The typical selection bias described in observational studies is due to conditioning on a common effect (one conditions on willingness to participate), as are Berkson's bias (conditioning on admission to hospital), loss to follow-up or missing data (conditioning on presence of data; occurs in both observational or randomized trials), some forms of Simpson's Paradox, etc [ 5, 12].
If two covariates both cause a third covariate, then adjustment for the third covariate (or an effect of the third covariate) creates a conditional association between the first two covariates (i.e. if one conditions on the child or descendant of the child, there is a conditional association between the parents), and could introduce bias [ 20].
However, it is well known that a directed Bayesian network and the corresponding undirected graph are not necessarily topologically identical: in the undirected graph for computing the partial correlations one conditions on all other nodes whereas in the directed graph one conditions only on a subset of nodes, in order to avoid conditioning "on the future" (i.e. on the dependent nodes).
2. Selection bias: occurs when one conditions on a common effect (e.g. Berkson's Bias, loss to follow-up, missing data, healthy worker bias, etc) such that there is now a conditional association between the exposure and the outcome.
The model is consistent with the graph in Figure 2, because and therefore, the effect of A on Y is confounded due to dependence between Y a, U, and W, even if one conditions on C. Note that although the model specifies an additive causal effect, the relation between Y0 and (A, Z, C) is otherwise unrestricted.
CTA is an often used strategy to investigate gene expression profiles from the biological point of views, since transcripts expressed differentially between more than one conditions are expected to represent the distinction between conditions.
