In some diseases it is well-known that a unimodal mortality pattern exists. A clear example
in developed countries is breast cancer, where mortality increased sharply until the
nineties and then decreased. This clear unimodal pattern is not necessarily applicable to all
regions within a country. In this paper, we develop statistical tools to check if the unimodality
pattern persists within regions using order restricted inference. Break points as well as
con dence intervals are also provided. In addition, a new test for checking monotonicity
against unimodality is derived allowing to discriminate between a simple increasing pattern
and an up-then-down response pattern. A comparison with the widely used joinpoint regression
technique under unimodality is provided. We show that the joinpoint technique could
fail when the underlying function is not piecewise linear. Results will be illustrated using
age-speci c breast cancer mortality data from Spain in the period 1975-2005.
