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Computational and Mathematical Methods in Medicine
Volume 2016, Article ID 7329158, 8 pages
Research Article

Sufficient Sample Size and Power in Multilevel Ordinal Logistic Regression Models

1Department of Statistics, Islamia College University, Peshawar, Pakistan
2Department of Statistics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa, Pakistan
3Department of Statistics, Shaheed Benazir Bhutto Women University, Peshawar, Pakistan

Received 13 June 2016; Revised 12 August 2016; Accepted 24 August 2016

Academic Editor: Zoran Bursac

Copyright © 2016 Sabz Ali et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For most of the time, biomedical researchers have been dealing with ordinal outcome variable in multilevel models where patients are nested in doctors. We can justifiably apply multilevel cumulative logit model, where the outcome variable represents the mild, severe, and extremely severe intensity of diseases like malaria and typhoid in the form of ordered categories. Based on our simulation conditions, Maximum Likelihood (ML) method is better than Penalized Quasilikelihood (PQL) method in three-category ordinal outcome variable. PQL method, however, performs equally well as ML method where five-category ordinal outcome variable is used. Further, to achieve power more than 0.80, at least 50 groups are required for both ML and PQL methods of estimation. It may be pointed out that, for five-category ordinal response variable model, the power of PQL method is slightly higher than the power of ML method.