BatchStBH.RdImplements the BatchSt-BH algorithm for online FDR control, as presented by Zrnic et al. (2020). This algorithm makes one modification to the original Storey-BH algorithm (Storey 2002), by adding 1 to the numerator of the null proportion estimate for more stable results.
BatchStBH(d, alpha = 0.05, gammai, lambda = 0.5, display_progress = FALSE)A dataframe with three columns: identifiers (`id'), batch numbers (`batch') and p-values (`pval').
Overall significance level of the FDR procedure, the default is 0.05.
Optional vector of \(\gamma_i\). A default is provided with \(\gamma_j\) proportional to \(1/j^(1.6)\).
Threshold for Storey-BH, must be between 0 and 1. Defaults to 0.5.
Logical. If TRUE prints out a progress bar for the algorithm runtime.
A dataframe with the original data d and the
indicator function of discoveries R. Hypothesis \(i\) is rejected
if the \(i\)-th p-value within the \(t\)-th batch is less than or equal
to \((r/n)\alpha_t\), where \(r\) is the rank of the \(i\)-th p-value
within an ordered set and \(n\) is the total number of hypotheses within
the \(t\)-th batch. If hypothesis \(i\) is rejected, R[i] = 1
(otherwise R[i] = 0).
The function takes as its input a dataframe with three columns: identifiers (`id'), batch numbers (`batch') and p-values (`pval').
The BatchSt-BH algorithm controls the FDR when the p-values in a batch are independent, and independent across batches. Given an overall significance level \(\alpha\), we choose a sequence of non-negative numbers \(\gamma_i\) such that they sum to 1. The algorithm runs the Storey Benjamini-Hochberg procedure on each batch, where the values of the adjusted significance thresholds \(\alpha_{t+1}\) depend on the number of previous discoveries.
Further details of the BatchSt-BH algorithm can be found in Zrnic et al. (2020).
Storey, J.D. (2002). A direct approach to false discovery rates. J. R. Statist. Soc. B: 64, Part 3, 479-498.
Zrnic, T., Jiang D., Ramdas A. and Jordan M. (2020). The Power of Batching in Multiple Hypothesis Testing. International Conference on Artificial Intelligence and Statistics: 3806-3815
sample.df <- data.frame(
id = c('A15432', 'B90969', 'C18705', 'B49731', 'E99902',
'C38292', 'A30619', 'D46627', 'E29198', 'A41418',
'D51456', 'C88669', 'E03673', 'A63155', 'B66033'),
pval = c(2.90e-08, 0.06743, 0.01514, 0.08174, 0.00171,
3.60e-05, 0.79149, 0.27201, 0.28295, 7.59e-08,
0.69274, 0.30443, 0.00136, 0.72342, 0.54757),
batch = c(rep(1,5), rep(2,6), rep(3,4)))
BatchStBH(sample.df)
#> id pval batch R alphai
#> 1 A15432 2.9000e-08 1 1 0.02187451
#> 2 B90969 6.7430e-02 1 0 0.02187451
#> 3 C18705 1.5140e-02 1 1 0.02187451
#> 4 B49731 8.1740e-02 1 0 0.02187451
#> 5 E99902 1.7100e-03 1 1 0.02187451
#> 6 C38292 3.6000e-05 2 1 0.04363561
#> 7 A30619 7.9149e-01 2 0 0.04363561
#> 8 D46627 2.7201e-01 2 0 0.04363561
#> 9 E29198 2.8295e-01 2 0 0.04363561
#> 10 A41418 7.5900e-08 2 1 0.04363561
#> 11 D51456 6.9274e-01 2 0 0.04363561
#> 12 C88669 3.0443e-01 3 0 0.02484982
#> 13 E03673 1.3600e-03 3 1 0.02484982
#> 14 A63155 7.2342e-01 3 0 0.02484982
#> 15 B66033 5.4757e-01 3 0 0.02484982