ee.wgee {ELCIC}

Estimating equation for weighted GEE (WGEE) for missing longitudinal data under the mechanism of missing at random and drop-out

Description

Calculate estimating equation from WGEE for missing longitudinal data under the mechanism of missing at random and drop-out. This estimating equation is used for joint selection of marginal mean and "working" correlation structure.

Usage

ee.wgee(y,x,r,pi,id,time,beta,rho,phi,dist,corstr)

Arguments

y

A vector containing outcomes. use NA to indicate missing outcomes.

x

A matrix containing covariates. The first column should be all ones corresponding to the intercept.

r

A vector indicating the observation of outcomes: 1 for observed records, and 0 for unobserved records.

pi

A vector containing observing probabilities across all observations.

id

A vector indicating subject id.

time

The number of observations for each subject.

beta

A plug-in estimator solved by an external estimation procedure, such as WGEE.

rho

A correlation coefficients obtained from an external estimation procedure, such as WGEE.

phi

An over-dispersion parameter obtained from an external estimation procedure, such as GEE.

dist

A specified distribution. It can be "gaussian", "poisson",and "binomial".

corstr

A candidate correlation structure. It can be "independence","exchangeable", and "ar1".

Value

A matrix containing values of calculated estimating equations.

Examples

## tests
# load data
data(wgeesimdata)
library(wgeesel)
data_wgee<-data.frame(do.call(cbind,wgeesimdata))
corstr<-"exchangeable"
dist<-"binomial"
id<-data_wgee$id
# obtain the estimates.
# Note that "obs_ind" is an indicator of observations in the missing data model.
fit<-wgee(y~x1+x2+x3,data_wgee,id,family=dist,corstr =corstr,
     scale = NULL,mismodel =obs_ind~x_mis1)
beta<-as.vector(summary(fit)$beta)
rho<-summary(fit)$corr
phi<-summary(fit)$phi
#calculate observing probabilies for all observations
gamma<-as.vector(summary(fit$mis_fit)$coefficients[,1])
x_mis<-wgeesimdata$x_mis
pi<-cond.prob(x_mis,gamma,id,time=3)
wgee.matrix<-ee.wgee(y=wgeesimdata$y,x=wgeesimdata$x,r=wgeesimdata$obs_ind,
pi=pi,id=wgeesimdata$id,time=3,beta=beta,rho=rho,phi=phi,dist=dist,corstr=corstr)
apply(wgee.matrix,1,mean)