ZvaluesfrommultinomPlots {clippda} | R Documentation

## 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

### 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.

### 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

### Author(s)

Stephen Nyangoma

### 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)

[Package clippda version 1.40.0 Index]