Fit a geeglm model using miAIPW

provides augmented inverse probability weighted estimates of parameters for GEE model of response variable using different covariance structure. The augmented terms are estimated by using multiple imputation model.

Usage

miAIPW(
  data,
  formula,
  id,
  visit,
  family,
  init.beta = NULL,
  init.alpha = NULL,
  init.phi = NULL,
  tol = 0.001,
  weights = NULL,
  corstr = "independent",
  maxit = 50,
  m = 2,
  pMat,
  method = NULL
)

Arguments

data: longitudinal data set where each subject's outcome has been measured at same time points and number of visits for each patient is similar. Covariance structure of the outcome variable like "unstuctured","independent","AR1" ,"Exchageable"
formula: formula for the response model
id: column name of id of subjects in the dataset
visit: column name of timepoints of visit in the dataset
family: name of the distribution for the response variable, For more information on how to use family objects, see family
init.beta: initial values for the regression coefficient of GEE model
init.alpha: initial values for the correlation structure
init.phi: initial values for the csale parameter for
tol: tolerance in calculation of coefficients
weights: A vector of weights for each observation. If an observation has weight 0, it is excluded from the calculations of any parameters. Observations with a NA anywhere (even in variables not included in the model) will be assigned a weight of 0. Weights are updated as the mentioned the details.
corstr: a character string specifying the correlation structure. It could "independent", "exchangeable", "AR-1", "unstructured"
maxit: maximum number iteration for newton-raphson
m: number of imputation used to update the missing score function value due incomplete data.
pMat: predictor matrix as obtained in mice
method: method option for mice model,for information see mice

Value

A list of objects containing the following objects

call: details about arguments passed in the function
beta: estimated regression coeffictient value for the response model
niter: number of iteration required
betalist: list of beta values at different iteration
weight: estimated weights for the observations
mu: mu values according glm
phi: etsimated phi value for the glm model
hessian: estimated hessian matrix obtained from the last iteration
betaSand: sandwich estimator value for the variance covariance matrix of the beta

Details

miAIPW

It uses the augmented inverse probability weighted method to reduce the bias due to missing values in GEE model for longitudinal data. The response variable $\mathbf{Y}$ is related to the coariates as $g(\mu)=\mathbf{X}\beta$, where g is the link function for the glm. The estimating equation is $$\sum_{i=1}^{k}\sum_{j=1}^{n}(\frac{\delta_{ij}}{\pi_{ij}}S(Y_{ij},\mathbf{X}_{ij},\mathbf{X}'_{ij})+(1-\frac{\delta_{ij}}{\pi_{ij}})\phi(\mathbf{V}=\mathbf{v}))=0$$ where $\delta_{ij}=1$ if there is missing value in covariates and 0 otherwise, $\mathbf{X}$ is fully observed all subjects and $\mathbf{X}'$ is partially missing, where $\mathbf{V}=(Y,\mathbf{X})$. The missing score function values due to incomplete data are estimated using an imputation model through mice which we have considered as $\phi(\mathbf{V}=\mathbf{v}))$. The estimated value $\phi(\mathbf{V}=\mathbf{v}))$ is obtained through multiple imputation.

References

Wang, C. Y., Shen-Ming Lee, and Edward C. Chao. "Numerical equivalence of imputing scores and weighted estimators in regression analysis with missing covariates." Biostatistics 8.2 (2007): 468-473.

Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184.

Vansteelandt, Stijn, James Carpenter, and Michael G. Kenward. "Analysis of incomplete data using inverse probability weighting and doubly robust estimators." Methodology: European Journal of Research Methods for the Behavioral and Social Sciences 6.1 (2010): 37.

Author

Atanu Bhattacharjee, Bhrigu Kumar Rajbongshi and Gajendra Kumar Vishwakarma

Examples

 if (FALSE) {
##
formula<-C6kine~ActivinRIB+ActivinRIIA+ActivinRIIAB+Adiponectin+AgRP+ALCAM
pMat<-mice::make.predictorMatrix(srdata1[names(srdata1)%in%all.vars(formula)])
m1<-miAIPW(data=srdata1,
formula<-formula,id='ID',
 visit='Visit',family='gaussian',init.beta = NULL,
init.alpha=NULL,init.phi=1,tol=.00001,weights = NULL,
corstr = 'exchangeable',maxit=4,m=2,pMat=pMat)
##
}