  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.
