LONDstar: LONDstar: Asynchronous online mFDR control based on number of...

In dsrobertson/onlineFDR: Online error rate control

LONDstar: Asynchronous online mFDR control based on number of discoveries

Description

Implements the LOND algorithm for asynchronous online testing, as presented by Zrnic et al. (2021).

Usage

LONDstar(
  d,
  alpha = 0.05,
  version,
  betai,
  batch.sizes,
  display_progress = FALSE
)

Arguments

d	Either a vector of p-values, or a dataframe with three columns: an identifier (‘id’), p-value (‘pval’), and either ‘decision.times’, or ‘lags’, depending on which version you're using. See version for more details.
alpha	Overall significance level of the procedure, the default is 0.05.
version	Takes values 'async', 'dep' or 'batch'. This specifies the version of LONDstar to use. version='async' requires a column of decision times (‘decision.times’). version='dep' requires a column of lags (‘lags’). version='batch' requires a vector of batch sizes (‘batch.sizes’).
betai	Optional vector of \beta_i. A default is provided as proposed by Javanmard and Montanari (2018), equation 31.
batch.sizes	A vector of batch sizes, this is required for version='batch'.
display_progress	Logical. If TRUE prints out a progress bar for the algorithm runtime.

Details

The function takes as its input either a vector of p-values, or a dataframe with three columns: an identifier (‘id’), p-value (‘pval’), or a column describing the conflict sets for the hypotheses. This takes the form of a vector of decision times or lags. Batch sizes can be specified as a separate argument (see below).

Zrnic et al. (2021) present explicit three versions of LONDstar:

1) version='async' is for an asynchronous testing process, consisting of tests that start and finish at (potentially) random times. The discretised finish times of the test correspond to the decision times. These decision times are given as the input decision.times for this version of the LONDstar algorithm.

2) version='dep' is for online testing under local dependence of the p-values. 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 LONDstar algorithm.

3) version='batch' is for controlling the mFDR in mini-batch testing, where a mini-batch represents a grouping of tests run asynchronously which result in dependent p-values. Once a mini-batch of tests is fully completed, a new one can start, testing hypotheses independent of the previous batch. The batch sizes are given as the input batch.sizes for this version of the LONDstar algorithm.

Given an overall significance level \alpha, LONDstar requires a sequence of non-negative non-increasing numbers \beta_i that sum to \alpha.

Note that these LONDstar algorithms control the modified FDR (mFDR).

Further details of the LONDstar algorithms can be found in Zrnic et al. (2021).

Value

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

References

Javanmard, A. and Montanari, A. (2018) Online Rules for Control of False Discovery Rate and False Discovery Exceedance. Annals of Statistics, 46(2):526-554.

Zrnic, T., Ramdas, A. and Jordan, M.I. (2021). Asynchronous Online Testing of Multiple Hypotheses. Journal of Machine Learning Research (to appear), https://arxiv.org/abs/1812.05068.

See Also

LOND presents versions of LOND for synchronous p-values, i.e. where each test can only start when the previous test has finished.

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),
decision.times = seq_len(15) + 1)

LONDstar(sample.df, version='async')

sample.df2 <- 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))

LONDstar(sample.df2, version='dep')

sample.df3 <- 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))

LONDstar(sample.df3, version='batch', batch.sizes = c(4,6,5))

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