param_fast_GW: Fast Exceedance control using the GW method

In Jiefei-Wang/exceedance: Multiple Hypothesis Testing While Controlling the Exceedance Probability of the False Discovery Proportion

Fast Exceedance control using the GW method

Description

Performing a fast exceedance control of the false discovery proportion(FDP) under the framework proposed by Genovese, C., & Wasserman, L. (2004), where FDP is defined by the number of false positives devided by the number of total rejections. The GW method requires an uniform(0,1) distributional test statistic and each value in the input data represents a p-value from a hypothesis. The sources of the data can be derived from any testing procedure (e.g. pvalues from testing high-throughput gene data). This function only supports specific uniform(0,1) distributional tests. please consider param_general_GW if you want a generic version of the GW method,

Usage

param_fast_GW(
  statistic = c("kth_p", "KS", "HC", "BJ", "Simes"),
  param1 = NULL,
  param2 = NULL,
  range_type = c("index", "proportion")
)

Arguments

statistic	character, the name of the statistic for the test, see details.
param1	integer, the first parameter for the statistic, see details.
param2	integer, the second parameter for the statistic, see details.
range_type	character, the type of the parameters, see details.

Details

Note: We will use the term samples and pvalues interchangebly to refer the data gathered by an inference procedure.

This function perform the fast GW algorithm, currently it supports the following test statistics:

• kth_p: The kth pvalue statistic

• KS: The Kolmogorov-Smirnov statistic

• HC: The higher criticism statistic

• BJ: The Berk-Jones statistic

For each statistic, you can specify the index of the ascending ordered samples to control which data will be considered in the test statistics. For example, the index of the kth pvalue statistic determines the value of k and use the kth smallest sample as its statistic. similarly, the index of KS, HC and BJ determines which ordered samples will be used to compute the test statistic.

By default, range_type = "index", which means param1 and param2 represent the index. However, the index can also depend on the sample size. Therefore, if range_type = "proportion", The index is determined by the formula max(floor(n*param),1), where n is the sample size.

For the kth pvalue statistic, param1 determine the value of k and must be a single integer or a 0-1 value depending on range_type.

For KS, HC and BJ, the formula to decide the index is a little bit complicated. If range_type = "index", param1 determines which small sample(s) will be considered as the evidence of significance. For example, if param1 = 2 and the second smallest sample is significantly small, it can lead to a significant result. Conversely, param2 determines which large sample(s) can be treated as significance. Both param1 and param2 can be a vector of integer. By default, if both param1 and param2 are null, it is equivalent to param1 = c(0, 1), param2 = NULL and range_type = "proportion".

If range_type = "proportion", param1 and param2 can be length 1 vectors, which will be explained as the index from 1 to max(floor(n*param),1), or they can be length 2 vectors, where the index ranges from max(floor(n*param[1]),1) to max(floor(n*param[2]),1).

Value

an exceedance_parameters object

Examples

## The 3rd pvalue statistic
param_fast_GW(statistic = "kth_p", param1 = 3)

## One-sided KS statistic
param_fast_GW(statistic = "KS", param1 = c(0,1), range_type = "proportion")

## One-sided KS statistic, 
## Test first 10 smallest pvalues only
param_fast_GW(statistic = "KS", param1 = 1:10, range_type = "index")

Jiefei-Wang/exceedance documentation built on May 11, 2022, 1:43 a.m.