Probability-Scale Residuals in HIV/AIDS Research: Diagnostics and Inference

TL;DR

This paper introduces probability-scale residuals (PSRs) as versatile tools for diagnostics and inference in HIV/AIDS research, demonstrating their application across various data types and models with real datasets.

Contribution

It presents the properties and applications of PSRs in HIV/AIDS studies, including diagnostics, correlation testing, and analysis of diverse datasets, which is a novel approach in this field.

Findings

PSRs effectively diagnose model fit in HIV data.

Partial Spearman's correlation can be constructed using PSRs.

Applied methods reveal insights in HIV-related datasets.

Abstract

The probability-scale residual (PSR) is well defined across a wide variety of variable types and models, making it useful for studies of HIV/AIDS. In this manuscript, we highlight some of the properties of the PSR and illustrate its application with HIV data. As a residual, it can be useful for model diagnostics; we demonstrate its use with ordered categorical data and semiparametric transformation models. The PSR can also be used to construct tests of residual correlation. In fact, partial Spearman's rank correlation between $X$ and $Y$ while adjusting for covariates $Z$ can be constructed as the correlation between PSRs from models of $Y$ on $Z$ and of $X$ on $Z$. The covariance of PSRs is also useful in some settings. We apply these methods to a variety of HIV datasets including 1) a study examining risk factors for more severe forms of cervical lesions among 145 women living with HIV in Zambia, 2) a study investigating the association between 21 metabolomic biomarkers among 70 HIV-positive patients in the southeastern United States, and 3) a genome wide association study investigating the association between single nucleotide polymorphisms and tenofovir clearance among 501 HIV-positive persons participating in a multi-site randomized clinical trial.