  Instrumental variable method is among the most commonly used causal inference
approaches for analyzing observational studies with unmeasured confounders.
Despite its popularity, the instruments' invalidity is a major concern for
practical applications and a fast-growing area of research is inference for the
causal effect with possibly invalid instruments. In this paper, we construct
uniformly valid confidence intervals for the causal effect when the instruments
are possibly invalid. We illustrate the post-selection problem of existing
inference methods relying on instrument selection. Our proposal is to search
for the value of the treatment effect such that a sufficient amount of
candidate instruments are taken as valid. We further devise a novel sampling
method, which, together with searching, lead to a more precise confidence
interval. Our proposed searching and sampling confidence intervals are shown to
be uniformly valid under the finite-sample majority and plurality rules. We
compare our proposed methods with existing inference methods over a large set
of simulation studies and apply them to study the effect of the triglyceride
level on the glucose level over a mouse data set.
