Fit a geeglm model using AIPW

Description

provides augmented inverse probability weighted estimates of parameters for GEE model of response variable using different covariance structure

Usage

AIPW(
  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

Details

AIPW

It uses the 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})).

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

Author(s)

Atanu Bhattacharjee, Bhrigu Kumar Rajbongshi and Gajendra Kumar Vishwakarma

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.

See Also

SIPW,miSIPW,miAIPW

Examples

 ## Not run: 
##
formula<-C6kine~ActivinRIB+ActivinRIIA+ActivinRIIAB+Adiponectin+AgRP+ALCAM
pMat<-mice::make.predictorMatrix(srdata1[names(srdata1)%in%all.vars(formula)])
m1<-AIPW(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=50,m=3,pMat=pMat)
##

## End(Not run)

Fit a geeglm model using meanScore

Description

provides mean score estimates of parameters for GEE model of response variable using different covariance structure

Usage

MeanScore(
  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

Details

meanScore

It uses the mean score method to reduce the bias due to missing covariate in GEE model.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}(\delta_{ij}S(Y_{ij},\mathbf{X}_{ij},\mathbf{X}'_{ij})+(1-\delta_{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.

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

Author(s)

Atanu Bhattacharjee, Bhrigu Kumar Rajbongshi and Gajendra Kumar Vishwakarma

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.

See Also

SIPW,miSIPW,miAIPW

Examples

 ## Not run: 
##
formula<-C6kine~ActivinRIB+ActivinRIIA+ActivinRIIAB+Adiponectin+AgRP+ALCAM
pMat<-mice::make.predictorMatrix(srdata1[names(srdata1)%in%all.vars(formula)])
m1<-MeanScore(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=50,m=2,pMat=pMat)
##

## End(Not run)

Model Selection criteria QIC

Description

It provides model selection criteria such as quasi-likelihood under the independence model criterion (QIC), an approximation to QIC under large sample i.e QICu and quasi likelihood

Usage

QICmiipw(model.R, model.indep, family)

Arguments

Details

QICmiipw

Value

returns a list containing QIC,QICu,Quasi likelihood

References

Pan, Wei. "Akaike's information criterion in generalized estimating equations." Biometrics 57.1 (2001): 120-125.

Examples

## Not run: 
 ##
 formula<-C6kine~ActivinRIB+ActivinRIIA+ActivinRIIAB+Adiponectin+AgRP+ALCAM
 pMat<-mice::make.predictorMatrix(srdata1[names(srdata1)%in%all.vars(formula)])
 m1<-MeanScore(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=50,m=2,pMat=pMat)
 m11<-MeanScore(data=srdata1,
             formula<-formula,id='ID',
             visit='Visit',family='gaussian',init.beta = NULL,
             init.alpha=NULL,init.phi=1,tol=.00001,weights = NULL,
            corstr = 'independent',maxit=50,m=2,pMat=pMat)
QICmiipw(model.R=m1,model.indep=m11,family="gaussian")
##

## End(Not run)

Fit a geeglm model using SIPW

Description

provides simple inverse probability weighted estimates of parameters for GEE model of response variable using different covariance structure

Usage

SIPW(
  data,
  formula,
  id,
  visit,
  family,
  init.beta = NULL,
  init.alpha = NULL,
  init.phi = NULL,
  tol = 0.001,
  weights = NULL,
  corstr = "independent",
  maxit = 10,
  maxvisit = NULL
)

Arguments

Details

SIPW

It uses the simple 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})

=0 where \delta_{ij}=1 if there is missing no value in covariates and 0 otherwise. \mathbf{X} is fully observed all subjects and \mathbf{X}' is partially missing.

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

Author(s)

Atanu Bhattacharjee, Bhrigu Kumar Rajbongshi and Gajendra Kumar Vishwakarma

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.

See Also

AIPW,miSIPW,miAIPW

Examples

 ## Not run: 
##
formula<-C6kine~ActivinRIB+ActivinRIIA+ActivinRIIAB+Adiponectin+AgRP+ALCAM
m1<-SIPW(data=srdata1,formula<-formula,id='ID',
visit='Visit',family='gaussian',corstr = 'exchangeable',maxit=5)
##

## End(Not run)

internal function for updating scale parameter

Description

internal function for updating scale parameter

Usage

UpdatePhi(y, x, vfun, mu, w)

Arguments

Fits a marginal model using AIPW

Description

provides augmented inverse probability weighted estimates of parameters for semiparametric marginal model of response variable of interest. The augmented terms are estimated by using multiple imputation model.

Usage

lmeaipw(
  data,
  M = 5,
  id,
  analysis.model,
  wgt.model,
  imp.model,
  qpoints = 4,
  psiCov,
  nu,
  psi,
  sigma = NULL,
  sigmaMiss,
  sigmaR,
  dist,
  link,
  conv = 1e-04,
  maxiter,
  maxpiinv = -1,
  se = TRUE,
  verbose = FALSE
)

Arguments

Details

lmeaipw

It uses the augmented inverse probability weighted method to reduce the bias due to missing values in response 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}^{n}\sum_{j=t_1}^{t_k}\int_{a_i}\int_{b_i}(\frac{\delta_{ij}}{\hat\pi_{ij}(a_i)}S(Y_{ij},\mathbf{X}_{ij};\beta)+(1-\frac{\delta_{ij}}{\hat\pi_{ij}(a_i)})\phi(\mathbf{V}_{ij},b_i;\psi))da_idb_i=0

where \delta_{ij}=1 if there is missing value in the response and 0 otherwise, \mathbf{X} is fully observed all subjects, where \mathbf{V}_{ij}=(\mathbf{X}_{ij},A_{ij}). The missing score function values due to incomplete data are estimated using an imputation model through FCS (here we have considered a mixed effect model) which we have considered as \phi(\mathbf{V}_{ij}=\mathbf{v}_{ij})). The estimated value \hat{\phi}(\mathbf{V}_{ij}=\mathbf{v}_{ij})) is obtained through multiple imputation. The working model for imputation of missing response is

Y_{ij}|b_i\sim N(\mathbf{V}_{ij}\psi+b_i,\sigma)\; ; b_i\sim N(0,\sigma_{miss})

and for the missing data probability

Logit(P(\delta_{ij}=1|\mathbf{V}_{ij}\nu+a_i))\;;a_i\sim N(0,\sigma_R)

Value

A list of objects containing the following objects

Call

details about arguments passed in the function

nr.conv

logical for checking convergence in Newton Raphson algorithm

nr.iter

number of iteration required

nr.diff

absolute difference for roots of Newton Raphson algorithm

beta

estimated regression coefficient for the analysis model

var.beta

Asymptotic SE for beta

Author(s)

Atanu Bhattacharjee, Bhrigu Kumar Rajbongshi and Gajendra Kumar Vishwakarma

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.

See Also

SIPW,miSIPW,miAIPW

Examples

 ## Not run: 
##
library(JMbayes2)
library(lme4)
library(insight)
library(numDeriv)
library(stats)
lmer(log(alkaline)~drug+age+year+(1|id),data=na.omit(pbc2))
data1<-pbc2
data1$alkaline<-log(data1$alkaline)
names(pbc2)
apply(pbc2,2,function(x){sum(is.na(x))})
r.ij<-ifelse(is.na(data1$alkaline)==T,0,1)
data1<-cbind.data.frame(data1,r.ij)
data1$drug<-factor(data1$drug,levels=c("placebo","D-penicil"),labels = c(0,1))
data1$sex<-factor(data1$sex,levels=c('male','female'),labels=c(1,0))
data1$drug<-as.numeric(as.character(data1$drug))
data1$sex<-as.numeric(as.character(data1$sex))
r.ij~year+age+sex+drug+serBilir+(1|id)
model.r<-glmer(r.ij~year+age+sex+drug+serBilir+(1|id),family=binomial(link='logit'),data=data1)
model.y<-lmer(alkaline~year+age+sex+drug+serBilir+(1|id),data=na.omit(data1))
nu<-model.r@beta
psi<-model.y@beta
sigma<-get_variance_residual(model.y)
sigmaR<-get_variance(model.r)$var.random
sigmaMiss<-get_variance(model.y)$var.random
m11<-lmeaipw(data=data1,id='id',
analysis.model = alkaline~year,
wgt.model=~year+age+sex+drug+serBilir+(1|id),
imp.model = ~year+age+sex+drug+serBilir+(1|id),
psiCov = vcov(model.y),nu=nu,psi=psi,
sigma=sigma,sigmaMiss=sigmaMiss,sigmaR=sigmaR,dist='gaussian',link='identity',
maxiter = 200)
m11
##

## End(Not run)

Fits a marginal model using IPW

Description

provides inverse probability weighted estimates of parameters for semiparametric marginal model of response variable of interest. The weights are computed using a generalized linear mixed effect model.

Usage

lmeipw(
  data,
  M = 5,
  id,
  analysis.model,
  wgt.model,
  qpoints = 4,
  nu,
  sigmaR,
  dist,
  link,
  conv = 1e-04,
  maxiter,
  maxpiinv = -1,
  se = TRUE,
  verbose = FALSE
)

Arguments

Details

lmeipw

It uses the simple inverse probability weighted method to reduce the bias due to missing values in response model for longitudinal data.The response variable \mathbf{Y} is related to the covariates as g(\mu)=\mathbf{X}\beta, where g is the link function for the glm. The estimating equation is

\sum_{i=1}^{n}\sum_{j=t_1}^{t_k}\int_{a_i}\frac{\delta_{ij}}{\hat\pi_{ij}(a_i)}S(Y_{ij},\mathbf{X}_{ij})da_i=0

where \delta_{ij}=1 if there is missing no value in response and 0 otherwise. \mathbf{X} is fully observed all subjects and for the missing data probability

Logit(P(\delta_{ij}=1|\mathbf{V}_{ij}\nu+a_i))\;;a_i\sim N(0,\sigma_R)

; where \mathbf{V}_{ij}=(\mathbf{X}_{ij},A_{ij})

Value

A list of objects containing the following objects

Call

details about arguments passed in the function

nr.conv

logical for checking convergence in Newton Raphson algorithm

nr.iter

number of iteration required

nr.diff

absolute difference for roots of Newton Raphson algorithm

beta

estimated regression coefficient for the analysis model

var.beta

Asymptotic SE for beta

Author(s)

Atanu Bhattacharjee, Bhrigu Kumar Rajbongshi and Gajendra Kumar Vishwakarma

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.

See Also

SIPW,miSIPW,miAIPW

Examples

 ## Not run: 
##
library(JMbayes2)
library(lme4)
library(insight)
library(numDeriv)
library(stats)
lmer(log(alkaline)~drug+age+year+(1|id),data=na.omit(pbc2))
data1<-pbc2
data1$alkaline<-log(data1$alkaline)
names(pbc2)
apply(pbc2,2,function(x){sum(is.na(x))})
r.ij<-ifelse(is.na(data1$alkaline)==T,0,1)
data1<-cbind.data.frame(data1,r.ij)
data1$drug<-factor(data1$drug,levels=c("placebo","D-penicil"),labels = c(0,1))
data1$sex<-factor(data1$sex,levels=c('male','female'),labels=c(1,0))
data1$drug<-as.numeric(as.character(data1$drug))
data1$sex<-as.numeric(as.character(data1$sex))
r.ij~year+age+sex+drug+serBilir+(1|id)
model.r<-glmer(r.ij~year+age+sex+drug+serBilir+(1|id),family=binomial(link='logit'),data=data1)
nu<-model.r@beta
sigmaR<-get_variance(model.r)$var.random
m11<-lmeipw(data=data1,id='id',
            analysis.model = alkaline~year,
            wgt.model=~year+age+sex+drug+serBilir+(1|id),
            nu=nu,sigmaR=sigmaR,dist='gaussian',link='identity',qpoints=4,
            maxiter = 200)
m11
##

## End(Not run)

Fits a marginal model using meanscore

Description

provides meanscore estimates of parameters for semiparametric marginal model of response variable of interest. The augmented terms are estimated by using multiple imputation model.

Usage

lmemeanscore(
  data,
  M = 5,
  id,
  analysis.model,
  imp.model,
  qpoints = 4,
  psiCov,
  psi,
  sigma = NULL,
  sigmaMiss,
  dist,
  link,
  conv = 1e-04,
  maxiter,
  maxpiinv = -1,
  se = TRUE,
  verbose = FALSE
)

Arguments

Details

lmemeanscore

It uses the mean score method to reduce the bias due to missing values in response 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}^{n}\sum_{j=t_1}^{t_k}\int_{b_i}(\delta_{ij}S(Y_{ij},\mathbf{X}_{ij})+(1-\delta_{ij})\phi(\mathbf{V}_{ij},b_i;\psi))db_i=0

where \delta_{ij}=1 if there is missing value in response and 0 otherwise, \mathbf{X} is fully observed all subjects and \mathbf{V}_{ij}=(\mathbf{X}_{ij},A_{ij}). The missing score function values due to incomplete data are estimated using an imputation model through mice which we have considered as

Y_{ij}|b_i\sim N(\mathbf{V}_{ij}\gamma+b_i,\sigma)\; ; b_i\sim N(0,\sigma_{miss})

through multiple imputation.

Value

A list of objects containing the following objects

Call

details about arguments passed in the function

nr.conv

logical for checking convergence in Newton Raphson algorithm

nr.iter

number of iteration required

nr.diff

absolute difference for roots of Newton Raphson algorithm

beta

estimated regression coefficient for the analysis model

var.beta

Asymptotic SE for beta

Author(s)

Atanu Bhattacharjee, Bhrigu Kumar Rajbongshi and Gajendra Kumar Vishwakarma

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.

See Also

SIPW,miSIPW,miAIPW

Examples

 ## Not run: 
##
library(JMbayes2)
library(lme4)
library(insight)
library(numDeriv)
library(stats)
lmer(log(alkaline)~drug+age+year+(1|id),data=na.omit(pbc2))
data1<-pbc2
data1$alkaline<-log(data1$alkaline)
names(pbc2)
apply(pbc2,2,function(x){sum(is.na(x))})
r.ij<-ifelse(is.na(data1$alkaline)==T,0,1)
data1<-cbind.data.frame(data1,r.ij)
data1$drug<-factor(data1$drug,levels=c("placebo","D-penicil"),labels = c(0,1))
data1$sex<-factor(data1$sex,levels=c('male','female'),labels=c(1,0))
data1$drug<-as.numeric(as.character(data1$drug))
data1$sex<-as.numeric(as.character(data1$sex))
model.y<-lmer(alkaline~year+age+sex+drug+serBilir+(1|id),data=na.omit(data1))
psi<-model.y@beta
sigma<-get_variance_residual(model.y)
sigmaMiss<-get_variance(model.y)$var.random
m11<-lmemeanscore(data=data1,id='id',
analysis.model = alkaline~year,
imp.model = ~year+age+sex+drug+serBilir+(1|id),
psiCov = vcov(model.y),psi=psi,
sigma=sigma,sigmaMiss=sigmaMiss,dist='gaussian',link='identity',qpoints = 4,
maxiter = 200)
m11
##

## End(Not run)

Fit a geeglm model using miAIPW

Description

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

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.

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

Author(s)

Atanu Bhattacharjee, Bhrigu Kumar Rajbongshi and Gajendra Kumar Vishwakarma

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.

See Also

SIPW,miSIPW,miAIPW

Examples

 ## Not run: 
##
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)
##

## End(Not run)

Fit a geeglm model using miSIPW

Description

provides simple inverse probability weighted estimates of parameters for GEE model of response variable using different covariance structure, missing values in covariates are multiply imputed for those subjects whose response is observed.

Usage

miSIPW(
  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

Details

miSIPW

It uses the simple 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})

=0 where \delta_{ij}=1 if there is missing no value in covariates and 0 otherwise. \mathbf{X} is fully observed all subjects and \mathbf{X}' is partially missing.

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

Author(s)

Atanu Bhattacharjee, Bhrigu Kumar Rajbongshi and Gajendra Kumar Vishwakarma

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.

See Also

SIPW,AIPW,miAIPW

Examples

 ## Not run: 
##
formula<-C6kine~ActivinRIB+ActivinRIIA+ActivinRIIAB+Adiponectin+AgRP+ALCAM
pMat<-mice::make.predictorMatrix(srdata1[names(srdata1)%in%all.vars(formula)])
m1<-miSIPW(data=srdata1,
formula=formula,id='ID',
visit='Visit',family='gaussian',init.beta = NULL,
init.alpha=NULL,init.phi=1,tol=0.001,weights = NULL,
corstr = 'exchangeable',maxit=50,m=2,pMat=pMat)
##

## End(Not run)

print method for ipw

Description

print method for ipw

Usage

print_ipw(x, ...)

Arguments

Value

print result for ipw object

print method for meanscore

Description

print method for meanscore

Usage

print_meanscore(x, ...)

Arguments

Value

print result for meanscore object

protein data

Description

Repeated measurement dataset, for each id we have four visit observations

Usage

data(srdata1)

Format

A dataframe with 164 rows and 9 columns

ID

ID of subjects

Visit

Number of times observations recorded

C6kine,.....,GFRalpha4

These are covariates

Examples

data(srdata1)

summary method for ipw

Description

summary method for ipw

Usage

summary_ipw(object, ...)

Arguments

Value

summary of ipw object

summary method for meanscore

Description

summary method for meanscore

Usage

summary_meanscore(object, ...)

Arguments

Value

summary of meanscore object

internal function for updating alpha

Description

internal function for updating alpha

Usage

updateALpha(y, x, vfun, mu, w, phi, corstr, ni, mv = NULL, id, visit)

Arguments

Details

arguments are from Fisher Scoring Algorithm

internal function for updating beta through Fisher Scoring

Description

internal function for updating beta through Fisher Scoring

Usage

updateBeta(y, x, vfun, mu, w, D, Ralpha, beta)

Arguments

internal function for sandwich estimator

Description

internal function for sandwich estimator

Usage

updateSandW(y, x, vfun, mu, w, D, Ralpha, beta, hessmat, blockdiag)

Arguments

Details

arguments are required for obtaining Sandwich Estimator for variance matrix of regression coefficient of GEE model