A nonparametric measure of local association for two-way contingency tables

In the analysis of contingency tables, the odds ratio is a measure commonly used to summarize the strength of association between two categorical variables, say R and S. When a vector of continuous variables X is also observed for each individual in the table, then it is important to analyze whether and how the degree of association (odds ratio) varies locally with X. In this article, several nonparametric estimators of this conditional or local odds ratio are proposed, to summarize the strength of local association between R and S given X. The nonparametric estimators are constructed using kernel regression, to allow for maximum flexibility. Confidence intervals based on these nonparametric estimators are also developed. Simulation studies show that our proposed (amended) local odds ratio estimators can outperform the model-based counterparts from logistic regression and Generalized Additive Models, without the need for a linearity or additivity assumption.