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.
Stat Methods Med Res. 2018 Sep;27(9):2775-2794. doi: 10.1177/0962280216686628. Epub 2017 Jan 8.
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.
纵向有序分类资料在生物医学研究中很常见。尽管在过去几十年中已经提出了多种分析此类数据的方法，但它们在几个方面受到限制。例如，比例优势模型中参数的限制可能导致收敛问题；基于等级的对齐秩变换方法对其他参数和与参数模型的分布假设施加限制。我们提出了一种新的基于等级的非参数方法，该方法对数据的分布而不是数据的分布进行建模，从而在没有约束条件的情况下进行有效的统计推断。我们首先构建交互作用的检验统计量，然后分别构建有或没有交互作用的主效应的检验统计量，同时推导出结的情况下的“调整系数”。进行了模拟研究，比较了基于等级的非参数和等级转换方差分析。结果表明，两种方法的 I 型错误都更接近先验水平，但基于等级的非参数的统计功效大于等级转换方差分析，表明前者效率更高。然后我们将基于等级的非参数方法应用于痤疮和骨质疏松症的两项真实研究，结果也说明了基于等级的非参数的有效性，特别是在分布偏斜的情况下。
