Statistical Methods for Ordinal Variables in HIV/AIDS Studies

摘要 艾滋病生物医学研究中的许多重要变量都是可排序的，一些统计方法 有序分类数据可以应用于连续数据，提供强大的分析方法， 比标准方法更少的假设。在第一轮赠款中，我们开发了一种新的剩余资金， 有序的结果，我们表明，斯皮尔曼的偏相关性可以计算使用这个新的 残差，我们演示了累积概率模型（CPM;也称为累积 链接模型）的连续响应变量。在这次更新申请中，我们专注于新颖和令人兴奋的 这些方法的扩展可能对艾滋病毒/艾滋病和其他疾病的分析产生重大影响， 生物医学数据。首先，分析连续响应的模型通常保留为有序的 分类数据是创新的，允许非常灵活的建模-特别是需要某种分类的数据。 和/或具有检测极限（例如，HIV病毒载量）。我们建议调查渐近 这些技术的性质，将其扩展到重复测量数据使用广义估计 方程的方法，并开发他们的设置与多个检测限。第二，我们的延伸 斯皮尔曼的等级相关消除了协变量的影响，或以协变量为条件，填补了 统计文献，并将在实践中普遍采用的斯皮尔曼的相关性， 生物医学研究我们建议扩展我们的方法来估计秩相关，两个协变量- 调整和未调整，双变量生存数据和纵向或集群数据之间。最后，在这个 在大数据时代，需要能够以计算高效的方式执行这些技术。 我们建议研究分而联合收割机和其他技术来拟合CPM和协变量调整 大型数据集中的斯皮尔曼相关性。我们将把我们的方法打包成免费的软件， 将我们的分析应用于艾滋病毒/艾滋病的重要研究。

ABSTRACT Many important variables in biomedical studies of HIV/AIDS are orderable, and some statistical methods for ordered categorical data can be applied to continuous data, providing robust analysis approaches that make fewer assumptions than standard approaches. In the first cycle of our grant, we developed a new residual for orderable outcomes, we showed that Spearman's partial correlation can be computed using this new residual, and we demonstrated the use of cumulative probability models (CPMs; also known as cumulative link models) with continuous response variables. In this renewal application, we focus on novel and exciting extensions of these methods that could have a large impact on the analysis of HIV/AIDS and other biomedical data. First, the analysis of continuous responses with models typically reserved for ordered categorical data is innovative and permits very flexible modeling – particularly of data that require some sort of transformation and/or have detection limits (e.g., HIV viral load). We propose to investigate the asymptotic properties of these techniques, extend them to repeated measures data using generalized estimating equations approaches, and develop them for settings with multiple detection limits. Second, our extension of Spearman's rank correlation to remove the effect of, or to condition on, covariates fills an important gap in the statistical literature and will be commonly employed in practice given the ubiquity of Spearman's correlation in biomedical studies. We propose to extend our approach to estimate the rank correlation, both covariate- adjusted and unadjusted, between bivariate survival data and to longitudinal or clustered data. Finally, in this era of big data, there is a need to be able to perform these techniques in a computationally efficient manner. We propose to study divide-and-combine and other techniques for fitting CPMs and covariate-adjusted Spearman's correlations in large datasets. We will package our methods in freely available software and apply our analyses to important studies of HIV/AIDS.