  Observational studies are valuable tools for inferring causal effects in the
absence of controlled experiments. However, these studies may be biased due to
the presence of some relevant, unmeasured set of covariates. The design of an
observational study has a prominent effect on its sensitivity to hidden biases,
and the best design may not be apparent without examining the data. One
approach to facilitate a data-inspired design is to split the sample into a
planning sample for choosing the design and an analysis sample for making
inferences. We devise a powerful and flexible method for selecting outcomes in
the planning sample when an unknown number of outcomes are affected by the
treatment. We investigate the theoretical properties of our method and conduct
extensive simulations that demonstrate pronounced benefits, especially at
higher levels of allowance for unmeasured confounding. Finally, we demonstrate
our method in an observational study of the multi-dimensional impacts of a
devastating flood in Bangladesh.
