Statistical Methods for Ordinal Variables in HIV/AIDS Studies

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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.