A Comparison of Statistical Methods for Analyzing Discrete Hierarchical Data: A Case Study of Family Data on Alcohol Abuse

Abstract

Although hierarchical correlated data are increasingly available and are being used in evidence-based medical practices and health policy decision making, there is a lack of information about the strengths and weaknesses of the methods of analysis with such data. In this paper, we describe the use of hierarchical data in a family study of alcohol abuse conducted in Edmonton, Canada, that attempted to determine whether alcohol abuse in probands is associated with abuse in their first-degree relatives. We review three methods of analyzing discrete hierarchical data to account for correlations among the relatives. We conclude that the best analytic choice for typical correlated discrete hierarchical data is by nonlinear mixed effects modeling using a likelihood-based approach or multilevel (hierarchical) modeling using a quasilikelihood approach, especially when dealing with heterogeneous patient data.

Share and Cite:

Y. Liang and K. Carriere, "A Comparison of Statistical Methods for Analyzing Discrete Hierarchical Data: A Case Study of Family Data on Alcohol Abuse," Open Journal of Statistics, Vol. 3 No. 4A, 2013, pp. 1-6. doi: 10.4236/ojs.2013.34A001.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] H. Goldstein, “Nonlinear Multilevel Models, with an Application to Discrete Response Data,” Biometrika, Vol. 78, No. 1, 1991, pp. 45-51. doi:10.1093/biomet/78.1.45
[2] K. Y. Liang and S. L. Zeger, “Longitudinal Data-Analysis Using Generalized Linear-Models,” Biometrika, Vol. 73, No. 1, 1986, pp. 13-22. doi:10.1093/biomet/73.1.13
[3] S. C. Newman and R. C. Bland, “A Population-Based Family Study of DSM-III Generalized Anxiety Disorder,” Psychological Medicine, Vol. 36, No. 9, 2006, pp. 12751281. doi:10.1017/S0033291706007732
[4] N. Mantel and W. Haenszel, “Statistical Aspects of the Analysis of Data from Retrospective Studies of Disease,” Journal of the National Cancer Institute, Vol. 22, No. 4, 1959, pp. 719-748.
[5] J. C. Pinheiro and D. M. Bates, “Approximations to the Log-Likelihood Function in the Nonlinear Mixed-Effects Model,” Journal of Computational and Graphical Statistics, Vol. 4, No. 1, 1995, pp. 12-35.
[6] J. Nocedal and S. J. Wright, “Numerical Optimization,” Springer-Verlag, New York, 1999. doi:10.1007/b98874
[7] N. E. Breslow and D. G. Clayton, “Approximate Inference in Generalized Linear Mixed Models,” Journal of the American Statistical Association, Vol. 88, No. 421, 1993, pp. 9-25.
[8] H. Goldstein and J. Rasbash, “Improved Approximations for Multilevel Models with Binary Responses,” Journal of the Royal Statistical Society Series A—Statistics in Society, Vol. 159, 1996, pp. 505-513.
[9] Y. Yano, S. L. Beal and L. B. Sheiner, “Evaluating Pharmacokinetic/Pharmacodynamic Models Using the Posterior Predictive Check,” Journal of Pharmacokinetics and Pharmacodynamics, Vol. 28, No. 2, 2001, pp. 171-192. doi:10.1023/A:1011555016423
[10] P. J. Williams and E. I. Ette, “Determination of Model Appropriateness,” In: H. C. Kimko and S. B. Duffull, Eds., Simulation for Designing Clinical Trials: A Pharmacokinetic-Pharmacodynamic Modeling Prospective, Marcel Dekker, New York, 2003, pp. 68-96.
[11] F. Mentre and S. Escolano, “Prediction Discrepancies for the Evaluation of Nonlinear Mixed-Effects Models,” Journal of Pharmacokinetics and Pharmacodynamics, Vol. 33, No. 3, 2006, pp. 345-367. doi:10.1007/s10928-005-0016-4
[12] K. Y. Liang, S. L. Zeger and B. Qaqish, “Multivariate Regression Analysis for Categorical Data,” Journal of the Royal Statistical Society, Series B, Vol. 54, No. 1, 1992, pp. 3-40.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.