LORDdep {onlineFDR} | R Documentation

## LORD (dep): Online FDR control based on recent discovery for dependent p-values

### Description

This funcion is deprecated, please use `LORD` instead with `version = 'dep'`.

### Usage

    LORDdep(
      d,
      alpha = 0.05,
      xi,
      w0 = alpha/10,
      b0 = alpha - w0,
      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.
`xi` | Optional vector of ξ_i. A default is provided to satisfy the condition given in Javanmard and Montanari (2018), example 3.7.
`w0` | Initial ‘wealth’ of the procedure. Defaults to α/10.
`b0` | The ‘payout’ for rejecting a hypothesis. Defaults to α - w_0.
`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

LORDdep implements the LORD procedure for online FDR control for dependent p-values, where LORD stands for (significance) Levels based On Recent Discovery, as presented by Javanmard and Montanari (2018).

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.

This modified LORD procedure controls FDR for dependent p-values. Given an overall significance level α, we choose a sequence of non-negative numbers ξ_i such that they satisfy a condition given in Javanmard and Montanari (2018), example 3.8.

The procedure depends on constants w_0 and b_0, where w_0 ≥ 0 represents the intial ‘wealth’ and b_0 > 0 represents the ‘payout’ for rejecting a hypothesis. We require w_0+b_0 ≤ α for FDR control to hold.

Further details of the modified LORD procedure can be found in Javanmard and Montanari (2018).

### Value

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

### 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]