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Stat Methods Med Res. 2018 Sep;27(9):2775-2794. doi: 10.1177/0962280216686628. Epub 2017 Jan 8.

A novel rank-based non-parametric method for longitudinal ordinal data.

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1 Department of Biostatistics, Guangdong Provincal Key Laboratory of Tropical Disease Research, School of Public Health, Southern Medical University, People's Republic of China.
2 School of traditional Chinese medicine, Southern Medical University, People's Republic of China.
3 Department of Biostatistics, Bioinformatics and Biomathematics, Georgetown University Medical Center, USA.
4 State Key Laboratory of Organ Failure Research, Southern Medical University, People's Republic of China.


Longitudinal ordinal data are common in biomedical research. Although various methods for the analysis of such data have been proposed in the past few decades, they are limited in several ways. For instance, the constraints on parameters in the proportional odds model may result in convergence problems; the rank-based aligned rank transform method imposes constraints on other parameters and the distributional assumptions with parametric model. We propose a novel rank-based non-parametric method that models the profile rather than the distribution of the data to make an effective statistical inference without the constraint conditions. We construct the test statistic of the interaction first, and then construct the test statistics of the main effects separately with or without the interaction, while "adjusted coefficient" for the case of ties is derived. A simulation study is conducted for comparison between rank-based non-parametric and rank-transformed analysis of variance. The results show that type I errors of the two methods are both maintained closer to the priori level, but the statistical power of rank-based non-parametric is greater than that of rank-transformed analysis of variance, suggesting higher efficiency of the former. We then apply rank-based non-parametric to two real studies on acne and osteoporosis, and the results also illustrate the effectiveness of rank-based non-parametric, particularly when the distribution is skewed.


Central limit theorem; longitudinal ordinal data; non-parametric method; profiles; rank

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