bonfInfinite {onlineFDR} | R Documentation

## Online FDR control based on a Bonferroni-like test

### Description

This funcion is deprecated, please use `Alpha_spending` instead.

### Usage

    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 sequentially with no batches.
`alpha` | Overall significance level of the FDR procedure, the default is 0.05.
`alphai` | Optional vector of α_i, where hypothesis i is rejected if the i-th p-value is less than or equal to α_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.

### 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 sequentially with no batches.

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

### 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`).

### 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.

[Package onlineFDR version 2.2.0 Index]