wgeesel (version 1.5)

wgee: Fit Weighted Generalized Estimating Equations (WGEE)

Description

wgee fits weighted generalized estimating equations (WGEE) with Newton Raphson algorithm. wgee has a syntax similar to glm and returns an object similar to a glm object.

Usage

wgee(model, data, id, family, corstr, scale = NULL, mismodel = NULL, maxit=200, tol=0.001)

Arguments

model

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.

data

a data frame containing the variables in the model.

id

a vector which identifies the clusters. The length of "id" should be the same as the number of observations. Data are assumed to be sorted so that observations on a cluster are contiguous rows for all entities in the formula.

family

a description of the error distribution and link function to be used in the model. This is a character string naming a family function. The following are permitted: "gaussian", "binomial", "poisson".

corstr

a character string specifies the working correlation structure. The following are permitted: "independence", "exchangeable", "ar1","unstructured".

scale

a numeric variable giving the value to which the scale parameter should be fixed; if NA, the scale parameter is not fixed.

mismodel

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the missingness model to be fitted.

maxit

maximum iteration number for Newton-Raphson algorithm.

tol

the tolorance for the Newton-Raphson algorithm to converge.

Value

beta

covariate effect estimates

var

variance covariances estimates for beta

w_r_square

weighted R square for continuous data

mu_fit

fitted values of response

scale

scale estimates

rho

rho estimates

weight

The weight of response y

model

WGEE model structure

x

covariates in WGEE

y

response in WGEE

mis_fit

esimates of the missingness model

call

the function to be called

id

as input

data

as input

family

as input

corstr

as input

Details

wgee analyzes longitudinal data with missing values by weighted genralized estimating equations (WGEE), proposed by Robins, Totnizky and Zhao (1995). WGEE can handle missing at random problem. The standard error of the estimates are calculated as described in (Fitzmaurice, Laird, and Ware, 2011) and Preisser, Lohman, and Rathouz (2002).

References

Fitzmaurice, G.M., Laird, N.M. and Ware, J.H., 2012. Applied longitudinal analysis (Vol. 998). John Wiley & Sons.

Liang, K.Y. and Zeger, S.L., 1986. Longitudinal data analysis using generalized linear models. Biometrika, pp.13-22.

Preisser, J.S., Lohman, K.K. and Rathouz, P.J., 2002. Performance of weighted estimating equations for longitudinal binary data with drop-outs missing at random. Statistics in medicine, 21(20), pp.3035-3054.

Robins, J.M., Rotnitzky, A. and Zhao, L.P., 1995. Analysis of semiparametric regression models for repeated outcomes in the presence of missing data. Journal of the American Statistical Association, 90(429), pp.106-121.

Rubin, D.B., 1976. Inference and missing data. Biometrika, pp.581-592.

See Also

geeglm (geepack)

Examples

# NOT RUN {
####Example1
data(imps)

fit <- wgee(IMPS79 ~ Drug+Sex+Time, data=imps, id=imps$ID, family="gaussian",
            corstr="exchangeable", scale=NULL, mismodel= R ~ Drug+Time)

#####Example2
data(seizure)

###reshapre the seizure data to "long" format
seiz.long <- reshape(seizure,
                     varying=list(c("base","y1", "y2", "y3", "y4")),
                     v.names="y", times=0:4, direction="long")
seiz.long <- seiz.long[order(seiz.long$id, seiz.long$time),]

###create missing value for seiz.long dataset
set.seed(12345)
obs <- exp(9+seiz.long$age*(-0.2))/(1+exp(9+seiz.long$age*(-0.2)))
R <- lapply(unique(seiz.long$id),function(x){
  idx=which(seiz.long$id==x)
  r=c()
  r[1]=1
  for(j in 2:length(idx)){
    if(r[j-1]==1){
      r[j]=rbinom(1,1,obs[idx[j]])
    }
    else r[j]=0
  }
  return(r)
})
remove_id <- which(sapply(R,sum)==1)
remove_idx <- which(seiz.long$id %in% remove_id==1)
seiz.long <- cbind(seiz.long,R=unlist(R))[-remove_idx,]
seiz.long$y_mis <- ifelse(seiz.long$R,seiz.long$y,NA)

###fit WGEE, not run ###
fit <- wgee(y_mis ~ age + trt + time, data=seiz.long, id=seiz.long$id,family="poisson",
            corstr="exchangeable",scale=NULL, mismodel= R ~ age)

# }