
  • Yao, F., Müller, H.-G. and Wang, J.-L. (2005). Functional data analysis for sparse longitudinal data. J. Amer. Statist. Assoc. 100 577–590.
  • Zhang, A., Hu, H., Sánchez, B. N., Ettinger, A. S., Park, S. K., Cantonwine, D., Schnaas, L., Wright, R. O., Lamadrid-Figueroa, H. and Tellez-Rojo, M. M. (2012). Association between prenatal lead exposure and blood pressure in children. Environ. Health Perspect. 120.
  • Zhao, Y., Shi, H. J., Xie, C. M., Chen, J., Laue, H. and Zhang, Y. H. (2015). Prenatal phthalate exposure, infant growth, and global DNA methylation of human placenta. Environ. Mol. Mutagen. 56 286–292.
  • Zhu, B., Taylor, J. M. G. and Song, P. X.-K. (2011). Semiparametric stochastic modeling of the rate function in longitudinal studies. J. Amer. Statist. Assoc. 106 1485–1495.

Supplemental materials

  • Supplement to “Bayesian analysis of infant’s growth dynamics with in utero exposure to environmental toxicants”. The supplementary document contains the details of the proposed MCMC algorithm and additional figures.
  • R code for NGM. An MCMC algorithm written in R code for the NGM is publicly available.