BatchPRDS: Online batch FDR control under Positive Dependence

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 \(\gamma_i\). A default is provided with \(\gamma_j\) proportional to \(1/j^(1.6)\).
display_progress: Logical. If TRUE prints out a progress bar for the algorithm runtime.

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).

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 \(\alpha\), we choose a sequence of non-negative numbers \(\gamma_i\) such that they sum to 1. The algorithm runs the Benjamini-Hochberg procedure on each batch, where the values of the adjusted significance thresholds \(\alpha_{t+1}\) depend on the number of previous discoveries.

Further details of the BatchPRDS algorithm can be found in Zrnic et al. (2020).

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)
#>        id       pval batch R      alphai
#> 1  A15432 2.9000e-08     1 1 0.021874508
#> 2  B90969 6.7430e-02     1 0 0.021874508
#> 3  C18705 1.5140e-02     1 0 0.021874508
#> 4  B49731 8.1740e-02     1 0 0.021874508
#> 5  E99902 1.7100e-03     1 1 0.021874508
#> 6  C38292 3.6000e-05     2 1 0.009621196
#> 7  A30619 7.9149e-01     2 0 0.009621196
#> 8  D46627 2.7201e-01     2 0 0.009621196
#> 9  E29198 2.8295e-01     2 0 0.009621196
#> 10 A41418 7.5900e-08     2 1 0.009621196
#> 11 D51456 6.9274e-01     2 0 0.009621196
#> 12 C88669 3.0443e-01     3 0 0.007543524
#> 13 E03673 1.3600e-03     3 1 0.007543524
#> 14 A63155 7.2342e-01     3 0 0.007543524
#> 15 B66033 5.4757e-01     3 0 0.007543524