swgee {swgee}

Simulation Extrapolation Inverse Probability Weighted Generalized Estimating Equations

Description

Implementation of the SIMEX inverse probability weighted GEE method for longitudinal data with missing observations and measurement error in covariates

Usage

swgee(formula, data = parent.frame(), id, family = family, 
    corstr = "independence", missingmodel, SIMEXvariable, SIMEX.err, 
    repeated = FALSE, repind = NULL, B = 50, lambda = seq(0, 2, 0.5))

Arguments

formula

specifies the model to be fitted, with the variables coming with data. This argument has the same format as the formula argument in the function geeglm from package geepack, of the form response ~ predictors. See documentation of geeglm and formula for details.

data

an optional data frame in which to interpret the variables occurring in the formula, along with the id variable.

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 family object as the family argument in the function gee from package gee. Families supported in swgee are gaussian, binomial, poisson, Gamma, and quasi. See documentation of gee and family for details.

corstr

a character string specifying the correlation structure. The following are permitted: "independence", "fixed", "stat_M_dep", "non_stat_M_dep", "exchangeable", "AR-M" and "unstructured".

missingmodel

specifies the misisng model to be fitted, of the form O~ predictors, where O is the missing data indicator.

SIMEXvariable

a vector of characters containing the name of the covariates subject to measurement error.

SIMEX.err

specifies the covariance matrix of measurement errors in error model.

repeated

This is the indicator if there are repeated measurements for the covariates with measurement error. The default value is FALSE.

repind

This is the index of the repeated measurement variables for each covariate with measurement error. It has an R list form. If repeated = TRUE, repind must be specified.

B

the number of simulated samples for the simulation step. The default is set to be 50.

lambda

a vector of lambdas for which the simulation step should be done.

Details

The quadratic extrapolation method is implemented as described in Cook and Stefanski

Value

call

the function call

family

family

corstr

correlation structure

SIMEXvariable

a vector of characters containing the name of the covariates subject to measurement error

B

the number of iterations

beta

the coefficients associated with the response process

alpha

the coefficients associated with the missing process

simex.plot

the estimates for every B and lambda

Author(s)

Juan Xiong<[e-mail]>, Grace Y. Yi<[e-mail]>

References

Cook, J.R. and Stefanski, L.A. (1994) Simulation-extrapolation estimation in parametric measurement error models. Journal of the American Statistical Association, 89, 1314-1328.

Carrol, R.J., Ruppert, D., Stefanski, L.A. and Crainiceanu, C. (2006) Measurement error in nonlinear models: A modern perspective., Second Edition. London: Chapman and Hall.

Yi, G. Y. (2008) A simulation-based marginal method for longitudinal data with dropout and mismeasured covariates. Biostatistics, 9, 501-512.

See Also

geeglm

Examples

require(gee)
data(BMI)
bmidata <- BMI

rho <- 0
sigma1 <- 0.5
sigma2 <- 0.5

sigma <- matrix(0,2,2)
sigma[1,1] <- sigma1*sigma1
sigma[1,2] <- rho*sigma1*sigma2
sigma[2,1] <- sigma[1,2]
sigma[2,2] <- sigma2*sigma2

set.seed(1000)
##naive method, ignore missingness and measurement error 
output1 <- gee(bbmi~sbp+chol+age, id = id, data = bmidata,
            family = binomial(link="logit"), corstr = "independence")

##swgee method ##########
output2 <- swgee(bbmi~sbp+chol+age, data = bmidata, id = id, 
            family = binomial(link="logit"),corstr = "independence", 
            missingmodel = O~bbmi+sbp+chol+age, SIMEXvariable = c("sbp","chol"), 
            SIMEX.err = sigma, repeated = FALSE, B = 20, lambda = seq(0, 2, 0.5))

summary(output2)