Online FDR control based on a Bonferroni-like test

This funcion is deprecated, please use Alpha_spending instead.

bonfInfinite(
  d,
  alpha = 0.05,
  alphai,
  random = TRUE,
  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.
alphai: Optional vector of \(\alpha_i\), where hypothesis \(i\) is rejected if the \(i\)-th p-value is less than or equal to \(\alpha_i\). 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.
date.format: Optional string giving the format that is used for dates.

Value

d.out: A dataframe with the original data d (which will be reordered if there are batches and random = TRUE), the adjusted signifcance thresholds alphai and the indicator function of discoveries R, where R[i] = 1 corresponds to hypothesis \(i\) being rejected (otherwise R[i] = 0).

Details

Implements online FDR control using a Bonferroni-like test.

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.

The procedure controls FDR for a potentially infinite stream of p-values by using a Bonferroni-like test. Given an overall significance level \(\alpha\), we choose a (potentially infinite) sequence of non-negative numbers \(\alpha_i\) such that they sum to \(\alpha\). Hypothesis \(i\) is rejected if the \(i\)-th p-value is less than or equal to \(\alpha_i\).

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.