sandwich {spass}

Calculate the robust covariance estimator for GEE given an

Description

sandwich calculates the covariance structure between timepoints given matrices yCov, D,V and correctionmatrix. This is done to be able to account for missingness in the Data.

Usage

sandwich(
  yCov,
  D,
  V,
  correctionmatrix,
  missing = rep(0, dim(yCov)[[2]]),
  missingtype = c("none", "monotone", "intermittened")
)

Arguments

yCov

yCov matrix containing either an estimation for the covariance between timepoints or an empirical covariance matrix itsel. see 'Details'.

D

D denotes the mean matrix of all entries of \Delta\mu_i/\delta\beta, where this is the average over all i patiens. see 'Details'.

V

V denotes the working covariance matrix. see 'Details'.

correctionmatrix

As of this version this matrix is needed to correct some calculations. see 'Details' to see for more details and how to correctly select matrices.

missing

vector which denotes the probability to experience a dropout at each timepoint. If missingtype is "none" then all entries are 0.

missingtype

String which describes the type of missingness occuring in the data. none if no missingnes occured, "monotone" if missing was monotone and "intermittened" if the missingness was independent across all timepoints.

Details

yCov is either empirical or the estimated covariance-matrix between timepoints which is needed to calculate the sandwich estimator. This matrix can either be generated by estimating the empirical covariance matrix using existing data or by using function gen_cov_cor to calculate a estimation for the covariance.

D denotes the estimation of n^-1* \sum_i^N \Delta\mu_i/\delta\beta, which means that D=E(D_i). As of yet this has the unfortunate side effect that E(D_i

Value

sandwich returns the robust covariance estimator of regression coefficients which are implicitly defined by D.

Source

sandwich computes the asymptotic sandwich covariance estimator and uses code contributed by Roland Gerard Gera.

References

Liang Kung-Yee, Zeger Scott L. (1986); Jung Sin-Ho, Ahn Chul (2003); Wachtlin Daniel Kieser Meinhard (2013)

Examples

#Let's assume we wish to calculate the robust variance estimator for  equation
#\eqn{y_{it}=\beta_0+\beta_1*I_{treat}+\beta_2*t+\beta_3*I _{treat}*t+\epsilon_{it}}.
#Furthermore we use the identitiy matrix as the working covariance matrix.
#The chance to get treatment is 60 percent and the observed timerange ranges from 0:5.

  ycov = gen_cov_cor(var = 3,rho = 0.25,theta = 1,Time = 0:5,cov = TRUE)
  D = matrix(c(1,0.6,0,0,
               1,0.6,1,0.6,
               1,0.6,2,1.2,
               1,0.6,3,1.8,
               1,0.6,4,2.4,
               1,0.6,5,3.0),nrow=4)

 D=t(D)
 V=diag(1,length(0:5))
 #We correct entries where E(D_i %*% D_i) is unequal to E(D_i)%*%E(D_i) (D %*% D).
 correctionmatrix=matrix(c(1,1,1,1,1,1/0.6,1,1/0.6,1,1,1,1,1,1/0.6,1,1/0.6),nrow=4)
 missingtype = "none"

 robust=sandwich(yCov=ycov,D=D,V=V,missingtype=missingtype,correctionmatrix=correctionmatrix)
 robust