A Nonparametric Measure of Local Association for two-way Contingency Tables

TL;DR

This paper introduces a nonparametric method to measure how the association between two categorical variables varies with continuous covariates, using kernel regression to estimate local odds ratios.

Contribution

It extends the classical odds ratio to a conditional, local measure with nonparametric estimators and confidence intervals, outperforming traditional model-based methods.

Findings

Nonparametric estimators outperform logistic regression and GAMs in simulations.

The method provides detailed insights into how associations vary with covariates.

Application to ICU data reveals age-related variation in patient survival associations.

Abstract

In contingency table analysis, the odds ratio is a commonly applied measure used to summarize the degree of association between two categorical variables, say R and S. Suppose now that for each individual in the table, a vector of continuous variables X is also observed. It is then vital to analyze whether and how the degree of association varies with X. In this work, we extend the classical odds ratio to the conditional case, and develop nonparametric estimators of this "pointwise odds ratio" to summarize the strength of local association between R and S given X. To allow for maximum flexibility, we make this extension using kernel regression. We develop confidence intervals based on these nonparametric estimators. We demonstrate via simulation that our pointwise odds ratio estimators can outperform model-based counterparts from logistic regression and GAMs, without the need for a linearity or additivity assumption. Finally, we illustrate its application to a dataset of patients from an intensive care unit (ICU), offering a greater insight into how the association between survival of patients admitted for emergency versus elective reasons varies with the patients' ages.