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Likelihood Inferences on Semiparametric Odds Ratio Model

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  • Hua Yun Chen
  • Daniel E. Rader
  • Mingyao Li

Abstract

A flexible semiparametric odds ratio model has been proposed to unify and to extend both the log-linear model and the joint normal model for data with a mix of discrete and continuous variables. The semiparametric odds ratio model is particularly useful for analyzing biased sampling designs. However, statistical inference of the model has not been systematically studied when more than one nonparametric component is involved in the model. In this article, we study the maximum semiparametric likelihood approach to estimation and inference of the semiparametric odds ratio model. We show that the maximum semiparametric likelihood estimator of the odds ratio parameter is consistent and asymptotically normally distributed. We also establish statistical inference under a misspecified semiparametric odds ratio model, which is important when handling weak identifiability in conditionally specified models under biased sampling designs. We use simulation studies to demonstrate that the proposed approaches have satisfactory finite sample performance. Finally, we illustrate the proposed approach by analyzing multiple traits in a genome-wide association study of high-density lipid protein. Supplementary materials for this article are available online.

Suggested Citation

  • Hua Yun Chen & Daniel E. Rader & Mingyao Li, 2015. "Likelihood Inferences on Semiparametric Odds Ratio Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1125-1135, September.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:511:p:1125-1135
    DOI: 10.1080/01621459.2014.948544
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    References listed on IDEAS

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    1. Gerhard Osius, 2004. "The association between two random elements: A complete characterization and odds ratio models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(3), pages 261-277, November.
    2. Hua Yun Chen, 2011. "A unified framework for studying parameter identifiability and estimation in biased sampling designs," Biometrika, Biometrika Trust, vol. 98(1), pages 163-175.
    3. Zhu, Hongtu & Zhang, Heping, 2006. "Asymptotics for estimation and testing procedures under loss of identifiability," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 19-45, January.
    4. Chen, Hua Yun, 2010. "Compatibility of conditionally specified models," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 670-677, April.
    5. Hua Yun Chen, 2003. "A note on the prospective analysis of outcome‐dependent samples," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 575-584, May.
    6. Lin, D.Y. & Zeng, D., 2006. "Likelihood-Based Inference on Haplotype Effects in Genetic Association Studies," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 89-104, March.
    7. Alan Huang & Paul J. Rathouz, 2012. "Proportional likelihood ratio models for mean regression," Biometrika, Biometrika Trust, vol. 99(1), pages 223-229.
    8. Nilanjan Chatterjee & Raymond J. Carroll, 2005. "Semiparametric maximum likelihood estimation exploiting gene-environment independence in case-control studies," Biometrika, Biometrika Trust, vol. 92(2), pages 399-418, June.
    9. Chen, Yi-Hau & Chatterjee, Nilanjan & Carroll, Raymond J., 2009. "Shrinkage Estimators for Robust and Efficient Inference in Haplotype-Based Case-Control Studies," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 220-233.
    10. Hua Yun Chen, 2004. "Nonparametric and Semiparametric Models for Missing Covariates in Parametric Regression," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1176-1189, December.
    11. Leonard Feldt, 1961. "The use of extreme groups to test for the presence of a relationship," Psychometrika, Springer;The Psychometric Society, vol. 26(3), pages 307-316, September.
    12. Kung‐Yee Liang & Jing Qin, 2000. "Regression analysis under non‐standard situations: a pairwise pseudolikelihood approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 773-786.
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