clippda (version 1.22.0)

ZvaluesfrommultinomPlots: A generic functon to plot Density of Z values from a simulation from a multinomial population using the balanced and unbalanced studies and a 3D representaion of the Z values

Description

A functon to plot Density of Z values from a simulation from a multinomial population using the balanced and unbalanced studies and a 3D representaion of the Z values. These plots are useful as visual tools for the confounding effects. The median values are indicated on these plots and these can be used as the consesus values of the effects of covariates in sample size calculations.

Usage

ZvaluesfrommultinomPlots(nsim,nobs,proposeddesign,balanceddesign,...)

Arguments

nsim

number of simulations to be done

nobs

number of multinomial observation

proposeddesign

a numeric vector with four elements indicating the design weights

balanceddesign

a numeric vector with all the four elements being one, indicating equal weights

...

other arguments

Value

density plot

Density plot of the Z values

3D plot of Z values

3D plot of the Z values against a two dimensional subspace of the 3-D space of multinomial probabilities

Details

This function generates saples from a given four cell multinomial populaton then uses the resulting multinomial probabilities in calculating the effect of covariates (Z values). Currently we implement a design arising from a proteomics study in which there is a binary confounder and a binary exposure. The cross-tabulation of the categories of these covariates results into a 4-cell multinomial categories.

References

Nyangoma SO, Ferreira JA, Collins SI, Altman DG, Johnson PJ, and Billingham LJ: Sample size calculations for planning clinical proteomic profiling studies using mass spectrometry. (Working paper)

See Also

Also see the function f.

Examples

#density plots

nsim=10000;nobs=300;proposeddesign=c(1,2,1,7);balanceddesign=c(1,1,1,1)

f=function (x,y,z) {
Z=(1-x-z)*(x+y)/(2*(((1-x-z)*(1-x-y)*(1-y-z))-(1-x-y-z)^2))
Z
}

mul_1=rmultinom(nsim, nobs, prob = proposeddesign)/nobs
mul_1=t(mul_1)

mul_1=data.frame(mul_1)


 
names(mul_1)=c('x','y','z')


x=mul_1$x
y=mul_1$y

z=mul_1$z

# compute Z values (see Nyangoma et al. 2009)

Z=f(x,y,z)


x1=x
y1=y

z1=Z


#########################################
#####  pr=c(1,1,1,1)# balanced design
#########################################

mul_2=rmultinom(nsim, nobs, prob = balanceddesign)/nobs
mul_2=t(mul_2)


mul_2=data.frame(mul_2) 
names(mul_2)=c('x','y','z')

x=mul_2$x
y=mul_2$y

z=mul_2$z

Zb=f(x,y,z)

x2=x
y2=y

z2=Zb

#####################################
#####################################
#summary(Zb)
pdf('ZvaluesDensityPlots.pdf')
densityZ=density(Z,bw=0.1)
densityZb=density(Zb,bw=0.1)

plot(density(Zb,bw=0.1),xlim=c(min(c(densityZ$x,densityZb$x)),max(c(densityZ$x,densityZb$x))),
ylim=c(min(c(densityZ$y,densityZb$y)),max(c(densityZ$y,densityZb$y))),col='blue',lwd=2,lty=1,xlab='confounding effect - Z values',main='')


lines(density(Z,bw=0.1),lwd=2,xlab='',main='')

abline(v=median(Z),lty=2,col='red')
abline(v=median(Zb),lty=2,col='green')

legend(max(c(densityZ$x,densityZb$x)) - 2, max(c(densityZ$y,densityZb$y)) - 0.2, legend=c("blanced","unblanced"), col = c("blue","black"), lty = 1)
dev.off()
####################################
####################################

library(lattice)
library(rgl)
 library(scatterplot3d)
a=c(x1,x2)
 b=c(y1,y2)
 Z1=c(z1,z2)
 
group=c(rep(1,10000),rep(2,10000))

Data=data.frame(a,b,Z=Z1,group)

Data$group=as.factor(Data$group)

Plot3D=cloud(b ~ a*Z,scales = list(arrows = FALSE), data=Data, group=group,screen = list(x = 30, y = -60),ylim=c(0,15),zlim=c(0.05,0.45),xlim=c(0,0.45))

Plot3D
nsim=10000;nobs=300;proposeddesign=c(1,2,1,7);balanceddesign=c(1,1,1,1)
ZvaluesfrommultinomPlots(nsim,nobs,proposeddesign,balanceddesign)