  Studies have shown that exposure to air pollution, even at low levels,
significantly increases mortality. As regulatory actions are becoming
prohibitively expensive, robust evidence to guide the development of targeted
interventions to reduce air pollution exposure is needed. In this paper, we
introduce a novel statistical method that splits the data into two subsamples:
(a) Using the first subsample, we consider a data-driven search for $\textit{de
novo}$ discovery of subgroups that could have exposure effects that differ from
the population mean; and then (b) using the second subsample, we quantify
evidence of effect modification among the subgroups with nonparametric
randomization-based tests. We also develop a sensitivity analysis method to
assess the robustness of the conclusions to unmeasured confounding bias. Via
simulation studies and theoretical arguments, we demonstrate that since we
discover the subgroups in the first subsample, hypothesis testing on the second
subsample can focus on theses subgroups only, thus substantially increasing the
statistical power of the test. We apply our method to the data of 1,612,414
Medicare beneficiaries in New England region in the United States for the
period 2000 to 2006. We find that seniors aged between 81-85 with low income
and seniors aged above 85 have statistically significant higher causal effects
of exposure to PM$_{2.5}$ on 5-year mortality rate compared to the population
mean.
