Differential effects and generic biases in observational studies

There are two treatments, each of which may be applied or withheld, yielding a 2 x 2 factorial arrangement with three degrees of freedom between groups. The differential effect of the two treatments is the effect of applying one treatment in lieu of the other. In randomised experiments, the differential effect is of no more or less interest than other treatment contrasts. Differential effects play a special role in certain observational studies in which treatments are not assigned to subjects at random, where differing outcomes may reflect biased assignments rather than effects caused by the treatments. Differential effects are immune to certain types of unobserved bias, called generic biases, which are associated with both treatments in a similar way. This is explored using several examples and models. Differential effects are not immune to differential biases, whose possible consequences are examined by sensitivity analysis.