Time-course microarray experiments harvested samples at several time
points. To reveal the dynamic gene expression changes over time, we need to identify
the significant genes and detect the patterns of gene expressions, which may bring
directional errors. Guo et al. (Biometrics 66(2):485–492, 2010) introduced a mixed
directional false discovery rate (mdFDR) controlled procedure, which controls the
sum of expected proportions of Type I and Type III errors among all rejections. In
this paper, we develop weighted p value procedures for mdFDR control and give out
some sufficient conditions to assure the (asymptotic) mdFDR control. Some weights
and their estimators are illustrated to satisfy the sufficient conditions. The proposed
weighted p value procedures are compared with the existing method by extensive
simulations. Based on the proposed weighted p values procedure, we provide multi-
ple CIs which control the false coverage-statement rate (FCR). We use the proposed
methods to analyze the time-course microarray data studied in Lobenhofer et al. (Mol
Endocrinol 16:1215–1229, 2002). Most of our findings are the same as those obtained
by the existing method. In addition, we identify some other important genes, such as
CDKN3 and NQO1.

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• Controlling mixed directional false discovery rate in multidimensional decisions with applications to microarray studies