Tiltmod Manual

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Package ‘tiltmod’
June 17, 2018
Type Package
Title Exponential Tilting Method for Reproducible Screening of Large
Scale Testing Problem
Version 0.0.1
Author Chong Ma
Maintainer Chong Ma 
Description Develop an exponential tilting method by conditioning on the false discovery rate to tilt a two component mixture of Beta distributions, yielding an tilted mixture model. Use a Boosted EM algorithm to fit a two-component mixture of Beta distributions for p-values or left tail areas of test statistics. The Boosted EM algorithm for the mixture model fitting is built in C++, which is quite fast and stable. The package also includes two utility functions to generate tilted false discovery rates and frequency network.
Depends R (>= 3.3.1)
License GPL (>= 2)
LinkingTo Rcpp, BH
Imports Rcpp (>= 0.12.15), stats, foreach, doParallel, plyr, utils,
igraph, edgeR, limma
Encoding UTF-8
LazyData true
RoxygenNote 6.0.1
URL https://github.com/chongma1989/tiltmod
NeedsCompilation yes
Archs i386, x64

R topics documented:
etilt . .
fnet . .
Marfan .
MBM .
pickrell
power .
tqvalue .
UBMM

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2
3
4
4
5
5
7
8
9

1

2

etilt

etilt

The exponential tilting function

Description
This function tilts the mixture model fitted from the training tail-areas (or p-values) by conditioning
on the average of local fdr’s from the testing tail-areas (or p-values)
Usage
etilt(xl, xt, f = NULL, h = NULL, m = NULL, interval = NULL,
rel.tol = .Machine$double.eps^0.25, ...)

Arguments
xl

The training left-tail areas (or p-values)

xt

The testing left-tail areas (or p-values)

f

The objective function is tilted. If either xl or f is NULL, f is fitted by UBMM.
Default is NULL.

h

The conditioning function. By default, h = (1-p)/f(x), where f (x) = (1 − p) ×
dunif orm(x) + p × dbeta(x, α, β).

m

The constant is used to find the optimal theta such that E(h(x))=m. If m is
NULL, m = mean(h(xt)). Default is NULL.

interval

The interval is used to search the optimal theta. Default is (-100L,100L).

rel.tol

the accuracy used in integrate.

...

Arguments to be passed to uniroot.

Value
A list includes theta, tau, tilt_tau, tilt_f, tilt_f0, tilt_f1, respectively.
Examples
xl=c(rbeta(100,0.5,0.5),runif(900))
xt=c(rbeta(300,2,3),runif(700))
## Not run:
etilt(xl,xt)
## End(Not run)

fnet

3

fnet

Frequency network

Description
This function displays the frequency network of discovered differentially expressed genes.

Usage
fnet(x, Simplify = FALSE, threshold = 0.05, max.ew = 2, max.size = 18,
node = TRUE, directed = FALSE, print.graph = TRUE, ...)

Arguments
x

A list of discovered differentially expressed genes

Simplify

logical indicating whether to discard the genes with lower relative freqency than
the threshold. Default is FALSE.

threshold

a numeric value determining the cutoff point, where the genes are discarded with
lower relative frequency than it. Default is 0.05.

max.ew

a numeric value. The maximum edge width in the network plot.

directed

A logical value, indicates whether the edges are shown in directions. Default is
FALSE.

print.graph

A logical value. Default is TRUE. If FALSE, then do not print the frequency
network.

...

Arguments to be passed to plot.igraph.

Value
A network plot.

Examples
x=list(c(1,3,4),c(2,4,5),c(3,5,1),c(4,1,2),c(5,2,3))
## Not run:
fnet(x)
fnet(x,layout=layout.fruchterman.reingold,vertex.color="grey60")
## End(Not run)

4

MBM

Marfan

Marfan

Description
Gene expression data includes the treatment group and 4132 gene expressions.
Usage
Marfan
Format
A data frame for 101 samples with 4133 variables: treatment, X1,...,X4132. treatment contains
41 samples from the control group and 60 samples from the Marfan group.
Source
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2174953/.

MBM

Fit a two-point mixture of Beta distributions

Description
Fit a two-point mixture of Beta distributions
Usage
MBM(x, w = as.numeric(c()), a0 = as.numeric(c()), a1 = as.numeric(c()),
precision = 1e-06, MaxIter = 10000L)
Arguments
x

A vector of numeric values

w

A vector of two numeric values, representing the weights of two Beta distributions. Default values are 0.5, respectively.

a0

Initial values of the alpha and beta for Beta distribution f0. Default values are 1
and 1, respectively.

a1

Initial values of the alpha and beta for Beta distribution f1. Default values are
0.5 and 0.5, respectively.

precision

The tolerance for convergence. Default value is 1e-6.

MaxIter

The maximum iteration for the EM algorithm. Default value is 10000L.

Value
A list of four components, including the converged weight, parameters for Beta distribution f0,
parameters for Beta distribution f1, and the convergence iteration, respectively.

pickrell

5

Examples
x0=rbeta(900,0.8,0.8)
x1=rbeta(100,0.2,0.2)
## Not run:
MBM(c(x0,x1),w=c(0.8,0.2),a0=c(1,1),a1=c(0.5,0.5))
## End(Not run)

pickrell

pickrell

Description
The RNA-Seq profiles were made of cell lines derived from lymphoblastoid cells from 69 different
Yoruba individuals from Ibadan, Nigeria. Pickrell data consists of 40 females and 29 males for
17310 gene counts data, which are well annotated and being at least 1 count-per-million (cpm) in at
least 20 samples. The raw RNA-Seq data for pickrell is available in R package tweeDEseqCountData.
Usage
pickrell
Format
A DGEList S4 class, contains the gene count data, sample information, and gene annotation data.
Source
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3089435/.

power

Empirical power analysis

Description
This function deals with power analysis by calculating the relevant TypeI error, power, and probability of being significant by given global false discovery rate.
Usage
power(q, x, w = NULL, a = NULL, precision = 1e-08, MaxIter = 10000L,
theta = NULL, alpha = 0.9, type = c("left tail area", "pvalue"),
rel.tol = .Machine$double.eps^0.25, tol = .Machine$double.eps^0.5)

6

power

Arguments
q

A numeric value or a vector of numerical value, represent global false discovery
rate used for power analysis.

x

A vector of numeric values, represent p-values or left-tail areas of test statistics
from a differential gene expression study.

w

A vector of two numeric values, represent the weights of the uniform and Beta
distributions. See UBMM.

a

A vector of two initial parameter values for Beta distribution. See UBMM.

precision

The precision for convergence. Default value is 1e-8.

MaxIter

The maximum iteration for the EM algorhthm.

theta

A numerical value, represents the exponential tilting parameter for the fitted
mixture model from x. Defualt is NULL.

alpha

A numeric value, used to determine the probably null region in method “m1"
(see tqvalue). Default is 0.9.

type

A character value, chosen from “left tail area” and “pvalue”. Default is “left tail
area”.

rel.tol

the accuracy used in integrate.

tol

the accuracy used in uniroot.

Value
A dataframe consists of q, TypeI, Power, ProbS, respectively. TypeI, Power, and ProbS are calculated based on the rejection region R(q) and the empirical mixture model for x.
q The global false discovery rates provided in arguments.
TypeI P (R(q)|H0 )
power P (R(q)|H1 )
ProbS P (R(q))
If theta is provided, then the results contain two data frames as above, one is calculated from the
non-exponential tilted mixture model and the other from the exponential tilted mixture model, respectively.
Examples
x=c(rbeta(50,0.5,0.5),runif(950))
q=seq(0.05,0.95,0.05)
## Not run:
power(q,x,alpha=0.9,type="left tail area")
power(q,x,theta=2,alpha=0.9,type="left tail area")
## End(Not run)

tqvalue

tqvalue

7

The exponential tilting mixture model

Description
This function tilts the mixture model fitted from the training tail-areas (or p-values) by conditioning
on the average of local fdr’s from the testing tail-areas (or p-values)
Usage
tqvalue(xl, xt, w = NULL, a = NULL, precision = 1e-08, MaxIter = 10000L,
interval = NULL, adjust = TRUE, method = c("m1", "m2"),
type = c("left tail area", "pvalue"), alpha = 0.9, q = 0.1,
ncores = 1, rel.tol = .Machine$double.eps^0.25,
tol = .Machine$double.eps^0.5)
Arguments
xl

The training left-tail areas (or p-values)

xt

The testing left-tail areas (or p-values)

w

A vector of two numeric values, representing the weights of the uniform and
Beta distributions. See UBMM.

a

A vector of two initial parameter values for Beta distribution. See UBMM.

precision

The precision for convergence. Default value is 1e-8.

MaxIter

The maximum iteration for the EM algorhthm.

interval

A vector of two numeric values, which determines the range to search the optimal theta. Default is c(-1000L,1000L).

adjust

Whether or not to do the model adjustment. Default is TRUE.

method

A character chosen from m1, m2. Default is m1.

type

A character value, chosen from “left tail area” and “pvalue”. Default is “left tail
area”.

alpha

A numeric value. Used in method “m1” to determine the probably null region.
Default is 0.9.

q

A numeric value. The global false discovery rate used in method “m2”, to determine the probable null region. Default is 0.1.

ncores

The number of cpus used for implementing this function.

rel.tol

the accuracy used in integrate.

tol

the accuracy used in uniroot.

Value
A dataframe includes xl, xt, fdr, FDR, tfdr, and tFDR, respectively. fdr and FDR are the local and
global false discovery rate for each value of xt. tfdr and tFDR are the corresponding tilted local and
global false discovery rate, respectively.
The optimal theta calculated by solving log(E(exp(thetah(x))))-ctheta, where c=mean(h(xt)).

8

UBMM

Examples
xl=c(rbeta(50,0.2,0.2),runif(950))
xt=c(rbeta(50,0.1,0.1),runif(950))
## Not run:
tqvalue(xl,xt,ncores=4,adjust=FALSE,type="left tail area")
## End(Not run)

UBMM

Fit a mixture of uniform and Beta distribution

Description
Fit a mixture of uniform and Beta distribution
Usage
UBMM(x, w = as.numeric(c()), a = as.numeric(c()), precision = 1e-08,
MaxIter = 10000L)
Arguments
x

A vector of numeric values

w

A vector of two numeric values, representing the weights of the uniform and
Beta distributions. Default values are 0.5, respectively.

a

Initial values of the alpha and beta for the Beta distribution. Defaults are obtained from MOM estimators.

precision

The tolerance for convergence. Default value is 1e-8.

MaxIter

The maximum iteration for the EM algorithm. Default value is 10000L.

Value
A list of three components, including the converged weight, parameters for Beta distribution, and
the convergence iteration, respectively.
Examples
x0=runif(900)
x1=rbeta(100,0.5,0.5)
UBMM(c(x0,x1),w=c(0.8,0.2),a=c(0.7,0.8))

Index
∗Topic datasets
Marfan, 4
pickrell, 5
etilt, 2
fnet, 3
integrate, 2, 6, 7
Marfan, 4
MBM, 4
pickrell, 5
plot.igraph, 3
power, 5
tqvalue, 6, 7
UBMM, 2, 6, 7, 8
uniroot, 2, 6, 7

9
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