A recent focus in health sciences has been the development of personalized medicine, which includes determining the population for which a given treatment is effective. The credible subgroups approach provides a pair of bounding subgroups for the benefiting subgroup in covariate space, constructed so that it is likely that one contains the benefiting subgroup and the other is entirely contained by it. This approach fully controls for the multiplicity inherent in testing for benefit at every covariate point, and does not require pre-specification of subgroups. We illustrate the approach in linear and semiparametric regression settings using data from trials of Alzheimer’s disease treatments.