Tiltmod Manual
User 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 <chongm@email.sc.edu>
Description Develop an exponential tilting method by conditioning on the false discov-
ery rate to tilt a two component mixture of Beta distributions, yielding an tilted mix-
ture model. Use a Boosted EM algorithm to fit a two-component mixture of Beta distribu-
tions for p-values or left tail areas of test statistics. The Boosted EM algorithm for the mix-
ture model fitting is built in C++, which is quite fast and stable. The package also in-
cludes 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
Rtopics documented:
etilt ............................................. 2
fnet ............................................. 3
Marfan............................................ 4
MBM ............................................ 4
pickrell ........................................... 5
power ............................................ 5
tqvalue............................................ 7
UBMM ........................................... 8
Index 9
1
2etilt
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)
fThe objective function is tilted. If either xl or f is NULL, f is fitted by UBMM.
Default is NULL.
hThe conditioning function. By default, h = (1-p)/f(x), where f(x) = (1 −p)×
duniform(x) + p×dbeta(x, α, β).
mThe 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
xA 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)
4MBM
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
xA vector of numeric values
wA vector of two numeric values, representing the weights of two Beta distribu-
tions. 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 tweeDEseqCount-
Data.
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 proba-
bility 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)
6power
Arguments
qA numeric value or a vector of numerical value, represent global false discovery
rate used for power analysis.
xA vector of numeric values, represent p-values or left-tail areas of test statistics
from a differential gene expression study.
wA vector of two numeric values, represent the weights of the uniform and Beta
distributions. See UBMM.
aA 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 calcu-
lated based on the rejection region R(q) and the empirical mixture model for x.
qThe 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, re-
spectively.
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 7
tqvalue 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)
wA vector of two numeric values, representing the weights of the uniform and
Beta distributions. See UBMM.
aA 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 opti-
mal 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.
qA numeric value. The global false discovery rate used in method “m2”, to de-
termine 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)).
8UBMM
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
xA vector of numeric values
wA vector of two numeric values, representing the weights of the uniform and
Beta distributions. Default values are 0.5, respectively.
aInitial values of the alpha and beta for the Beta distribution. Defaults are ob-
tained 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))
