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Figure1-resolution.R
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Figure1-resolution.R
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## Figure 1 Resolution for varying relatedness using GRM, encGRM and encG-reg
## encGRMsource.R includes functions:
## RandomMatrixEncryption()
## GenerateGeno()
## GenerateGeno_r()
source("encGRMsource.R")
library(ggplot2)
library(ggpubr)
library(egg)
library(svglite)
library(gridExtra)
library(grid)
library(cowplot)
library(jcolors)
color = c("grey80","#66CD00","#009ACD","#FF4500")
n1 = 200 # sample size in cohort 1
n2 = 200 # sample size in cohort 2
alpha = 0.05/(n1*n2) # type I error
beta = 0.1 # type II error two tail test
D = 3 # top degree of relatedness included in simulation
r = c(0:(D-1)) # a vector of various degree of relatedness included in simulation
n_cp = c(10,10,10,0) # numbers for each degree of relatedness
n1_0 = n1-sum(n_cp) # remaining sample size of unrelated individuals in cohort 1
n2_0 = n2-sum(n_cp) # remaining sample size of unrelated individuals in cohort 2
setavec=(0.5)^r # a vector of expected relatedness score for various degree of relatedness
Mvec = ceiling(2 * ( ( qnorm(1-beta)*sqrt(1+setavec^2) + qnorm(1-alpha) ) / setavec )^2)
# a vector of various number of markers based on Eq3 (2 times larger)
#### GRM vs encG-reg ####
count=1
dt = list()
for(m in 1:length(Mvec))
{
M = Mvec[m]
for(k in 1:m)
{
K = ceiling(1/(1/(( ( qnorm(1-beta)*sqrt(1-setavec[k]^2) + qnorm(1-alpha) ) / setavec[k] )^2 )-1/Mvec[m])) # based on Eq4
# Genotypes
freq = runif(M, 0.05, 0.5)
X1 = matrix(NA, 0, M)
X2 = matrix(NA, 0, M)
for(i in 1:D)
{
Gr = GenerateGeno_r(freq, n_cp[i], r[i], FALSE)
X1 = rbind(X1, Gr[[1]])
X2 = rbind(X2, Gr[[2]])
}
X1 = rbind(X1, GenerateGeno(freq, n1_0))
X2 = rbind(X2, GenerateGeno(freq, n2_0))
X1 = scale(X1)
X2 = scale(X2)
## Encryption
S = matrix(rnorm(M*K,sd=sqrt(1/M)), M, K)
X1hat <- tcrossprod(X1, t(S))
X2hat <- tcrossprod(X2, t(S))
X1hat <- t(apply(X1hat, 1, scale))
X2hat <- t(apply(X2hat, 1, scale))
## GRM and encG-reg
G21hat = tcrossprod(X2hat, X1hat)/ K
G21 = tcrossprod(X2, X1) / M
## Save data
yin = qnorm(0.05/n1/n2)*sqrt(1/M)
xin = qnorm(0.05/n1/n2)*sqrt(1/M+1/K)
lab = lab_relations_true(n1, n2, n_cp)
R = k-1
dt[[count]] = data.frame(x=as.vector(G21hat), y=as.vector(G21), lab=as.factor(lab), R=R, M=M, K=K, yin=yin, xin=xin)
dt[[count]] = dt[[count]] %>% dplyr::arrange(lab)
count=count+1
}
}
## main plot
p = list()
for (i in 1:(count-1))
{
M = dt[[i]]$M[1]
K = dt[[i]]$K[1]
p[[i]] = ggplot(dt[[i]], aes(x=x,y=y,grp=lab))+
geom_point(aes(color=lab), size=0.3) +
geom_hline(aes(yintercept = yin), color="blue", alpha=0.5, linetype = 5) +
geom_hline(aes(yintercept = -yin), color="blue", alpha=0.5, linetype = 5) +
geom_vline(aes(xintercept = xin), color="red", alpha=0.5, linetype = 5) +
geom_vline(aes(xintercept = -xin), color="red", alpha=0.5, linetype = 5) +
scale_x_continuous(name = "", limits=c(-1.15, 1.15)) +
scale_y_continuous(name = "",limits=c(-1.15, 1.15)) +
scale_color_manual(values=color, name="Relatedness",
labels=c("Unrelated","Identical","1st-degree","2nd-degree")) +
labs(title = bquote(italic(m[e])~"="~.(M)~","~italic(k)~"="~.(K)))+
theme_article()+
theme(legend.position = "none",
plot.title = element_text(hjust = 0.5, size = 9),
axis.line = element_line(colour = "black"),
panel.border = element_blank())
}
## distribution plot
dpy = list()
for(m in 1:length(Mvec))
{
M = Mvec[m]
dpy[[m]] = ggplot()+
stat_function(fun = dnorm, args = list( 0, sqrt( 1/M)), n = 1000, color = color[1])+
stat_function(fun = dnorm, args = list( 1, sqrt((1+(0.25)^0)/M)), n = 1000, color = color[2])+
stat_function(fun = dnorm, args = list(1/2, sqrt((1+(0.25)^1)/M)), n = 1000, color = color[3])+
stat_function(fun = dnorm, args = list(1/4, sqrt((1+(0.25)^2)/M)), n = 1000, color = color[4])+
scale_x_continuous(name = "", limits=c(-1.15, 1.15), position = "top") +
scale_y_reverse(name = "") +
coord_flip()+
theme_article()+
theme(legend.position = "none",
axis.line = element_line(colour = "black"),
axis.text = element_blank(),
axis.ticks = element_blank(),
panel.border = element_blank())
}
dpx = list()
for(k in 1:D)
{
m = D
M = Mvec[m]
K = ceiling(1/(1/(( ( qnorm(1-beta)*sqrt(1-setavec[k]^2) + qnorm(1-alpha) ) / setavec[k] )^2 )-1/Mvec[m]))
dpx[[k]] = ggplot()+
stat_function(fun = dnorm, args = list( 0, sqrt( 1/M + 1/K)), n = 1000, color = color[1])+
stat_function(fun = dnorm, args = list( 1, sqrt((1-(0.25)^0)/M + (1-(0.25)^0)/K)), n = 1000, color = color[2])+
stat_function(fun = dnorm, args = list(1/2, sqrt((1-(0.25)^1)/M + (1-(0.25)^1)/K)), n = 1000, color = color[3])+
stat_function(fun = dnorm, args = list(1/4, sqrt((1-(0.25)^2)/M + (1-(0.25)^2)/K)), n = 1000, color = color[4])+
scale_x_continuous(name = "", limits=c(-1.15, 1.15)) +
scale_y_continuous(name = "") +
theme_article()+
theme(legend.position = "none",
axis.line = element_line(colour = "black"),
axis.text = element_blank(),
axis.ticks = element_blank(),
panel.border = element_blank())
}
## blank plot
blankPlot = ggplot()+geom_blank(aes(1,1)) +
cowplot::theme_nothing()
## fig lengend
leg <- get_legend(p[[1]] +
theme(legend.position = "right", legend.title = element_text(size = 12)) +
guides(color = guide_legend(override.aes = list(size=2))))
## output
final = egg::ggarrange(dpy[[1]] , p[[1]] , blankPlot, blankPlot,
dpy[[2]] , p[[2]] , p[[3]] , blankPlot,
dpy[[3]] , p[[4]] , p[[5]] , p[[6]] ,
blankPlot, dpx[[1]] , dpx[[2]] , dpx[[3]] ,
nrow = 4 , ncol = 4 , widths = c(1,2,2,2),heights = c(2,2,2,1))
final = annotate_figure(final, left = "Relatedness by GRM", bottom = "Relatedness by encG-reg")
png("simu-MvsK-encG-reg.png", width = 750, height = 700)
# pdf("simu-MvsK-encG-reg.pdf", width = 10, height = 9)
ggpubr::ggarrange(final, as_ggplot(leg), nrow = 1, widths = c(6,1))
dev.off()
#### GRM vs encGRM ####
count=1
dt = list()
for(m in 1:length(Mvec))
{
M = Mvec[m]
for(k in 1:m)
{
K = ceiling(1/(1/(( ( qnorm(1-beta)*sqrt(1+setavec[k]^2) + qnorm(1-alpha) ) / setavec[k] )^2 )-1/Mvec[m]))
# Genotypes
freq = runif(M, 0.05, 0.5)
X1 = matrix(NA, 0, M)
X2 = matrix(NA, 0, M)
for(i in 1:D)
{
Gr = GenerateGeno_r(freq, n_cp[i], r[i], FALSE)
X1 = rbind(X1, Gr[[1]])
X2 = rbind(X2, Gr[[2]])
}
X1 = rbind(X1, GenerateGeno(freq, n1_0))
X2 = rbind(X2, GenerateGeno(freq, n2_0))
X1 = scale(X1)
X2 = scale(X2)
## Encryption
S = matrix(rnorm(M*K,sd=sqrt(1/M)), M, K)
X1hat <- tcrossprod(X1, t(S))
X2hat <- tcrossprod(X2, t(S))
## GRM and encG-reg
G21hat = tcrossprod(X2hat, X1hat)/ K
G21 = tcrossprod(X2, X1) / M
## Save data
yin = qnorm(0.05/n1/n2)*sqrt(1/M)
xin = qnorm(0.05/n1/n2)*sqrt(1/M+1/K)
lab = lab_relations_true(n1, n2, n_cp)
R = k-1
dt[[count]] = data.frame(x=as.vector(G21hat), y=as.vector(G21), lab=as.factor(lab), R=R, M=M, K=K, yin=yin, xin=xin)
dt[[count]] = dt[[count]] %>% dplyr::arrange(lab)
count=count+1
}
}
## main plot
p = list()
for (i in 1:(count-1))
{
M = dt[[i]]$M[1]
K = dt[[i]]$K[1]
p[[i]] = ggplot(dt[[i]], aes(x=x,y=y,grp=lab))+
geom_point(aes(color=lab), size=0.3) +
geom_hline(aes(yintercept = yin), color="blue", alpha=0.5, linetype = 5) +
geom_hline(aes(yintercept = -yin), color="blue", alpha=0.5, linetype = 5) +
geom_vline(aes(xintercept = xin), color="red" , alpha=0.5, linetype = 5) +
geom_vline(aes(xintercept = -xin), color="red" , alpha=0.5, linetype = 5) +
scale_x_continuous(name = "", limits=c(-1.15, 1.15)) +
scale_y_continuous(name = "", limits=c(-1.15, 1.15)) +
scale_color_manual(values=color, name="Relatedness",
labels=c("Unrelated","Identical","1st-degree","2nd-degree")) +
labs(title = bquote(italic(m[e])~"="~.(M)~","~italic(k)~"="~.(K)))+
theme_article()+
theme(legend.position = "none",
plot.title = element_text(hjust = 0.5, size = 9),
axis.line = element_line(colour = "black"),
panel.border = element_blank())
}
## distribution plot
dpy = list()
for(m in 1:length(Mvec))
{
M = Mvec[m]
dpy[[m]] = ggplot()+
stat_function(fun = dnorm, args = list( 0, sqrt( 1/M)), n = 1000, color = color[1])+
stat_function(fun = dnorm, args = list( 1, sqrt((1+(0.25)^0)/M)), n = 1000, color = color[2])+
stat_function(fun = dnorm, args = list(1/2, sqrt((1+(0.25)^1)/M)), n = 1000, color = color[3])+
stat_function(fun = dnorm, args = list(1/4, sqrt((1+(0.25)^2)/M)), n = 1000, color = color[4])+
scale_x_continuous(name = "", limits=c(-1.15, 1.15), position = "top") +
scale_y_reverse(name = "") +
coord_flip()+
theme_article()+
theme(legend.position = "none",
axis.line = element_line(colour = "black"),
axis.text = element_blank(),
axis.ticks = element_blank(),
panel.border = element_blank())
}
dpx = list()
for(k in 1:D)
{
m = D
K = ceiling(1/(1/(( ( qnorm(1-beta)*sqrt(1+setavec[k]^2) + qnorm(1-alpha) ) / setavec[k] )^2 )-1/Mvec[m]))
M = Mvec[m]
dpx[[k]] = ggplot()+
stat_function(fun = dnorm, args = list( 0, sqrt( 1/M + 1/K)), n = 1000, color = color[1])+
stat_function(fun = dnorm, args = list( 1, sqrt((1+(0.25)^0)/M + (1+(0.25)^0)/K)), n = 1000, color = color[2])+
stat_function(fun = dnorm, args = list(1/2, sqrt((1+(0.25)^1)/M + (1+(0.25)^1)/K)), n = 1000, color = color[3])+
stat_function(fun = dnorm, args = list(1/4, sqrt((1+(0.25)^2)/M + (1+(0.25)^2)/K)), n = 1000, color = color[4])+
scale_x_continuous(name = "", limits=c(-1.15, 1.15)) +
scale_y_continuous(name = "") +
theme_article()+
theme(legend.position = "none",
axis.line = element_line(colour = "black"),
axis.text = element_blank(),
axis.ticks = element_blank(),
panel.border = element_blank())
}
## blank plot
blankPlot = ggplot()+geom_blank(aes(1,1)) +
cowplot::theme_nothing()
## fig lengend
leg <- get_legend(p[[1]] +
theme(legend.position = "right", legend.title = element_text(size = 12)) +
guides(color = guide_legend(override.aes = list(size=2))))
## output
final = egg::ggarrange(dpy[[1]] , p[[1]] , blankPlot, blankPlot,
dpy[[2]] , p[[2]] , p[[3]] , blankPlot,
dpy[[3]] , p[[4]] , p[[5]] , p[[6]] ,
blankPlot, dpx[[1]] , dpx[[2]] , dpx[[3]] ,
nrow = 4 , ncol = 4 , widths = c(1,2,2,2),heights = c(2,2,2,1))
final = annotate_figure(final, left = "Relatedness by GRM", bottom = "Relatedness by encGRM")
png("simu-MvsK-encGRM.png", width = 750, height = 700)
# pdf("simu-MvsK-encGRM.pdf", width = 10, height = 9)
ggpubr::ggarrange(final, as_ggplot(leg), nrow = 1, widths = c(6,1))
dev.off()