online_fallback: Online fallback procedure for FWER control

In dsrobertson/onlineFDR: Online error rate control

Online fallback procedure for FWER control

Description

Implements the online fallback procedure of Tian and Ramdas (2021), which guarantees strong FWER control under arbitrary dependence of the p-values.

Usage

online_fallback(
  d,
  alpha = 0.05,
  gammai,
  random = TRUE,
  display_progress = FALSE,
  date.format = "%Y-%m-%d"
)

Arguments

d	Either a vector of p-values, or a dataframe with three columns: an identifier (‘id’), date (‘date’) and p-value (‘pval’). If no column of dates is provided, then the p-values are treated as being ordered in sequence, arriving one at a time.
alpha	Overall significance level of the FDR procedure, the default is 0.05.
gammai	Optional vector of \gamma_i. A default is provided as proposed by Javanmard and Montanari (2018), equation 31.
random	Logical. If TRUE (the default), then the order of the p-values in each batch (i.e. those that have exactly the same date) is randomised.
display_progress	Logical. If TRUE prints out a progress bar for the algorithm runtime.
date.format	Optional string giving the format that is used for dates.

Details

The function takes as its input either a vector of p-values or a dataframe with three columns: an identifier (‘id’), date (‘date’) and p-value (‘pval’). The case where p-values arrive in batches corresponds to multiple instances of the same date. If no column of dates is provided, then the p-values are treated as being ordered in sequence, arriving one at a time. Given an overall significance level \alpha, we choose a sequence of non-negative non-increasing numbers \gamma_i that sum to 1.

The online fallback procedure provides a uniformly more powerful method than Alpha-spending, by saving the significance level of a previous rejection. More specifically, the procedure tests hypothesis H_i at level

\alpha_i = \alpha \gamma_i + R_{i-1} \alpha_{i-1}

where R_i = 1\{p_i \leq \alpha_i\} denotes a rejected hypothesis.

Further details of the online fallback procedure can be found in Tian and Ramdas (2021).

Value

out

A dataframe with the original data d (which will be reordered if there are batches and random = TRUE), the LORD-adjusted significance thresholds \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

Tian, J. and Ramdas, A. (2021). Online control of the familywise error rate. Statistical Methods for Medical Research, 30(4):976–993.

Examples

sample.df <- data.frame(
id = c('A15432', 'B90969', 'C18705', 'B49731', 'E99902',
    'C38292', 'A30619', 'D46627', 'E29198', 'A41418',
    'D51456', 'C88669', 'E03673', 'A63155', 'B66033'),
date = as.Date(c(rep('2014-12-01',3),
               rep('2015-09-21',5),
                rep('2016-05-19',2),
                '2016-11-12',
               rep('2017-03-27',4))),
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))

online_fallback(sample.df, random=FALSE)

set.seed(1); online_fallback(sample.df)

set.seed(1); online_fallback(sample.df, alpha=0.1)

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