BatchStBH: BatchStBH: Online batch FDR control using the St-BH procedure

In dsrobertson/onlineFDR: Online error rate control

BatchStBH: Online batch FDR control using the St-BH procedure

Description

Implements 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.

Usage

BatchStBH(d, alpha = 0.05, gammai, lambda = 0.5, display_progress = FALSE)

Arguments

d	A dataframe with three columns: identifiers (‘id’), batch numbers (‘batch’) and p-values (‘pval’).
alpha	Overall significance level of the FDR procedure, the default is 0.05.
gammai	Optional vector of \gamma_i. A default is provided with \gamma_j proportional to 1/j^(1.6).
lambda	Threshold for Storey-BH, must be between 0 and 1. Defaults to 0.5.
display_progress	Logical. If TRUE prints out a progress bar for the algorithm runtime.

Details

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).

Value

out

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).

References

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

Examples

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)

dsrobertson/onlineFDR documentation built on April 21, 2023, 8:17 p.m.