  Association models for a pair of random elements $X$ and $Y$ (e.g., vectors)
are considered which specify the odds ratio function up to an unknown parameter
$\bolds\theta$. These models are shown to be semiparametric in the sense that
they do not restrict the marginal distributions of $X$ and $Y$. Inference for
the odds ratio parameter $\bolds\theta$ may be obtained from sampling either
$Y$ conditionally on $X$ or vice versa. Generalizing results from Prentice and
Pyke, Weinberg and Wacholder and Scott and Wild, we show that asymptotic
inference for $\bolds\theta$ under sampling conditional on $Y$ is the same as
if sampling had been conditional on $X$. Common regression models, for example,
generalized linear models with canonical link or multivariate linear,
respectively, logistic models, are association models where the regression
parameter $\bolds\beta$ is closely related to the odds ratio parameter
$\bolds\theta$. Hence inference for $\bolds\beta$ may be drawn from samples
conditional on $Y$ using an association model.
