  This paper introduces the sequential CRT, which is a variable selection
procedure that combines the conditional randomization test (CRT) and Selective
SeqStep+. Valid p-values are constructed via the flexible CRT, which are then
ordered and passed through the selective SeqStep+ filter to produce a list of
discoveries. We develop theory guaranteeing control on the false discovery rate
(FDR) even though the p-values are not independent. We show in simulations that
our novel procedure indeed controls the FDR and are competitive with -- and
sometimes outperform -- state-of-the-art alternatives in terms of power.
Finally, we apply our methodology to a breast cancer dataset with the goal of
identifying biomarkers associated with cancer stage.
