ADDIS_spending: ADDIS-spending: Adaptive discarding algorithm for online FWER...
In onlineFDR: Online error control

Description Usage Arguments Details Value References See Also Examples

Implements the ADDIS algorithm for online FWER control, where ADDIS stands for an ADaptive algorithm that DIScards conservative nulls, as presented by Tian and Ramdas (2019b). The procedure compensates for the power loss of Alpha-spending, by including both adaptivity in the fraction of null hypotheses and the conservativeness of nulls.

1	ADDIS_spending(d, alpha = 0.05, gammai, lambda = 0.25, tau = 0.5, dep = FALSE)

`d`	Either a vector of p-values, or a dataframe with three columns: an identifier (‘id’), p-value (‘pval’), and lags (‘lags’).
`alpha`	Overall significance level of the 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).
`lambda`	Optional parameter that sets the threshold for ‘candidate’ hypotheses. Must be between 0 and 1, defaults to 0.25.
`tau`	Optional threshold for hypotheses to be selected for testing. Must be between 0 and 1, defaults to 0.5.
`dep`	Logical. If `TRUE` runs the version for locally dependent p-values

The function takes as its input either a vector of p-values, or a dataframe with three columns: an identifier (‘id’), p-value (‘pval’), and lags, if the dependent version is specified (see below). Given an overall significance level α, ADDIS depends on constants λ and τ, where λ < τ. Here τ \in (0,1) represents the threshold for a hypothesis to be selected for testing: p-values greater than τ are implicitly ‘discarded’ by the procedure, while λ \in (0,1) sets the threshold for a p-value to be a candidate for rejection: ADDIS-spending will never reject a p-value larger than λ. The algorithms also require a sequence of non-negative non-increasing numbers γ_i that sum to 1.

The ADDIS-spending procedure provably controls the FWER in the strong sense for independent p-values. Note that the procedure also controls the generalised familywise error rate (k-FWER) for k > 1 if α is replaced by min(1, kα).

Tian and Ramdas (2019b) also presented a version for handling local dependence. More precisely, for any t>0 we allow the p-value p_t to have arbitrary dependence on the previous L_t p-values. The fixed sequence L_t is referred to as ‘lags’, and is given as the input lags for this version of the ADDIS-spending algorithm.

Further details of the ADDIS-spending algorithms can be found in Tian and Ramdas (2019b).

d.out

A dataframe with the original p-values pval, the adjusted testing levels α_i and the indicator function of discoveries R. Hypothesis i is rejected if the i-th p-value is less than or equal to α_i, in which case R[i] = 1 (otherwise R[i] = 0).

Tian, J. and Ramdas, A. (2019b). Online control of the familywise error rate. arXiv preprint, https://arxiv.org/abs/1910.04900.

ADDIS provides online control of the FDR.

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),
lags = rep(1,15))

ADDIS_spending(sample.df) #independent

ADDIS_spending(sample.df, dep = TRUE) #Locally dependent