We consider situations where data have been collected such that the sampling
depends on the outcome of interest and possibly further covariates, as for
instance in case-control studies. Graphical models represent assumptions about
the conditional independencies among the variables. By including a node for the
sampling indicator, assumptions about sampling processes can be made explicit.
We demonstrate how to read off such graphs whether consistent estimation of the
association between exposure and outcome is possible. Moreover, we give
sufficient graphical conditions for testing and estimating the causal effect of
exposure on outcome. The practical use is illustrated with a number of
examples.Comment: Published in at http://dx.doi.org/10.1214/10-STS340 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
