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Semiparametric Bayesian hierarchical models for heterogeneous population in nonlinear mixed effect model: application to gastric emptying studies

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  • Huaiye Zhang
  • Inyoung Kim
  • Chun Gun Park

Abstract

Gastric emptying studies are frequently used in medical research, both human and animal, when evaluating the effectiveness and determining the unintended side-effects of new and existing medications, diets, and procedures or interventions. It is essential that gastric emptying data be appropriately summarized before making comparisons between study groups of interest and to allow study the comparisons. Since gastric emptying data have a nonlinear emptying curve and are longitudinal data, nonlinear mixed effect (NLME) models can accommodate both the variation among measurements within individuals and the individual-to-individual variation. However, the NLME model requires strong assumptions that are often not satisfied in real applications that involve a relatively small number of subjects, have heterogeneous measurement errors, or have large variation among subjects. Therefore, we propose three semiparametric Bayesian NLMEs constructed with Dirichlet process priors, which automatically cluster sub-populations and estimate heterogeneous measurement errors. To compare three semiparametric models with the parametric model we propose a penalized posterior Bayes factor. We compare the performance of our semiparametric hierarchical Bayesian approaches with that of the parametric Bayesian hierarchical approach. Simulation results suggest that our semiparametric approaches are more robust and flexible. Our gastric emptying studies from equine medicine are used to demonstrate the advantage of our approaches.

Suggested Citation

  • Huaiye Zhang & Inyoung Kim & Chun Gun Park, 2014. "Semiparametric Bayesian hierarchical models for heterogeneous population in nonlinear mixed effect model: application to gastric emptying studies," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(12), pages 2743-2760, December.
  • Handle: RePEc:taf:japsta:v:41:y:2014:i:12:p:2743-2760
    DOI: 10.1080/02664763.2014.928848
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    1. P. Damlen & J. Wakefield & S. Walker, 1999. "Gibbs sampling for Bayesian non‐conjugate and hierarchical models by using auxiliary variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 331-344, April.
    2. Petrone, Sonia & Raftery, Adrian E., 1997. "A note on the Dirichlet process prior in Bayesian nonparametric inference with partial exchangeability," Statistics & Probability Letters, Elsevier, vol. 36(1), pages 69-83, November.
    3. Chib, Siddhartha & Greenberg, Edward, 2010. "Additive cubic spline regression with Dirichlet process mixture errors," Journal of Econometrics, Elsevier, vol. 156(2), pages 322-336, June.
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    1. Sun, Peng & Kim, Inyoung & Lee, Ki-Ahm, 2018. "Dual-semiparametric regression using weighted Dirichlet process mixture," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 162-181.

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