Statistical Methods for Ordinal Variables in HIV/AIDS Studies

ABSTRACT Many important variables in biomedical studies of HIV/AIDS are skewed, ordinal, or a mix of the two (e.g., data with detection limits). Rank-based statistical methods for ordered categorical data can be applied to these types of data, providing robust analysis approaches that make fewer assumptions than standard approaches. In past cycles of our grant, we developed semiparametric cumulative probability models (CPMs) to analyze skewed, ordinal, or mixed response data; we demonstrated good properties of these approaches theoretically, via simulations, and in real-world data; and we extended these approaches to settings with clustered data. In this renewal application, we focus on novel and exciting extensions of these methods that could have a large impact on the analysis of biomedical data. First, we will develop distribution prediction models by extending CPMs to allow flexible inclusion of predictor variables via penalization (e.g., ridge regression, lasso, and elastic net) and tree-based approaches (e.g., random forests and boosting). Second, we will develop rank-based methods to estimate robust causal population parameters (i.e., estimands) that quantify the effect of a treatment in observational studies with skewed, ordinal, or mixed response outcomes. Our robust estimands include the quantile treatment effect, the probability treatment effect, and the Mann- Whitney/Wilcoxon/probabilistic index treatment effect, and variations of these estimands conditional on covariates. These causal estimands will be estimated in a robust, rank-based manner using CPMs. Third, we will use CPMs to extend modern difference in differences (DID) methods to permit estimation of robust estimands using rank-based methods in simple two-group two-time period settings and more complicated settings with staggered treatment adoption. Fourth, we will develop simple and unifying sample size formulas and analysis methods for cluster randomized controlled trials with skewed, ordinal, or mixed response data. We will package our methods in freely available software and apply our analyses to important studies of HIV/AIDS.