# Adjusted effect size, area under the curve, and c-statistic for evaluating the association between uric acid and mortality in US adults using unweighted and survey-weighted regression, propensity, and prognostic score

## TL;DR

This study shows that higher uric acid levels are linked to increased mortality risk in US adults, emphasizing the need for proper statistical weighting in complex survey data.

## Contribution

The study introduces and compares survey-weighted and unweighted methods for analyzing the association between uric acid and mortality in complex survey data.

## Key findings

- Uric acid levels are consistently associated with increased mortality risk across various weighted and unweighted analyses.
- Survey-weighted analyses showed improved predictive performance in specific prevalence and exposure conditions.
- Higher uric acid levels are strongly linked to all-cause mortality, especially in individuals over 60 years old.

## Abstract

Population-based surveys and databases are useful sources for developing prognostic and diagnostic models requiring receiver operating characteristic (ROC) or precision-recall curve (PRC) analyses. The performance of the models is typically summarized with the area under the ROC (rAUC) or PR curves (pAUC) or c-statistic, depending on the study design and analysis. However, these surveys and databases sometimes involve sampling weights due to complex sampling designs. The sampling weights need to be included in the analysis to produce accurate estimates of effect size as well as performance measures. Different types of adjusted analyses, including survey-weighted adjusted analysis, propensity score weight-adjusted (PropSWA), and prognostic score weight-adjusted (ProgSWA) analyses, are typically performed using logistic or Cox regressions as per the study objectives and outcome. We applied these adjusted analyses and compared the effect sizes with or without incorporating sampling weights in the analyses. We explored the relationship between uric acid levels and all-cause mortality in US adults using the National Health and Nutrition Examination Survey dataset, which employs a complex sampling design requiring weight-adjusted analyses. All the models, including unweighted (hazard ratio (HR): 1.09; 95% confidence interval (CI) [1.05–1.12]), survey-weighted (HR: 1.09; 95% CI [1.06–1.12]), unweighted ProgSWA (HR: 1.11; 95% CI [1.07–1.15]), survey-weighted ProgSWA (HR: 1.12; 95% CI [1.09–1.16]), unweighted PropSWA (HR: 1.18; 95% CI [1.12–1.24]), and weighted PropSWA (HR: 1.16; 95% CI [1.10–1.22]) analyses yielded a consistent and positive association between uric acid levels and risk of mortality. These associations were unchanged in various sensitivity analyses. We found marked differences in effect size and predictive performance measures between weighted and unweighted analyses, especially with four categories of uric acid levels. In simulation studies, a survey-weighted propensity model performed better in low-prevalence settings and with skewed exposure. In contrast, survey-weighted prognostic models performed better in high-prevalence settings, particularly with unbalanced exposure and missing data. Our study found a strong association between higher uric acid levels and all-cause mortality in US adults, indicating the importance of proper screening and management of hyperuricemia, particularly in individuals aged >60 years. Based on intensive simulation and real data analyses, we strongly recommend incorporating weights while analyzing studies involving complex sampling designs. Our Stata codes will facilitate analysts to perform a variety of statistical analyses depending on the study objective, presence of confounders, and type of outcomes in survey-weighted data analysis.