LORDdep: LORD (dep): Online FDR control based on recent discovery for...

In dsrobertson/onlineFDR: Online error rate control

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 in sequence, arriving one at a time.
alpha	Overall significance level of the FDR procedure, the default is 0.05.
xi	Optional vector of \xi_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 \alpha/10.
b0	The ‘payout’ for rejecting a hypothesis. Defaults to \alpha - 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 in sequence, arriving one at a time.

This modified LORD procedure controls FDR for dependent p-values. Given an overall significance level \alpha, we choose a sequence of non-negative numbers \xi_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 \ge 0 represents the intial ‘wealth’ and b_0 > 0 represents the ‘payout’ for rejecting a hypothesis. We require w_0+b_0 \le \alpha 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 \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.

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