Estimating Local False Discovery Rates Using Empirical Bayes Methods

Description

New empirical Bayes methods aiming at analyzing the association of single nucleotide polymorphisms (SNPs) to some particular disease are implemented in this package. The package uses local false discovery rate (LFDR) estimates of SNPs within a sample population defined as a "reference class" and discovers if SNPs are associated with the corresponding disease. Although SNPs are used throughout this document, other biological data such as protein data and other gene data can be used. Karimnezhad, Ali and Bickel, D. R. (2016) <http://hdl.handle.net/10393/34889>.

Details

Author(s)

Ali Karimnezhad, Johnary Kim, Anna Akpawu, Justin Chitpin and David R Bickel

Maintainer: Ali Karimnezhad <ali_karimnezhad@yahoo.com>

References

Karimnezhad, A. and Bickel, D. R. (2016). Incorporating prior knowledge about genetic variants into the analysis of genetic association data: An empirical Bayes approach. Working paper. Retrieved from http://hdl.handle.net/10393/34889

See Also

For more information on how to interpret the outputs, look at the supplementary file in the vignette directory, "Using the LFDREmpiricalBayes Package."

Provides Reliable LFDR Estimates by Selecting an Appropriate Reference Class

Description

Selects an appropriate reference class given two reference classes. Considers two vecotr of LFDR estimates computed based on the two alternative reference classes and provides a vector of more reliable LFDR estimates.

Usage

ME.log(stat,lfdr.C,p0.C,ncp.C,p0.S,ncp.S,a=3,lower.p0=0,upper.p0=1,
lower.ncp=0.1,upper.ncp=50,length.p0=200,length.ncp=200)

Arguments

Details

The terms ‘separate’ and ‘combined’ reference classes are used when one sample population (reference class) is a subset of the other. Detailed explanations can be found in the vignette "Using the LFDREmpiricalBayes Package".

Value

Returns the following values:

Note

The vector of test statistics: stat, need to be positive values in order for the function ME.log to work.

Author(s)

Code: Ali Karimnezhad.
Documentation: Johnary Kim and Anna Akpawu.

References

Karimnezhad, A. and Bickel, D. R. (2016). Incorporating prior knowledge about genetic variants into the analysis of genetic association data: An empirical Bayes approach. Working paper. Retrieved from http://hdl.handle.net/10393/34889

Examples

#import the function ``lfdr.mle'' from package``LFDR.MLE''
library(LFDR.MLE)

#Consider a separate reference class and a combined reference class below:

n.SNPs.S<-3  # number of SNPs in the separate reference class
n.SNPs.Sc<-2 # number of SNPs in the complement of the separate reference class.

#Create a series of test statistics for SNPs in the separate reference class.
stat.Small<-rchisq(n.SNPs.S,df=1,ncp=0)
ncp.Sc<-10

#Create a series of test statistics for SNPs in the combined reference class.
stat.Big<-c(stat.Small,rchisq(n.SNPs.Sc,df=1,ncp=ncp.Sc))

#Using lfdr.mle, a series of arguments are used.
dFUN=dchisq; lower.ncp = .1; upper.ncp = 50;
lower.p0 = 0; upper.p0 = 1;

#Maximum Likelihood estimates for the LFDRs of SNPs in the created
# separate reference class.

#Separate reference class.
estimates.S<-lfdr.mle(x=stat.Small,dFUN=dchisq,df=1,lower.ncp = lower.ncp,
upper.ncp = upper.ncp)
LFDR.Small<-estimates.S$LFDR
p0.Small<-estimates.S$p0.hat
ncp.Small<-estimates.S$ncp.hat

# Maximum Likelihood estimates for the LFDRs of SNPs in the created combined
# reference class.
estimates.C<-lfdr.mle(x=stat.Big,dFUN=dchisq,df=1,lower.ncp = lower.ncp,
upper.ncp = upper.ncp)
LFDR.Big<-estimates.C$LFDR
p0.Big<-estimates.C$p0.hat
ncp.Big<-estimates.C$ncp.hat


#The first three values of the combined reference class correspond to the
#separate reference class in this example
LFDR.SBig<-LFDR.Big[1:3]

LFDR.ME<-ME.log(stat=stat.Small,lfdr.C=LFDR.SBig,p0.C=p0.Big,ncp.C=ncp.Big,
p0.S=p0.Small,ncp.S=ncp.Small)

LFDR.ME

Based on the Robust Bayes Approach, Performs a Multiple Hyothesis Testing Problem under an Squared Error Loss Function

Description

Assuming a squared error loss function, it provides Robust Bayes estimates of the LFDR estimates giving credit to both separate and combined reference classes.

Usage

PRGM.action(x1,x2)

Arguments

Value

The output is a vector of the LFDR estimates based on the two reference classes.

Author(s)

Code: Ali Karimnezhad.
Documentation: Johnary Kim and Anna Akpawu.

References

Karimnezhad, A. and Bickel, D. R. (2016). Incorporating prior knowledge about genetic variants into the analysis of genetic association data: An empirical Bayes approach. Working paper. Retrieved from http://hdl.handle.net/10393/34889

Examples

#LFDR reference class values generated

#First reference class
LFDR.Separate <- c(0.14, 0.8, 0.16, 0.30)
#Second reference class
LFDR.Combined <- c(0.21, 0.61, 0.12, 0.10)

output <- PRGM.action(LFDR.Separate, LFDR.Combined)

# Vector of the LFDR estimates
output

Based on a Decision-Theoretic Approach, Performs a Multiple Hyothesis Testing Problem under an Squared Error Loss Function

Description

Assuming a squared error loss function, it provides three caution-type actions using estimated LFDRs computed based on both separate and combined reference classes.

Usage

SEL.caution.parameter(x1,x2)

Arguments

Value

Much like caution.parameter.actions, this function returns three vectors of equal size as seen below:

For each index of the vectors, the squared error loss values are given.

Author(s)

Code: Ali Karimnezhad.
Documentation: Johnary Kim and Anna Akpawu.

References

Karimnezhad, A. and Bickel, D. R. (2016). Incorporating prior knowledge about genetic variants into the analysis of genetic association data: An empirical Bayes approach. Working paper. Retrieved from http://hdl.handle.net/10393/34889

Examples

#Similar to caution.parameter actions we have the following classes

#First reference class
LFDR.Separate <- c(0.14, 0.8, 0.16, 0.30)
#Second reference class
LFDR.Combined <- c(0.21, 0.61, 0.12, 0.10)

output <- SEL.caution.parameter(LFDR.Separate, LFDR.Combined)

# Three caution cases with SEL values.
output

Based on a Decision-Theoretic Approach, Performs a Multiple Hypothesis Testing Problem under a Zero-One Loss Function

Description

Assuming a zero-onr loss function, it provides three caution-type actions using estimated LFDRs computed based on both separate and combined reference classes.

Usage

caution.parameter.actions(x1,x2,l1=4,l2=1) # default values l1=4 and l2=1
# to obtain a threshold of 20%.

Arguments

Details

Accepts previously obtained LFDR estimates of SNPs falling inside the intersection of the separate and combined reference classes. The LFDR estimates of some biological feature (SNP or gene) within a sample population that we will refer to as ‘reference class’. If a reference class, containing LFDR estimates is a subset of the other, it is referred to as ‘separate class’. The entire set of LFDR estimates is called a ‘combined’ reference class. Then, a multiple hypothesis problem is conducted using three caution-type estimators. The threshold set for rejecting the null hypothesis is derived from pre-specified l1 and l2 values. Since having a type-I error is worse than a type-II error, l1 is recommende to be greater than l2.

In generating the output, there are two potential outputs for each index of the three caution-type actions. Check the Value section for the corresponding caution-type actions.

For each index of the output, one of two potential outputs based on Bayes action are shown:

For each corresponding index in the output, the decision on whether to reject or not reject the null hypothesis for biological feature can be based on CGM1, CGM0, and CGM0.5 decisions. Check See Also for more details on how to better interpret the outputs.

Value

Outputs three vectors of equal size as seen below:

Note that the length of the input vectors x1 and x2 determines the number of null hypothesis values seen in the output.

Note

A limitation to the code is that both reference classes: x1 and x2 must be of the same vector length.

Author(s)

Code: Ali Karimnezhad.
Documentation: Justin Chitpin, Anna Akpawu and Johnary Kim.

References

Karimnezhad, A. and Bickel, D. R. (2016). Incorporating prior knowledge about genetic variants into the analysis of genetic association data: An empirical Bayes approach. Working paper. Retrieved from http://hdl.handle.net/10393/34889

See Also

For more information on how to interpret the outputs, look at the vignette, “Using LFDREmpiricalBayes”.

Examples

#LFDR reference class values generated

#First reference class (separate class)
LFDR.Separate <- c(.14,.8,.251,.30)
#Second reference class (combined class)
LFDR.Combined <- c(.21,.61,.0888,.10)

# Default threshold at (20%).
output <- caution.parameter.actions(x1=LFDR.Separate, x2=LFDR.Combined)

# Three caution cases
output