AFNC: Performs AFNC

In zjdaye/AFNC: Adaptive False Negative Control (AFNC)

Description

AFNC takes a vector of p-values and determines the variables (SNPs) selected by AFNC. The AFNC can retain a high proportion of signals by discarding variants from the Noise region using adaptive false negative control (Jeng et al. 2016). Proportion of signals is estimated from the data.

Usage

AFNC(p.value, alpha = 0.05, beta = 0.1, cd, c0 = NULL)

Arguments

p.value	d-vector of p-values.
alpha	level of family-wise error rate for false positive control using the Bonferroni.
beta	level of signal missing rate for false negative control using the AFNC.
cd	c_d for controlling Type I error rate under the global null, must be pre-computed using estimate.cd.
c0	maximum number of the most significant p-values considered. If NULL, c0 will be set to \min( \max(5000,0.1*d), d ), such that at least 10% of the p-values are considered.

Details

The algorithm implemented in this function is as follows. (See Jeng et al. (2016) for further details.)

1. The p-values are ordered at decreasing significance.

2. The signal proportion estimator \hat{π} and estimated number of signals \hat{s} = \hat{π} * d are obtained using estimate.signal.proportion.

3. Two cutoff positions, t_α and T_fn, are determined to separate the Signal, Indistinguishable, and Noise regions. (See Figure 1 of Jeng et al. (2016) for illustration of the Signal, Indistinguishable, and Noise regions of inference.)

4. Finally, variables (SNPs) with ordered p-values ranked at or before t_α are selected by Bonferroni for family-wise false positive control. Variables (SNPs) with ordered p-values ranked at or before T_fn are selected by the AFNC procedure for adaptive false negative control.

Value

bonferroni	Two vectors (index, p.value). index is a vector of indices of variables (SNPs) selected by the Bonferroni, and p.value is the corresponding p-values.
afnc	Two vectors (index, p.value). index is a vector of indices of variables (SNPs) selected by the AFNC, and p.value is the corresponding p-values.
t.alpha	Two values (rank, p.value). rank specifies the rank by which all variants ranked at or before t_α are retained for controlling false positives by Bonferroni. p.value is the corresponding p-value, such that all variants less than or equal to p.value are retained.
T.fn	Two values (rank, p.value). rank specifies the rank by which all variants ranked at or before t_α are retained for adaptive false negative control (AFNC). p.value is the corresponding p-value, such that all variants less than or equal to p.value are retained.
signal.proportion	The estimated signal proportion \hat{π}.
number.signals	The estimated number of signals \hat{s} = \hat{π} * d.

References

Jeng, X.J., Daye, Z.J., Lu, W., and Tzeng, J.Y. (2016) Rare Variants Association Analysis in Large-Scale Sequencing Studies at the Single Locus Level.

Examples

# Estimate signal proportions
set.seed(1)
cd = estimate.cd(d=length(p.value), alpha=0.05)
afnc = AFNC(p.value, alpha=0.05, beta=0.1, cd=cd)$afnc
selected = afnc$index # selected variables
selected.p.value = afnc$p.value # p-values of selected variables

zjdaye/AFNC documentation built on May 4, 2019, 11:23 p.m.