BatchPRDS {onlineFDR} | R Documentation

## BatchPRDS: Online batch FDR control under Positive Dependence

### Description

Implements the BatchPRDS algorithm for online FDR control, where PRDS stands for positive regression dependency on a subset, as presented by Zrnic et al. (2020).

### Usage

    BatchPRDS(d, alpha = 0.05, gammai, 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 γ_i. A default is provided with γ_j proportional to 1/j^(1.6).
`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 BatchPRDS algorithm controls the FDR when the p-values in one batch are positively dependent, and independent across batches. Given an overall significance level α, we choose a sequence of non-negative numbers γ_i such that they sum to 1. The algorithm runs the Benjamini-Hochberg procedure on each batch, where the values of the adjusted significance thresholds α_{t+1} depend on the number of previous discoveries.

Further details of the BatchPRDS 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)α_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

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)))

    BatchPRDS(sample.df)

[Package onlineFDR version 2.2.0 Index]