| RCreliability.in {RCreliability} | R Documentation |
RCreliability.in
Description
This function corrects the bias in estimated regression coefficients due to classical additive measurement error (i.e., within-person variation) in logistic regressions under the partially or fully replicated design. The output includes naive and corrected estimators for the regression coefficients; for the variance estimates of the corrected estimators, the extra variation due to estimating the parameters in the measurement error model is ignored or taken into account.
Usage
RCreliability.in(r, z, W=NULL, Y)
Arguments
r |
number of replicates in the reliability study, vector of length n, where n is the number of subjects in the reliability study. Note: For each subject, the covariates with error in the reliability study should have the same number of replicates. |
z |
covariates measured with error in the reliability study, a list with p elements, each element in a form of a n*max(r) matrix; subjects with less observations than max(r) should also have max(r) columns with the unobserved elements filled with NA. |
W |
covariates without measurement errors, a n*q matrix, where q stands for the number of covariates without measurement errors. Default is NULL. |
Y |
response variable in the main study, vector of length n. Values should be 0 or 1 in this logistic regression setting. |
Value
A list with 3 table of regression statistics.
Naive estimates |
Estimates of regression coefficients ignoring the measurement errors. |
Corrected estimates |
Regression calibration estimates without taking into account the extra variation due to estimating the parameters in the measurement error model. |
Corrected estimates, taking into account the extra variation due to estimating the parameters in the measurement error model |
Regression calibration estimates taking into account the extra variation due to estimating the parameters in the measurement error model. |
Author(s)
Yu Lu, Molin Wang
References
Carroll RJ, Ruppert D, Stefanski L, Crainiceanu CM. Measurement Error in Nonlinear Models: A Modern Perspective. 2nd ed. New York: Chapman & Hall/CRC; 2006
See Also
RCreliability.ex function
Examples
library(RCreliability)
library(mgcv)
# Regression on only one covariates measured with error
x<-rnorm(3000,0,1)
#ICC=0.7 generate z
r<-c(rep(1,1500),rep(3,700),rep(4,800))
z<-list(rbind(cbind(x[1:1500]+rnorm(1500,0,sqrt(0.4)),NA,NA,NA),
cbind(x[1501:2200]+rnorm(700,0,sqrt(0.4)),
x[1501:2200]+rnorm(700,0,sqrt(0.4)),
x[1501:2200]+rnorm(700,0,sqrt(0.4)),NA),
cbind(x[2201:3000]+rnorm(800,0,sqrt(0.4)),
x[2201:3000]+rnorm(800,0,sqrt(0.4)),
x[2201:3000]+rnorm(800,0,sqrt(0.4)),
x[2201:3000]+rnorm(800,0,sqrt(0.4)))))
#prevalence=0.105
p<-exp(-2.2+log(1.5)*x)/(1+exp(-2.2+log(1.5)*x))
Y<-sapply(p,function(x) rbinom(1,1,x))
fit1 <- RCreliability.in(r,z,W=NULL,Y)
fit1
# Regression on one covariates measured with error and one confounder
x<-rnorm(3000,0,1)
#ICC=0.7 generate z
r<-c(rep(1,1500),rep(3,700),rep(4,800))
z<-list(rbind(cbind(x[1:1500]+rnorm(1500,0,sqrt(0.4)),NA,NA,NA),
cbind(x[1501:2200]+rnorm(700,0,sqrt(0.4)),
x[1501:2200]+rnorm(700,0,sqrt(0.4)),
x[1501:2200]+rnorm(700,0,sqrt(0.4)),NA),
cbind(x[2201:3000]+rnorm(800,0,sqrt(0.4)),
x[2201:3000]+rnorm(800,0,sqrt(0.4)),
x[2201:3000]+rnorm(800,0,sqrt(0.4)),
x[2201:3000]+rnorm(800,0,sqrt(0.4)))))
W<-sapply(x, function(t){if(t>median(x)) {return(rbinom(1,1,0.5))}
if(t<=median(x)){return(rbinom(1,1,0.3))}})
#prevalence about 0.104
p<-exp(-2.4+log(1.5)*x+log(1.5)*W)/(1+exp(-2.4+log(1.5)*x+log(1.5)*W))
Y<-sapply(p,function(x) rbinom(1,1,x))
fit2<-RCreliability.in(r,z,W=W,Y)
fit2
# Regression on two covariates measured with error and no confounder
x<-rmvn(3000,c(0,0),matrix(c(1,0.3,0.3,1),nrow=2))
#ICC=0.7 generate z
r<-c(rep(1,1500),rep(2,500),rep(3,400),rep(4,600))
z<-list(rbind(cbind(x[1:1500,1]+rnorm(1500,0,sqrt(0.4)),NA,NA,NA),
cbind(x[1501:1500,1]+rnorm(500,0,sqrt(0.4)),
x[1501:1500,1]+rnorm(500,0,sqrt(0.4)),NA,NA),
cbind(x[2001:2400,1]+rnorm(400,0,sqrt(0.4)),
x[2001:2400,1]+rnorm(400,0,sqrt(0.4)),
x[2001:2400,1]+rnorm(400,0,sqrt(0.4)),NA),
cbind(x[2401:3000,1]+rnorm(600,0,sqrt(0.4)),
x[2401:3000,1]+rnorm(600,0,sqrt(0.4)),
x[2401:3000,1]+rnorm(600,0,sqrt(0.4)),
x[2401:3000,1]+rnorm(600,0,sqrt(0.4)))),
rbind(cbind(x[1:1500,2]+rnorm(1500,0,sqrt(0.4)),NA,NA,NA),
cbind(x[1501:1500,2]+rnorm(500,0,sqrt(0.4)),
x[1501:1500,2]+rnorm(500,0,sqrt(0.4)),NA,NA),
cbind(x[2001:2400,2]+rnorm(400,0,sqrt(0.4)),
x[2001:2400,2]+rnorm(400,0,sqrt(0.4)),
x[2001:2400,2]+rnorm(400,0,sqrt(0.4)),NA),
cbind(x[2401:3000,2]+rnorm(600,0,sqrt(0.4)),
x[2401:3000,2]+rnorm(600,0,sqrt(0.4)),
x[2401:3000,2]+rnorm(600,0,sqrt(0.4)),
x[2401:3000,2]+rnorm(600,0,sqrt(0.4)))))
#prevalence about 0.105
p<-exp(-2.3+log(1.5)*rowSums(x))/(1+exp(-2.3+log(1.5)*rowSums(x)))
Y<-sapply(p,function(x) rbinom(1,1,x))
fit3<-RCreliability.in(r,z, W=NULL,Y)
fit3
# Regression on two covariates measured with error and two confounders
x<-rmvn(3000,c(0,0,0),matrix(c(1,0.3,0.2,0.3,1,0.5,0.2,0.5,1),nrow=3))
w2<-sapply(x[,1], function(t){if(t>median(x[,1])) {return(rbinom(1,1,0.5))}
if(t<=median(x[,1])){return(rbinom(1,1,0.3))}})
#ICC=0.7 generate z
r<-c(rep(1,1500),rep(2,500),rep(3,400),rep(4,600))
W<-cbind(x[,3],w2)
z<-list(rbind(cbind(x[1:1500,1]+rnorm(1500,0,sqrt(0.4)),NA,NA,NA),
cbind(x[1501:1500,1]+rnorm(500,0,sqrt(0.4)),
x[1501:1500,1]+rnorm(500,0,sqrt(0.4)),NA,NA),
cbind(x[2001:2400,1]+rnorm(400,0,sqrt(0.4)),
x[2001:2400,1]+rnorm(400,0,sqrt(0.4)),
x[2001:2400,1]+rnorm(400,0,sqrt(0.4)),NA),
cbind(x[2401:3000,1]+rnorm(600,0,sqrt(0.4)),
x[2401:3000,1]+rnorm(600,0,sqrt(0.4)),
x[2401:3000,1]+rnorm(600,0,sqrt(0.4)),
x[2401:3000,1]+rnorm(600,0,sqrt(0.4)))),
rbind(cbind(x[1:1500,2]+rnorm(1500,0,sqrt(0.4)),NA,NA,NA),
cbind(x[1501:1500,2]+rnorm(500,0,sqrt(0.4)),
x[1501:1500,2]+rnorm(500,0,sqrt(0.4)),NA,NA),
cbind(x[2001:2400,2]+rnorm(400,0,sqrt(0.4)),
x[2001:2400,2]+rnorm(400,0,sqrt(0.4)),
x[2001:2400,2]+rnorm(400,0,sqrt(0.4)),NA),
cbind(x[2401:3000,2]+rnorm(600,0,sqrt(0.4)),
x[2401:3000,2]+rnorm(600,0,sqrt(0.4)),
x[2401:3000,2]+rnorm(600,0,sqrt(0.4)),
x[2401:3000,2]+rnorm(600,0,sqrt(0.4)))))
#prevalence about 0.104
p<-exp(-2.65+log(1.5)*rowSums(x[,1:3])+log(1.5)*w2)/
(1+exp(-2.65+log(1.5)*rowSums(x[,1:3])+log(1.5)*w2))
Y<-sapply(p,function(x) rbinom(1,1,x))
fit4<-RCreliability.in(r,z,W=W,Y)
fit4