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Effect_Size_Converter.html
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<h1 class="title toc-ignore">Polygenic Score Effect Size Conversion</h1>
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<hr />
<p>This page describes provides an interative tool for converting between polygenic score effect size metrics for binary outcomes.</p>
<p><br/></p>
<hr />
<div id="conversion-tool" class="section level1">
<h1>Conversion tool</h1>
<p><br/></p>
<iframe height="350" width="100%" frameborder="no" src="https://opain.shinyapps.io/Effect_size_converter/">
</iframe>
<hr />
</div>
<div id="methods" class="section level1 tabset">
<h1>Methods</h1>
<div id="from-cohens-d" class="section level2 tabset">
<h2>From Cohen’s <i>d</i></h2>
<div id="to-auc" class="section level3">
<h3>to AUC</h3>
<pre class="r"><code>auc<-pnorm(abs(d)/sqrt(2), 0, 1)
# d = Cohen's d
# auc = Area-Under-the-ROC-Curve</code></pre>
<p>Reference for Cohen’s <i>d</i> to AUC conversion: <a href="https://pubmed.ncbi.nlm.nih.gov/16254746/">Rice, M. E., & Harris, G. T. (2005). Comparing effect sizes in follow-up studies: ROC Area, Cohen’s d, and r. Law and Human Behavior, 29(5), 615.</a></p>
<hr />
</div>
<div id="to-or-1sd" class="section level3">
<h3>to OR (1SD)</h3>
<pre class="r"><code>or<-exp(d*sqrt(1 + d^2*input$p*(1-input$p)))
# d = Cohen's d
# or = OR (1SD)
# p = Sampling Fraction</code></pre>
<p>Cohen’s <i>d</i> to OR (1SD) conversion derived by <a href="https://twitter.com/stats_bonkers">Alexandra Gillett</a>. Proofs <a href="">here</a>.</p>
<hr />
</div>
<div id="to-observed-scale-r2" class="section level3">
<h3>to Observed scale <i>R</i><sup>2</sup></h3>
<pre class="r"><code>r2<-(d/sqrt(((p+(1-p))^2/(p*(1-p)))+d^2))^2
# d = Cohen's d
# p = Sampling Fraction
# r2 = R-squared on observed scale</code></pre>
<p>Reference for Cohen’s <i>d</i> to observed <i>R</i><sup>2</sup>: <a href="https://eric.ed.gov/?id=ED433353">Aaron, B., Kromrey, J. D., & Ferron, J. (1998). Equating" r“-based and” d"-based effect size indices: problems with a commonly recommended formula. ERIC Clearinghouse.</a></p>
<hr />
</div>
<div id="to-liability-scale-r2" class="section level3">
<h3>to Liability scale <i>R</i><sup>2</sup></h3>
<pre class="r"><code>r2<-(d/sqrt(((p+(1-p))^2/(p*(1-p)))+d^2))^2
r2l<-r2l_r2(k=k, r2=r2, p=0.5)
# d = Cohen's d
# p = Sampling Fraction
# k = Population Prevelance
# r2 = R-squared on observed scale
# r2l = R-squared on liability scale
r2l_r2 <- function(k, r2, p) {
x= qnorm(1-k)
z= dnorm(x)
i=z/k
C= k*(1-k)*k*(1-k)/(z^2*p*(1-p))
theta= i*((p-k)/(1-k))*(i*((p-k)/(1-k))-x)
h2l_R2 = C*r2 / (1 + C*theta*r2)
h2l_R2
}</code></pre>
<p>Reference for observed <i>R</i><sup>2</sup> to liability <i>R</i><sup>2</sup> conversion: <a href="https://pubmed.ncbi.nlm.nih.gov/22714935/">Lee, S. H., Goddard, M. E., Wray, N. R., & Visscher, P. M. (2012). A better coefficient of determination for genetic profile analysis. Genetic Epidemiology, 36(3), 214–224.</a></p>
<hr />
</div>
</div>
<div id="to-cohens-d" class="section level2 tabset">
<h2>To Cohen’s <i>d</i></h2>
<div id="from-auc" class="section level3">
<h3>from AUC</h3>
<pre class="r"><code>d<-sqrt(2)*qnorm(auc)
# d = Cohen's d
# auc = Area-Under-the-ROC-Curve</code></pre>
<p>Reference for AUC to Cohen’s <i>d</i> conversion: <a href="https://pubmed.ncbi.nlm.nih.gov/16254746/">Rice, M. E., & Harris, G. T. (2005). Comparing effect sizes in follow-up studies: ROC Area, Cohen’s d, and r. Law and Human Behavior, 29(5), 615.</a></p>
<hr />
</div>
<div id="from-or-1sd" class="section level3">
<h3>from OR (1SD)</h3>
<pre class="r"><code>f<-function(d,OR,p){OR - (exp(d*sqrt(1 + d^2*p*(1-p))))}
d<-uniroot(f, p=p, OR=or, interval=c(-1, 1), extendInt = "yes", tol=6e-12)$root
# d = Cohen's d
# or = OR (1SD)
# p = Sampling Fraction</code></pre>
<p>OR (1SD) to Cohen’s <i>d</i> conversion derived by <a href="https://twitter.com/stats_bonkers">Alexandra Gillett</a>. Proofs <a href="">here</a>.</p>
<hr />
</div>
<div id="from-observed-scale-r2" class="section level3">
<h3>from Observed scale <i>R</i><sup>2</sup></h3>
<pre class="r"><code>d<-sqrt((p+(1-p))^2/(p*(1-p)))*sqrt(r2)/sqrt(1-r2)
# d = Cohen's d
# p = Sampling Fraction
# r2 = R-squared on observed scale</code></pre>
<p>Reference for observed scale <i>R</i><sup>2</sup> to Cohen’s <i>d</i> conversion: <a href="https://eric.ed.gov/?id=ED433353">Aaron, B., Kromrey, J. D., & Ferron, J. (1998). Equating" r“-based and” d"-based effect size indices: problems with a commonly recommended formula. ERIC Clearinghouse.</a></p>
<hr />
</div>
<div id="from-liability-scale-r2" class="section level3">
<h3>from Liability scale <i>R</i><sup>2</sup></h3>
<pre class="r"><code>r2<-r2_r2l(k=k,r2l=r2l,p=p)
d<-sqrt((p+(1-p))^2/(p*(1-p)))*sqrt(r2)/sqrt(1-r2)
# d = Cohen's d
# p = Sampling Fraction
# k = Population Prevelance
# r2 = R-squared on observed scale
# r2l = R-squared on liability scale
r2_r2l <- function(k, r2l, p) {
#Lee SH, Goddard ME, Wray NR, Visscher PM. (2012)
x= qnorm(1-k)
z= dnorm(x)
i=z/k
C= k*(1-k)*k*(1-k)/(z^2*p*(1-p))
theta= i*((p-k)/(1-k))*(i*((p-k)/(1-k))-x)
r = sqrt(r2l)/sqrt(C-(C*(r2l)*theta))
r2<-r^2
r2
}</code></pre>
<p>Reference for liability <i>R</i><sup>2</sup> to observed <i>R</i><sup>2</sup> conversion: <a href="https://pubmed.ncbi.nlm.nih.gov/22714935/">Lee, S. H., Goddard, M. E., Wray, N. R., & Visscher, P. M. (2012). A better coefficient of determination for genetic profile analysis. Genetic Epidemiology, 36(3), 214–224.</a></p>
<hr />
</div>
</div>
<div id="section" class="section level2 unnumbered">
<h2></h2>
</div>
</div>
<div id="validation" class="section level1">
<h1>Validation</h1>
<p>Here we vaidate the above conversion by comparison against observed values in simulated data.</p>
<p>Conversions into and from Cohen’s <i>d</i> assume equal variance of the polygenic scores in cases and controls. We test this assumption <a href="">here</a>, and find this assumption often true, but in the presence of large genetic effects, can be violated. Therefore, we also validate the assumptions in scenarios where the variance of polygenic scores is not equal in cases and controls.</p>
<hr />
<div id="equal-variance-assumption" class="section level2">
<h2>Equal variance assumption</h2>
<p>Simulate a continuous predictor (polygenic score) and binary outcome (phenotype), varying the magnitude of association, population prevalence and sampling ratio of the binary outcome.</p>
<details>
<p><summary>Show simulation</summary></p>
<pre class="r"><code>set.seed(1)
n<-5000 # Number of individuals in simulation
res<-NULL
for(d in c(0.5, 1, 2)){ # Cohen's D
for(p in c(0.01, 0.1, 0.3, 0.5)){ # Sampling fraction
for(k in c(0.01, 0.1, 0.3, 0.5)){ # Population prevalence fraction
prs_con<-rnorm(round(n*(1-p)), 0, 1)
prs_cas<-rnorm(n-length(prs_con), d, 1)
sim_dat<-data.frame(y=c(rep(0, length(prs_con)), rep(1, length(prs_cas))),
x=c(prs_con, prs_cas))
sim_dat$x<-as.numeric(scale(as.numeric(sim_dat$x)))
mod<-summary(mod_int<-glm('y ~ x', family='binomial', data=sim_dat))
r2_obs<-cor(predict(mod_int, sim_dat), sim_dat$y)^2
library(effsize)
library(pROC)
library(fmsb)
h2l_R2 <- function(k, r2, p) {
#Lee SH, Goddard ME, Wray NR, Visscher PM. (2012)
x= qnorm(1-k)
z= dnorm(x)
i=z/k
C= k*(1-k)*k*(1-k)/(z^2*p*(1-p))
theta= i*((p-k)/(1-k))*(i*((p-k)/(1-k))-x)
h2l_R2 = C*r2 / (1 + C*theta*r2)
h2l_R2
}
tmp<-data.frame( n=n,
n_con=length(prs_con),
n_cas=length(prs_cas),
p=p,
k=k,
d=-cohen.d(x ~ as.factor(y), data=sim_dat)$estimate,
auc=auc(y ~ x, data=sim_dat),
OR=exp(coef(mod)[2,1]),
R2_Obs=r2_obs,
R2_Liab=h2l_R2(k=k, r2=r2_obs, p=p))
res<-rbind(res, tmp)
}
}
}</code></pre>
</details>
<hr />
<p>Convert the observed Cohen’s <i>d</i> into the other metrics and plot comparison between observed and estimated values.</p>
<hr />
<details>
<p><summary>Show conversion</summary></p>
<pre class="r"><code># Convert D to AUC, OR and liability R2
r2_d<-function(d,p){
n_case<-p
n_con<-1-p
a<-(n_case+n_con)^2/(n_case*n_con)
r=d/sqrt(a+d^2)
r2<-r^2
r2
}
conv_res<-res
for(i in 1:nrow(res)){
conv_res$est_auc[i]<-pnorm(res$d[i]/sqrt(2), 0, 1)
conv_res$est_OR[i]<-exp(res$d[i]*sqrt(1 + res$d[i]^2*res$p[i]*(1-res$p[i])))
conv_res$est_R2_Obs[i]<-r2_d(d=res$d[i], p=res$p[i])
conv_res$est_R2_Liab[i]<-h2l_R2(k=conv_res$k[i], r2=conv_res$est_R2_Obs[i], p=res$p[i])
}
library(ggplot2)
library(cowplot)
# Plot AUC comparison
plots<-list()
plots[[1]]<-ggplot(conv_res, aes(x=auc, y=est_auc, colour=as.factor(p), shape=as.factor(k))) +
geom_abline(intercept=0, slope=1) +
labs(title="AUC Comparison", x='Observed AUC', y="Estimated AUC", colour="Sampling", shape="Prevelance") +
geom_point() +
theme_half_open() +
background_grid()
# Plot OR comparison
plots[[2]]<-ggplot(conv_res, aes(x=OR, y=est_OR, colour=as.factor(p), shape=as.factor(k))) +
geom_abline(intercept=0, slope=1) +
labs(title="OR Comparison", x='Observed OR', y="Estimated OR", colour="Sampling", shape="Prevelance") +
geom_point() +
theme_half_open() +
background_grid()
# Plot Observed R2 comparison
plots[[3]]<-ggplot(conv_res, aes(x=R2_Obs, y=est_R2_Obs, colour=as.factor(p), shape=as.factor(k))) +
geom_abline(intercept=0, slope=1) +
labs(title="Observed R2 Comparison", x='Observed Observed R2', y="Estimated Observed R2", colour="Sampling", shape="Prevelance") +
geom_point() +
theme_half_open() +
background_grid()
# Plot Liability R2 comparison
plots[[4]]<-ggplot(conv_res, aes(x=R2_Liab, y=est_R2_Liab, colour=as.factor(p), shape=as.factor(k))) +
geom_abline(intercept=0, slope=1) +
labs(title="Liability R2 Comparison", x='Observed Liability R2', y="Estimated Liability R2", colour="Sampling", shape="Prevelance") +
geom_point() +
theme_half_open() +
background_grid()
dir.create('~/brc_scratch/Software/MyGit/GenoPred/Images/Effect_Size_Converter')
png('~/brc_scratch/Software/MyGit/GenoPred/Images/Effect_Size_Converter/from_d.png', units='px', res=300, width=3000, height=1750)
plot_grid(plotlist=plots, ncol = 2)
dev.off()</code></pre>
</details>
<details>
<summary>Show observed vs. estimated metrics</summary> <img src="Images/Effect_Size_Converter/from_d.png" alt="Estimated from Cohen’s d" />
</details>
<p><br/></p>
<hr />
<p>Convert observed values for oher metrics into Cohen’s <i>d</i>.</p>
<details>
<p><summary>Show conversion</summary></p>
<pre class="r"><code># Convert AUC, OR and liability R2 into Cohen's D
r2_h2l <- function(k, h2l, p) {
#Lee SH, Goddard ME, Wray NR, Visscher PM. (2012)
x= qnorm(1-k)
z= dnorm(x)
i=z/k
C= k*(1-k)*k*(1-k)/(z^2*p*(1-p))
theta= i*((p-k)/(1-k))*(i*((p-k)/(1-k))-x)
r = sqrt(h2l)/sqrt(C-(C*(h2l)*theta))
r2<-r^2
r2
}
d_r2<-function(r2,p){
r<-sqrt(r2)
n_case<-p
n_con<-1-p
a<-(n_case+n_con)^2/(n_case*n_con)
d<-sqrt(a)*r/sqrt(1-r^2)
d
}
conv_res<-res
for(i in 1:nrow(res)){
r2_from_h2l<-r2_h2l(k=res$k[i],h2l=res$R2_Liab[i], p=res$p[i])
conv_res$est_d_using_auc[i]<-sqrt(2)*qnorm(res$auc[i])
f<-function(d,OR,p){OR - (exp(d*sqrt(1 + d^2*p*(1-p))))}
conv_res$est_d_using_OR[i]<-uniroot(f, p=res$p[i], OR=res$OR[i], interval=c(-1, 1), extendInt = "yes", tol=6e-12)$root
conv_res$est_d_using_R2_Obs[i]<-d_r2(r2=res$R2_Obs[i], p=res$p[i])
conv_res$est_d_using_R2_Liab[i]<-d_r2(r2=r2_from_h2l, p=res$p[i])
}
library(ggplot2)
library(cowplot)
# Plot AUC comparison
plots<-list()
plots[[1]]<-ggplot(conv_res, aes(x=d, y=est_d_using_auc, colour=as.factor(p), shape=as.factor(k))) +
geom_abline(intercept=0, slope=1) +
labs(title="Cohen's d Comparison", x="Observed", y="Estimated from AUC", colour="Sampling", shape="Prevelance") +
geom_point() +
theme_half_open() +
background_grid()
# Plot OR comparison
plots[[2]]<-ggplot(conv_res, aes(x=d, y=est_d_using_OR, colour=as.factor(p), shape=as.factor(k))) +
geom_abline(intercept=0, slope=1) +
labs(title="Cohen's d Comparison", x="Observed", y="Estimated from OR", colour="Sampling", shape="Prevelance") +
geom_point() +
theme_half_open() +
background_grid()
# Plot Observed R2 comparison
plots[[3]]<-ggplot(conv_res, aes(x=d, y=est_d_using_R2_Obs, colour=as.factor(p), shape=as.factor(k))) +
geom_abline(intercept=0, slope=1) +
labs(title="Cohen's d Comparison", x="Observed", y="Estimated from Observed R2", colour="Sampling", shape="Prevelance") +
geom_point() +
theme_half_open() +
background_grid()
# Plot Liability R2 comparison
plots[[4]]<-ggplot(conv_res, aes(x=d, y=est_d_using_R2_Liab, colour=as.factor(p), shape=as.factor(k))) +
geom_abline(intercept=0, slope=1) +
labs(title="Cohen's d Comparison", x="Observed", y="Estimated from Liability R2", colour="Sampling", shape="Prevelance") +
geom_point() +
theme_half_open() +
background_grid()
png('~/brc_scratch/Software/MyGit/GenoPred/Images/Effect_Size_Converter/to_d.png', units='px', res=300, width=3000, height=1750)
plot_grid(plotlist=plots, ncol = 2)
dev.off()</code></pre>
</details>
<details>
<summary>Show observed vs. estimated Cohen’s <i>d</i></summary> <img src="Images/Effect_Size_Converter/from_d.png" alt="Estimating Cohen’s d" />
</details>
<p><br/></p>
<hr />
</div>
<div id="unequal-variance-assumption" class="section level2">
<h2>Unequal variance assumption</h2>
<p>In <a href="">observed data</a> maximum difference in case-control polygenic score SD was 0.15. Use this difference when simulating data.</p>
<details>
<p><summary>Show simulation</summary></p>
<pre class="r"><code>set.seed(1)
n<-5000 # Number of individuals in simulation
res<-NULL
for(d in c(0.5, 1, 2)){ # Cohen's D
for(p in c(0.01, 0.1, 0.3, 0.5)){ # Sampling fraction
for(k in c(0.01, 0.1, 0.3, 0.5)){ # Population prevalence fraction
prs_con<-rnorm(round(n*(1-p)), 0, 1)
prs_cas<-rnorm(n-length(prs_con), d, 1.15)
sim_dat<-data.frame(y=c(rep(0, length(prs_con)), rep(1, length(prs_cas))),
x=c(prs_con, prs_cas))
sim_dat$x<-as.numeric(scale(as.numeric(sim_dat$x)))
mod<-summary(mod_int<-glm('y ~ x', family='binomial', data=sim_dat))
r2_obs<-cor(predict(mod_int, sim_dat), sim_dat$y)^2
library(effsize)
library(pROC)
library(fmsb)
h2l_R2 <- function(k, r2, p) {
#Lee SH, Goddard ME, Wray NR, Visscher PM. (2012)
x= qnorm(1-k)
z= dnorm(x)
i=z/k
C= k*(1-k)*k*(1-k)/(z^2*p*(1-p))
theta= i*((p-k)/(1-k))*(i*((p-k)/(1-k))-x)
h2l_R2 = C*r2 / (1 + C*theta*r2)
h2l_R2
}
tmp<-data.frame( n=n,
n_con=length(prs_con),
n_cas=length(prs_cas),
p=p,
k=k,
d=-cohen.d(x ~ as.factor(y), data=sim_dat)$estimate,
auc=auc(y ~ x, data=sim_dat),
OR=exp(coef(mod)[2,1]),
R2_Obs=r2_obs,
R2_Liab=h2l_R2(k=k, r2=r2_obs, p=p))
res<-rbind(res, tmp)
}
}
}</code></pre>
</details>
<hr />
<p>Convert the observed Cohen’s <i>d</i> into the other metrics and plot comparison between observed and estimated values.</p>
<hr />
<details>
<p><summary>Show conversion</summary></p>
<pre class="r"><code># Convert D to AUC, OR and liability R2
r2_d<-function(d,p){
n_case<-p
n_con<-1-p
a<-(n_case+n_con)^2/(n_case*n_con)
r=d/sqrt(a+d^2)
r2<-r^2
r2
}
conv_res<-res
for(i in 1:nrow(res)){
conv_res$est_auc[i]<-pnorm(res$d[i]/sqrt(2), 0, 1)
conv_res$est_OR[i]<-exp(res$d[i]*sqrt(1 + res$d[i]^2*res$p[i]*(1-res$p[i])))
conv_res$est_R2_Obs[i]<-r2_d(d=res$d[i], p=res$p[i])
conv_res$est_R2_Liab[i]<-h2l_R2(k=conv_res$k[i], r2=conv_res$est_R2_Obs[i], p=res$p[i])
}
library(ggplot2)
library(cowplot)
# Plot AUC comparison
plots<-list()
plots[[1]]<-ggplot(conv_res, aes(x=auc, y=est_auc, colour=as.factor(p), shape=as.factor(k))) +
geom_abline(intercept=0, slope=1) +
labs(title="AUC Comparison", x='Observed AUC', y="Estimated AUC", colour="Sampling", shape="Prevelance") +
geom_point() +
theme_half_open() +
background_grid()
# Plot OR comparison
plots[[2]]<-ggplot(conv_res, aes(x=OR, y=est_OR, colour=as.factor(p), shape=as.factor(k))) +
geom_abline(intercept=0, slope=1) +
labs(title="OR Comparison", x='Observed OR', y="Estimated OR", colour="Sampling", shape="Prevelance") +
geom_point() +
theme_half_open() +
background_grid()
# Plot Observed R2 comparison
plots[[3]]<-ggplot(conv_res, aes(x=R2_Obs, y=est_R2_Obs, colour=as.factor(p), shape=as.factor(k))) +
geom_abline(intercept=0, slope=1) +
labs(title="Observed R2 Comparison", x='Observed Observed R2', y="Estimated Observed R2", colour="Sampling", shape="Prevelance") +
geom_point() +
theme_half_open() +
background_grid()
# Plot Liability R2 comparison
plots[[4]]<-ggplot(conv_res, aes(x=R2_Liab, y=est_R2_Liab, colour=as.factor(p), shape=as.factor(k))) +
geom_abline(intercept=0, slope=1) +
labs(title="Liability R2 Comparison", x='Observed Liability R2', y="Estimated Liability R2", colour="Sampling", shape="Prevelance") +
geom_point() +
theme_half_open() +
background_grid()
dir.create('~/brc_scratch/Software/MyGit/GenoPred/Images/Effect_Size_Converter')
png('~/brc_scratch/Software/MyGit/GenoPred/Images/Effect_Size_Converter/from_d_unequal.png', units='px', res=300, width=3000, height=1750)
plot_grid(plotlist=plots, ncol = 2)
dev.off()</code></pre>
</details>
<details>
<summary>Show observed vs. estimated metrics</summary> <img src="Images/Effect_Size_Converter/from_d_unequal.png" alt="Estimated from Cohen’s d" />
</details>
<p><br/></p>
<hr />
<p>Convert observed values for oher metrics into Cohen’s <i>d</i>.</p>
<details>
<p><summary>Show conversion</summary></p>
<pre class="r"><code># Convert AUC, OR and liability R2 into Cohen's D
r2_h2l <- function(k, h2l, p) {
#Lee SH, Goddard ME, Wray NR, Visscher PM. (2012)
x= qnorm(1-k)
z= dnorm(x)
i=z/k
C= k*(1-k)*k*(1-k)/(z^2*p*(1-p))
theta= i*((p-k)/(1-k))*(i*((p-k)/(1-k))-x)
r = sqrt(h2l)/sqrt(C-(C*(h2l)*theta))
r2<-r^2
r2
}
d_r2<-function(r2,p){
r<-sqrt(r2)
n_case<-p
n_con<-1-p
a<-(n_case+n_con)^2/(n_case*n_con)
d<-sqrt(a)*r/sqrt(1-r^2)
d
}
conv_res<-res
for(i in 1:nrow(res)){
r2_from_h2l<-r2_h2l(k=res$k[i],h2l=res$R2_Liab[i], p=res$p[i])
conv_res$est_d_using_auc[i]<-sqrt(2)*qnorm(res$auc[i])
f<-function(d,OR,p){OR - (exp(d*sqrt(1 + d^2*p*(1-p))))}
conv_res$est_d_using_OR[i]<-uniroot(f, p=res$p[i], OR=res$OR[i], interval=c(-1, 1), extendInt = "yes", tol=6e-12)$root
conv_res$est_d_using_R2_Obs[i]<-d_r2(r2=res$R2_Obs[i], p=res$p[i])
conv_res$est_d_using_R2_Liab[i]<-d_r2(r2=r2_from_h2l, p=res$p[i])
}
library(ggplot2)
library(cowplot)
# Plot AUC comparison
plots<-list()
plots[[1]]<-ggplot(conv_res, aes(x=d, y=est_d_using_auc, colour=as.factor(p), shape=as.factor(k))) +
geom_abline(intercept=0, slope=1) +
labs(title="Cohen's d Comparison", x="Observed", y="Estimated from AUC", colour="Sampling", shape="Prevelance") +
geom_point() +
theme_half_open() +
background_grid()
# Plot OR comparison
plots[[2]]<-ggplot(conv_res, aes(x=d, y=est_d_using_OR, colour=as.factor(p), shape=as.factor(k))) +
geom_abline(intercept=0, slope=1) +
labs(title="Cohen's d Comparison", x="Observed", y="Estimated from OR", colour="Sampling", shape="Prevelance") +
geom_point() +
theme_half_open() +
background_grid()
# Plot Observed R2 comparison
plots[[3]]<-ggplot(conv_res, aes(x=d, y=est_d_using_R2_Obs, colour=as.factor(p), shape=as.factor(k))) +
geom_abline(intercept=0, slope=1) +
labs(title="Cohen's d Comparison", x="Observed", y="Estimated from Observed R2", colour="Sampling", shape="Prevelance") +
geom_point() +
theme_half_open() +
background_grid()
# Plot Liability R2 comparison
plots[[4]]<-ggplot(conv_res, aes(x=d, y=est_d_using_R2_Liab, colour=as.factor(p), shape=as.factor(k))) +
geom_abline(intercept=0, slope=1) +
labs(title="Cohen's d Comparison", x="Observed", y="Estimated from Liability R2", colour="Sampling", shape="Prevelance") +
geom_point() +
theme_half_open() +
background_grid()
png('~/brc_scratch/Software/MyGit/GenoPred/Images/Effect_Size_Converter/to_d_unequal.png', units='px', res=300, width=3000, height=1750)
plot_grid(plotlist=plots, ncol = 2)
dev.off()</code></pre>
</details>
<details>
<summary>Show observed vs. estimated Cohen’s <i>d</i></summary> <img src="Images/Effect_Size_Converter/from_d_unequal.png" alt="Estimating Cohen’s d" />
</details>
<p><br/></p>
</div>
</div>
</div>
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