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\begin{document}
\SweaveOpts{engine=R,echo=FALSE,pdf=TRUE}
\title{A Genetic Analysis Package with R}
\author{Jing Hua Zhao}
\date{}
\maketitle

\begin{center}
MRC Epidemiology Unit, University of Cambridge, Cambridge, UK \\
\url{http://www.mrc-epid.cam.ac.uk/people/jing-hua-zhao}
\end{center}

\tableofcontents

% library(tools)
% Rnwfile<- file.path("/gap/inst/doc","gap.Rnw")
% Sweave(Rnwfile,pdf=TRUE,eps=TRUE,stylepath=TRUE,driver=RweaveLatex())

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Introduction}

This package was initiated to integrate some C/Fortran/SAS programs I have written 
or used over the years. As such, it would rather be a long-term project, but an
immediate benefit would be something complementary to other packages currently
available from CRAN, e.g. {\bf genetics}, {\bf hwde}, etc. I hope eventually this will
be part of a bigger effort to fulfill most of the requirements foreseen by many, 
e.g. ~\cite{guo00}, within the portable environment of R for data management, 
analysis, graphics and object-oriented programming. My view has been outlined
more formally in ~\cite{zt06a} and ~\cite{zt06b} in relation to other package
systems. Also reported are ~\cite{zhao05} and ~\cite{zhao06} on package {\bf kinship}.\\

The number of functions are quite limited and experimental, but I already feel
the enormous advantage by shifting to R and would like sooner rather than later
to share my work with others. I will not claim this work as exclusively done by
me, but would like to invite others to join me and enlarge the collections and
improve them.

\section{Implementation}

The following list shows the data and functions currently available.

\begin{tabular}{ll}
\\
* ANALYSIS *\\
\\
AE3               &      AE model using nuclear family trios\\
bt                &      Bradley-Terry model for contingency table\\
ccsize            &      Power and sample size for case-cohort design\\
fbsize            &      Sample size for family-based linkage and association design\\
gc.em             &      Gene counting for haplotype analysis\\
gcontrol          &      genomic control\\
gcontrol2         &      genomic control based on p values\\
gcp               &      Permutation tests using GENECOUNTING\\
genecounting      &      Gene counting for haplotype analysis\\
gif               &      Kinship coefficient and genetic index of familiality\\
grmMCMC           &      Mixed modeling with genetic relationship matrices\\
hap               &      Haplotype reconstruction\\
hap.em            &      Gene counting for haplotype analysis\\
hap.score         &      Score statistics for association of traits with haplotypes\\
htr               &      Haplotype trend regression\\
hwe               &      Hardy-Weinberg equilibrium test for a multiallelic marker\\
hwe.cc            &      A likelihood ratio test of population Hardy-Weinberg equilibrium \\
hwe.hardy         &      Hardy-Weinberg equilibrium test using MCMC\\
kin.morgan        &      kinship matrix for simple pedigree\\
LD22              &      LD statistics for two diallelic markers\\
LDkl              &      LD statistics for two multiallelic markers\\
masize            &      Sample size calculation for mediation analysis\\
mia               &      multiple imputation analysis for hap\\
mtdt              &      Transmission/disequilibrium test of a multiallelic marker\\
mtdt2             &      Transmission/disequilibrium test of a multiallelic marker\\
                  &      by Bradley-Terry model\\
mvmeta            &      Multivariate meta-analysis based on generalized least squares\\
pbsize            &      Power for population-based association design\\
pbsize2           &      Power for case-control association design\\
pfc               &      Probability of familial clustering of disease\\
pfc.sim           &      Probability of familial clustering of disease\\
pgc               &      Preparing weight for GENECOUNTING\\
print.hap.score   &      Print a hap.score object\\
s2k               &      Statistics for 2 by K table\\
tscc              &      Power calculation for two-stage case-control design\\
\end{tabular}

\begin{tabular}{ll}
\\
* GRAPHICS *\\
\\
asplot            &      Regional association plot\\
ESplot            &      Effect-size plot\\
mhtplot           &      Manhattan plot\\
mhtplot2          &      Manhattan plot with annotations\\
pedtodot          &      Converting pedigree(s) to dot file(s)\\
plot.hap.score    &      Plot haplotype frequencies versus haplotype score statistics\\
qqfun             &      Quantile-comparison plots\\
qqunif            &      Q-Q plot for uniformly distributed random variable\\
\end{tabular}

\begin{tabular}{ll}
\\
* DATASETS *\\
\\
PD                &      A study of Parkinson's disease and APOE, LRRK2, SNCA makers \\
aldh2             &      ALDH2 markers and alcoholism\\
apoeapoc          &      APOE/APOC1 markers and schizophrenia\\
cf                &      Cystic Fibrosis data\\
crohn             &      Crohn's disease data\\
fa                &      Friedreich ataxia data\\
fsnps             &      A case-control data involving four SNPs with missing genotype\\
hla               &      HLA markers and schizophrenia\\
l51               &      An example pedigree data\\
lukas             &      An example pedigree\\
mao               &      A study of Parkinson's disease and MAO gene\\
meyer             &      A pedigree data on 282 animals deriving from two generations\\
nep499            &      A study of Alzheimer's disease with eight SNPs and APOE\\
\end{tabular}

\begin{tabular}{ll}
\\
* UTILITIES *\\
\\
SNP               &      Functions for single nucleotide polymorphisms (SNPs)\\
BFDP              &      Bayesian false-discovery probability\\
FPRP              &      False-positive report probability\\
ab                &      Test/Power calculation for mediating effect\\
b2r               &      Obtain correlation coefficients and their variance-covariances\\
chow.test         &      Chow's test for heterogeneity in two regressions\\
comp.score        &      score statistics for testing genetic linkage of quantitative trait\\
h2                &      Heritability estimation according to twin correlations\\
                  &      for case-control studies\\
klem              &      Haplotype frequency estimation based on a genotype table\\
                  &      of two multiallelic markers\\
makeped           &      A function to prepare pedigrees in post-MAKEPED format\\
metap             &      Meta-analysis of p values\\
metareg           &      Fixed and random effects model for meta-analysis\\
muvar             &      Means and variances under 1- and 2- locus (diallelic) QTL model\\
read.ms.output    &      A utility function to read ms output\\
twinan90          &      Classic twin models\\
whscore           &      Whittemore-Halpern scores for allele-sharing\\
GRM functions     &      ReadGRM, ReadGRMBin, ReadGRMPLINK, ReadGRMPCA, WriteGRM, WriteGRMBin, WriteGRMSAS\\
                  &      handle genomic relationship matrix involving other software\\
heritability functions & h2G, VR, h2GC, h2l give point estimates as with their variances\\
                       & for continuous traits and binary traits under liability threshold model and\\
                       & case-control sampling\\
\\
\end{tabular}

Assuming proper installation, you will be able to obtain the list by typing
\texttt{library(help=gap)} or view the list within a web browser via 
\texttt{help.start()}. Assuming that you have already loaded the package via
\texttt{library(gap)}, you can use \texttt{lsf.str("package:gap")} and 
\texttt{data(package="gap")} to generate a list of functions and a list
of datasets, respectvely. If this looks odd to you, you might try 
\texttt{search()} within \texttt{R} to examine what is available in your
environment before issuing the \texttt{lsf.str} command.\\
<<echo=TRUE>>=
library(gap)
search()
lsf.str("package:gap")
data(package="gap")$results
@

A PDF version of this file can be viewed with command \texttt{vignette("gap",package="gap")}.\\

You can cut and paste examples at end of each function's documentation.\\

Both \textit{genecounting} and \textit{hap} are able to handle SNPs and multiallelic
markers, with the former be flexible enough to include features such as X-linked data
and the later being able to handle large number of SNPs. But they are unable to
recode allele labels automatically, so functions \textit{gc.em} and \textit{hap.em}
are in \textit{haplo.em} format and used by a modified function \textit{hap.score} in
association testing.\\

It is notable that multilocus data are handled differently from that in {\bf hwde} and
elegant definitions of basic genetic data can be found in the {\bf genetics} package.\\

Incidentally, I found my C mixed-radixed sorting routine as in \cite{zhao03} is much
faster than R's internal function.\\

With exceptions such as function \textit{pfc} which is very computer-intensive, most
functions in the package can easily be adapted for analysis of large datasets involving
either SNPs or multiallelic markers. Some are utility functions, e.g. \textit{muvar}
and \textit{whscore}, which will be part of the other analysis routines in the future.\\

The benefit with R compared to standalone programs is that for users, all functions have
unified format. For developers, it is able to incorporate their C/C++ programs more
easily and avoid repetitive work such as preparing own routines for matrix algebra and
linear models. Further advantage can be taken from packages in {\bf Bioconductor}, which
are designed and written to deal with large number of genes.\\

\section{Independent programs}

To facilitate comparisons and individual preferences, I have made the source codes
available for 2LD, EHPLUS, GENECOUNTING, HAP which have enjoyed great popularity ahead
of the genomewide association studies (GWAS) therefore are likely to be more familiar
than their R couunterparts in \texttt{gap}. However, you need to follow their instructions
to compile for a particular computer system.\\

I have included {ms} code (which is required by \texttt{read.ms.output}) and .xls files
to accompany {\em read.ms.output} and {\em FPRP} and {\em BFDP} functions as with a 
classic twin example for ACE model in {\bf OpenMx}. The package is now available from
CRAN and earlier it can be installed with command,

\begin{Schunk}
\begin{Scode}
source('http://openmx.psyc.virginia.edu/getOpenMx.R')
\end{Scode}
\end{Schunk}

For these models it is actually simpler to use facilities as in package {\bf mets}, which I
now suggest.\\

A final category is \texttt{twinan90}, which is now dropped from the package function list
due to difficulty to keep up with the requirements by the \texttt{R} environment but 
nevertheless you will still be able to compile and use otherwise.

\section{Demos}

You can also try several simple examples via \textit{demo}:

\begin{Schunk}
\begin{Scode}
library(gap)
demo(gap)
\end{Scode}
\end{Schunk}

\section{Examples}

I would like to highlight {\em pedtodot} {\em pbsize}, {\em fbsize} and {\em ccsize} functions
used for pedigree drawing and power/sample calculations in a genome-wide asssociatoin study as
reported in~\cite{zhao07}.\\

\subsection{Pedigree drawing}
I have included the original file for the {\em R News} as well as put examples in separate 
vignettes. They can be accessed via \texttt{vignette("rnews",package="gap")} and 
\texttt{vignette("pedtodot", package="gap")}, respectively.\\

\subsection{Kinship calculation}
Next, I will provide an example for kinship calculation using {\em kin.morgan}.
It is recommended that individuals in a pedigree are ordered so that parents
always precede their children. In this regard, package {\bf pedigree} can be
used, and package {\bf kinship2} can be used to produce pedigree diagram as with
kinship matrix.

\subsubsection*{Pedigree diagram}
<<echo=TRUE>>=
# pedigree diagram
data(lukas,package="gap")
library(kinship2)
ped <- with(lukas,pedigree(id,father,mother,sex))
pdf("figures/lukas.pdf",height=14,width=15)
plot(ped)
dev.off()
@

The pedigree diagram is as follows,

\includegraphics[height=14cm,width=15cm]{figures/lukas.pdf}

\subsubsection*{Kinship calculation}
We then turn to the kinship calculation.

<<echo=TRUE>>=
# unordered individuals
library(gap)
gk1 <- kin.morgan(lukas)
write.table(gk1$kin.matrix,"results/gap_1.txt",quote=FALSE)

library(kinship2)
kk1 <- kinship(lukas[,1],lukas[,2],lukas[,3])
write.table(kk1,"results/kinship_1.txt",quote=FALSE)

d <- gk1$kin.matrix-kk1
sum(abs(d))

# order individuals so that parents precede their children
library(pedigree)
op <- orderPed(lukas)
olukas <- lukas[order(op),]
gk2 <- kin.morgan(olukas)

write.table(olukas,"olukas.csv",quote=FALSE)
write.table(gk2$kin.matrix,"results/gap_2.txt",quote=FALSE)

kk2 <- kinship(olukas[,1],olukas[,2],olukas[,3])
write.table(kk2,"results/kinship_2.txt",quote=FALSE)

z <- gk2$kin.matrix-kk2
sum(abs(z))
@

We see that in the second case, the result agrees with {\bf kinship2}.

\subsection{Study design}
\subsubsection*{Family-based design}
The example involving family-based design is as follows,
<<echo=TRUE>>=
library(gap)
models <- matrix(c(
         4.0, 0.01,
         4.0, 0.10,
         4.0, 0.50, 
         4.0, 0.80,
         2.0, 0.01,
         2.0, 0.10,
         2.0, 0.50,
         2.0, 0.80,
         1.5, 0.01,    
         1.5, 0.10,
         1.5, 0.50,
         1.5, 0.80), ncol=2, byrow=TRUE)
outfile <- "fbsize.txt"
cat("gamma","p","Y","N_asp","P_A","H1","N_tdt","H2","N_asp/tdt","L_o","L_s\n",
    file=outfile,sep="\t")
for(i in 1:12) {
    g <- models[i,1]
    p <- models[i,2]
    z <- fbsize(g,p)
    cat(z$gamma,z$p,z$y,z$n1,z$pA,z$h1,z$n2,z$h2,z$n3,z$lambdao,z$lambdas,
        file=outfile,append=TRUE,sep="\t")
    cat("\n",file=outfile,append=TRUE)
}
table1 <- read.table(outfile,header=TRUE,sep="\t")
nc <- c(4,7,9)
table1[,nc] <- ceiling(table1[,nc])
dc <- c(3,5,6,8,10,11)
table1[,dc] <- round(table1[,dc],2)
unlink(outfile)
# APOE-4, Scott WK, Pericak-Vance, MA & Haines JL
# Genetic analysis of complex diseases 1327
g <- 4.5
p <- 0.15
cat("\nAlzheimer's:\n\n")
fbsize(g,p)
table1
@

\subsubsection*{Population-based design}
The example involving population-based design is as follows,
<<echo=TRUE>>=
library(gap)
kp <- c(0.01,0.05,0.10,0.2)
models <- matrix(c(
          4.0, 0.01,
          4.0, 0.10,
          4.0, 0.50, 
          4.0, 0.80,
          2.0, 0.01,
          2.0, 0.10,
          2.0, 0.50,
          2.0, 0.80,
          1.5, 0.01,    
          1.5, 0.10,
          1.5, 0.50,
          1.5, 0.80), ncol=2, byrow=TRUE)
outfile <- "pbsize.txt"
cat("gamma","p","p1","p5","p10","p20\n",sep="\t",file=outfile)
for(i in 1:dim(models)[1])
{
   g <- models[i,1]
   p <- models[i,2]
   n <- vector()
   for(k in kp) n <- c(n,ceiling(pbsize(k,g,p)))
   cat(models[i,1:2],n,sep="\t",file=outfile,append=TRUE)
   cat("\n",file=outfile,append=TRUE)
} 
table5 <- read.table(outfile,header=TRUE,sep="\t")
table5
@

\subsubsection*{Case-cohort design}
For case-cohort design, we obtain results for ARIC and EPIC studies.
<<echo=TRUE>>=
library(gap)
# ARIC study
outfile <- "aric.txt"
n <- 15792
pD <- 0.03
p1 <- 0.25
alpha <- 0.05
theta <- c(1.35,1.40,1.45)
beta1 <- 0.8
s_nb <- c(1463,722,468)
cat("n","pD","p1","hr","q","power","ssize\n",file=outfile,sep="\t")
for(i in 1:3)
{
  q <- s_nb[i]/n
  power <- ccsize(n,q,pD,p1,alpha,log(theta[i]))
  ssize <- ccsize(n,q,pD,p1,alpha,log(theta[i]),beta1)
  cat(n,"\t",pD,"\t",p1,"\t",theta[i],"\t",q,"\t",signif(power,3),"\t",ssize,"\n",
      file=outfile,append=TRUE)
}
read.table(outfile,header=TRUE,sep="\t")
unlink(outfile)
# EPIC study
outfile <- "epic.txt"
n <- 25000
alpha <- 0.00000005
power <- 0.8
s_pD <- c(0.3,0.2,0.1,0.05)
s_p1 <- seq(0.1,0.5,by=0.1)
s_hr <- seq(1.1,1.4,by=0.1)
cat("n","pD","p1","hr","alpha","ssize\n",file=outfile,sep="\t")
# direct calculation
for(pD in s_pD)
{
   for(p1 in s_p1)
   {
      for(hr in s_hr)
      {
         ssize <- ccsize(n,q,pD,p1,alpha,log(hr),power)
         if (ssize>0) cat(n,"\t",pD,"\t",p1,"\t",hr,"\t",alpha,"\t",ssize,"\n",
                          file=outfile,append=TRUE)
      }
   }
}
read.table(outfile,header=TRUE,sep="\t")
unlink(outfile)
@

\subsection{Graphics examples}
I now include some figures from the documentation that may be of interest.\\

\subsubsection*{Genome-wide association}
The following code is used to obtain a Q-Q plot via {\em qqunif} function,
<<echo=TRUE>>=
library(gap)
pdf("figures/qqunif.pdf",height=10,width=10)
u_obs <- runif(1000)
r <- qqunif(u_obs,pch=21,bg="blue",bty="n")
u_exp <- r$y
hits <- u_exp >= 2.30103
points(r$x[hits],u_exp[hits],pch=21,bg="green")
dev.off()
@

\includegraphics[height=10cm,width=10cm]{figures/qqunif.pdf}

Based on a chicken genome scan data, the code below generates a Manhattan plot, demonstrating
the use of gaps to separate chromosomes.

<<echo=TRUE>>=
library(gap)
load("4w.rda")
ord <- with(d,order(chr,pos))
d <- d[ord,]
pdf("figures/4w.pdf",height=9,width=10)
oldpar <- par()
par(cex=0.6)
colors <- c(rep(c("blue","red"),15),"red")
mhtplot(d,control=mht.control(colors=colors,gap=1000),pch=19,srt=0)
axis(2,cex.axis=2)
suggestiveline <- -log10(3.60036E-05)
genomewideline <- -log10(1.8E-06)
abline(h=suggestiveline, col="blue")
abline(h=genomewideline, col="green")
abline(h=0)
dev.off()
@

\includegraphics[scale=0.25,width=\linewidth]{figures/4w.pdf}

The code below obtains a Manhattan plot with gene annotation,
<<echo=TRUE>>=
library(gap)
png("figures/mhtplot.png",height=10,width=16,units="cm",res=300)
data <- with(mhtdata,cbind(chr,pos,p))
glist <- c("IRS1","SPRY2","FTO","GRIK3","SNED1","HTR1A","MARCH3","WISP3","PPP1R3B",
           "RP1L1","FDFT1","SLC39A14","GFRA1","MC4R")
hdata <- subset(mhtdata,gene%in%glist)[c("chr","pos","p","gene")]
color <- rep(c("lightgray","gray"),11)
glen <- length(glist)
hcolor <- rep("red",glen)  
par(las=2, xpd=TRUE, cex.axis=1.8, cex=0.4)
ops <- mht.control(colors=color,yline=1.5,xline=3)
hops <- hmht.control(data=hdata,colors=hcolor)
mhtplot(data,ops,hops,pch=19)
axis(2,pos=2,at=1:16)
title("Manhattan plot with genes highlighted",cex.main=1.8)
dev.off()
@

\includegraphics[height=10cm,width=16cm]{figures/mhtplot.png}

All these look familiar, so revised form of the function called {\bf mhtplot2} was
created for additional features such as centering the chromosome ticks, allowing for 
more sophisticated coloring schemes, using prespecified fonts, etc. Please refer to
the function's documentation example.

The code below obtains a regional association plot with the {\em asplot} function,
<<echo=TRUE>>=
library(gap)
pdf("figures/asplot.pdf",height=14,width=14)
asplot(CDKNlocus, CDKNmap, CDKNgenes, best.pval=5.4e-8, sf=c(3,6))
title("CDKN2A/CDKN2B Region")
dev.off()
@

\includegraphics[height=14cm,width=14cm]{figures/asplot.pdf}

The function predates the currently popular {\bf locuszoom} software but leaves
the option open for generating such plots on the fly and locally.

\subsubsection*{Effect size plot}
The code below obtains an effect size plot via the {ESplot} function.
<<echo=TRUE>>=
library(gap)
pdf("figures/ESplot.pdf",height=10,width=10)
options(stringsAsFactors=FALSE)
testdata <- data.frame(models=c("Basic model","Adjusted","Moderately adjusted",
                       "Heavily adjusted","Other"),
OR = c(4.5,3.5,2.5,1.5,1),
SElogOR = c(0.2,0.1,0.5,0.5,0.2))
ESplot(testdata,v=1)
title("This is a fictitious plot")
dev.off()
@

\includegraphics[height=10cm,width=10cm]{figures/ESplot.pdf}

Note that all these can serve as templates to customize features of your own.\\

\section{Polygenic modeling}

In line with the recent surge of interest in the polygenic models, a separate
vignette is available through \texttt{vignette("h2",package="gap")} demonstrating
aspect of the models on heritability.

\section{Known bugs}

Unaware of any bug. However, better memory management is expected.

\section{Summary}

I believe by now the package should have given you a flavour of initiatives
I have made so far in relation to how the project was envisaged. More importantly,
it is clear that availability of the package will serve as a platform on which 
future work can be accumulated and collaboration can be built.

\section{Bibliographic note}

The main references are ~\cite{chow60, guo92, wcn92, gholamic94,
hartung08, risch96, spielman96, risch97, miller97, sham97, elston75,
sham98, devlin99, zhao99, guo00, hirotsu01, 
zhao02, zaykin02, zhao04, wacholder04, wang05,
skol06, wakefield07}.

\bibliography{gap}
\end{document}

% Date last modified: 19-2-2015
