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A novel application of a bivariate regression model for binary and continuous outcomes to studies of fetal toxicity

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  • Julie S. Najita
  • Yi Li
  • Paul J. Catalano

Abstract

Public health concerns over the occurrence of birth defects and developmental abnormalities that may occur as a result of prenatal exposure to drugs, chemicals and other environmental factors has led to an increasing number of developmental toxicity studies. Because fetal pups are commonly evaluated for multiple outcomes, data analysis frequently involves a joint modelling approach. We focus on modelling clustered binary and continuous outcomes in the setting where both outcomes are potentially observable in all offspring but, owing to practical limitations, the continuous outcome is only observed in a subset of offspring. The subset is not a simple random sample but is selected by the experimenter under a prespecified probability model. Although joint models for binary and continuous outcomes have been developed when both outcomes are available for every fetus, many existing approaches are not directly applicable when the continuous outcome is not observed in a simple random sample. We adapt a likelihood-based approach for jointly modelling clustered binary and continuous outcomes when the continuous response is missing by design and missingness depends on the binary trait. The approach takes into account the probability that a fetus is selected in the subset. Through the use of a partial likelihood, valid estimates can be obtained by a simple modification to the partial likelihood score. Data involving the herbicide 2,4,5-trichlorophenoxyacetic-acid are analysed. Simulation results confirm the approach. Copyright (c) 2009 Royal Statistical Society.

Suggested Citation

  • Julie S. Najita & Yi Li & Paul J. Catalano, 2009. "A novel application of a bivariate regression model for binary and continuous outcomes to studies of fetal toxicity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(4), pages 555-573.
  • Handle: RePEc:bla:jorssc:v:58:y:2009:i:4:p:555-573
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    References listed on IDEAS

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    1. Ralitza V. Gueorguieva, 2005. "Comments about Joint Modeling of Cluster Size and Binary and Continuous Subunit-Specific Outcomes," Biometrics, The International Biometric Society, vol. 61(3), pages 862-866, September.
    2. Faes, Christel & Geys, Helena & Aerts, Marc & Molenberghs, Geert, 2006. "A hierarchical modeling approach for risk assessment in developmental toxicity studies," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1848-1861, December.
    3. Meredith M. Regan & Paul J. Catalano, 1999. "Likelihood Models for Clustered Binary and Continuous Out comes: Application to Developmental Toxicology," Biometrics, The International Biometric Society, vol. 55(3), pages 760-768, September.
    4. D. B. Dunson, 2000. "Bayesian latent variable models for clustered mixed outcomes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 355-366.
    5. David B. Dunson & Zhen Chen & Jean Harry, 2003. "A Bayesian Approach for Joint Modeling of Cluster Size and Subunit-Specific Outcomes," Biometrics, The International Biometric Society, vol. 59(3), pages 521-530, September.
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