  We review typical design problems encountered in the planning of
observational studies and propose a unifying framework that allows us to use
the same concepts and notation for different problems. In the framework, the
design is defined as a probability measure in the space of observational
processes that determine whether the value of a variable is observed for a
specific unit at the given time. The optimal design is then defined, according
to Bayesian decision theory, to be the one that maximizes the expected utility
related to the design. We present examples on the use of the framework and
discuss methods for deriving optimal or approximately optimal designs.
