# [R] simulate data with binary outcome and correlated predictors

From: Delphine COURVOISIER <Delphine.Courvoisier_at_hcuge.ch>
Date: Tue, 11 Nov 2008 15:17:50 +0100

Hi,

I would like to simulate data with a binary outcome and a set of predictors that are correlated. I want to be able to fix the number of event (Y=1) vs. non-event (Y=0). Thus, I fix this and then simulate the predictors. I have 2 questions: 1. When the predictors are continuous, I can use mvrnorm(). However, if I have continuous, ordinal and binary predictors, I'm not sure how to simulate accurately the relationships between predictors. 2. To specify the coefficients of the regression of Y on predictors, I must specify separately the predictors for Y=1 and Y=0, I can vary the mean and the variance/covariances of the predictors. However, with this approach, it is harder to determine precisely the coefficients of the predictors. Any help on how to be as precise as possible on the betas would be nice.

Here is the code I wrote where all predictors are continuous with variance =1 and correlations between predictors vary for each condition of Y.

library(MASS)
N<-1000

nbX<-3
propSick<-0.2
corrSick<-.8
corrHealthy<-.9

sigma0<-matrix(corrHealthy,nbX,nbX)
diag(sigma0)<-1
sigma1<-matrix(corrSick,nbX,nbX)
diag(sigma1)<-1
dataHealthy<-mvrnorm(N*(1-propSick),c(0,0,0),sigma0) dataSick<-mvrnorm(N*propSick,c(1,1,1),sigma1)

dataS<-as.data.frame(matrix(0,ncol=4,nrow=N)) dimnames(dataS)[[2]]<-c("IV1","IV2","IV3","DV") dataS\$DV[1:(N*propSick)]<-1
dataS\$DV<-factor(dataS\$DV)
dataS[1:(N*propSick),1:3]<-dataSick
dataS[(N*propSick+1):N,1:3]<-dataHealthy

thanks in advance for any suggestions,

Delphine Courvoisier
Clinical Epidemiology Division
University of Geneva Hospital
+4122 37 29029

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