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Biostatistics Advance Access published online on December 1, 2007
Biostatistics, doi:10.1093/biostatistics/kxm040
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© The Author 2007. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Bayesian modeling of embryonic growth using latent variables

James C. Slaughter*

Department of Biostatistics, Vanderbilt University School of Medicine, T-2319 Medical Center North, Nashville, TN 37232-2158, USA james.c.slaughter{at}vanderbilt.edu

Amy H. Herring

Department of Biostatistics, McGavran-Greenberg Hall, CB 7420, and Carolina Population Center, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-7420, USA

Katherine E. Hartmann

Institute for Medicine and Public Health, Vanderbilt University Medical Center, Suite 6000, Medical Center East, Nashville, TN 37232-0014, USA

* To whom correspondence should be addressed.

In a growth model, individuals move progressively through a series of states in which each state is indicative of developmental status. Interest lies in estimating the rate of progression through each state while incorporating covariates that might affect the transition rates. We develop a Bayesian discrete-time multistate growth model for inference from cross-sectional data with unknown initiation times. For each subject, data are collected at only one time point at which we observe the state as well as covariates that measure developmental progress. We link the developmental progress variables to an underlying latent growth variable that can also affect the state transition rates. A subject with slow latent growth will then have relatively small developmental progress covariates and move through state transitions slowly. We then examine the association between latent growth and the probability of future events in a novel study of embryonic development and pregnancy loss. Using a Markov chain Monte Carlo (MCMC) algorithm for posterior computation, we found evidence in favor of a previously hypothesized but unproven association between slow growth early in pregnancy and increased risk of future spontaneous abortion.

Keywords: Bayesian; Current status; Data augmentation; Interval censoring; Latent variable; Pregnancy; Structural equations

Received October 27, 2006; revised September 7, 2007; accepted for publication September 18, 2007.


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