Package 'geesmv'

Title: Modified Variance Estimators for Generalized Estimating Equations
Description: Generalized estimating equations with the original sandwich variance estimator proposed by Liang and Zeger (1986), and eight types of more recent modified variance estimators for improving the finite small-sample performance.
Authors: Ming Wang <[email protected]>
Maintainer: Zheng Li <[email protected]>
License: GPL (>= 3)
Version: 1.3
Built: 2024-11-12 06:31:32 UTC
Source: CRAN

Help Index

Modified Variance Estimators for Generalized Estimating Equations

Description

Generalized estimating equations with the original sandwich variance estimator proposed by Liang and Zeger (1986), and eight types of more recent modified variance estimators for improving the finite small-sample performance.

Details

Generalized estimating equations with the original sandwich variance estimator proposed by Liang and Zeger (1986), and eight types of more recent modified variance estimators for improving the finite small-sample performance.

GEE.var.pan(), GEE.var.gst() and GEE.var.wl() are only for the balanced data, while the others can be used for both balanced and unbalanced data.

Author(s)

Ming Wang <[email protected]>

Maintainer: Zheng Li <[email protected]>

References

De Backer M, De Vroey C, Lesaffre E, Scheys I, De Keyser P. Twelve weeks of continuous oral therapy for toenail onychomycosis caused by dermatophytes: a double-blind comparative trial of terbinafine 250 mg/day versus itraconazole 200 mg/day. Journal of the American Academy of Dermatology 1998; 38: 57-63.

Fay MP and Graubard BI. Small-sample adjustments for Wald-type tests using sandwich estimators. Biometrics 2001;57: 1198-1206.

Gosho M, Sato Y and Takeuchi H. Robust covariance estimator for small-sample adjustment in the generalized estimating equations: A simulation study. Science Journal of Applied Mathematics and Statistics 2014;2(1):20-25.

Kauermann G and Carroll RJ. A note on the efficiency of sandwich covariance matrix estimation. Journal of the American Statistical Association 2001;96: 1387-1398.

Morel JG, Bokossa MC, and Neerchal NK. Small sample correction for the variance of GEE estimators. Biometrical Journal 2003;45(4): 395-409.

MacKinnon JG. Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties. Journal of Econometrics 1985;29: 305-325.

Mancl LA and DeRouen TA. A covariance estimator for GEE with improved small-sample properties. Biometrics 2001;57: 126-134.

Pan W. On the robust variance estimator in Generalized Estimating Equations. Biometrika 2001;88: 901-906.

Pottho R. F. and Roy, S. W. A generalized multivariate analysis of variance model useful especially for growth curve problems. Biometrika 1964;51:313-326

Thall PF, and Vail SC. Some covariance models for longitudinal count data with overdispersion. Biometrics 1990; 46: 657-671.

Wang M and Long Q. Modified robust variance estimator for generalized estimating equations with improved small-sample performance. Statistics in Medicine 2011;30(11): 1278-1291.

Zeger SL and Liang KY. Longitudinal data analysis for discrete and continuous outcomes. Biometrics 1986; 121-130.

See Also

GEE.var.lz()

GEE.var.mk()

GEE.var.kc()

GEE.var.pan()

GEE.var.fg()

GEE.var.gst()

GEE.var.md()

GEE.var.mbn()

GEE.var.wl()

Examples

### Run the data analysis using the package using seizure dataset (Poisson);
data(seizure)
seizure$subject <- 1:length(seizure[,1])
data_alt <- reshape(seizure, direction="long", idvar="subject", timevar="Time", 
                   varying=names(seizure)[1:4], v.names="response", times=1:4) 
data_alt <- data_alt[order(data_alt$subject),]
data_alt <- data_alt[,c(4,1:3,5,6)]

### independence working correlation structure;
formula <- response~base+trt+Time
lz.ind <- GEE.var.lz(formula,id="subject",family=poisson,
               data_alt,corstr="independence")
               
mk.ind <- GEE.var.mk(formula,id="subject",family=poisson,
                data_alt,corstr="independence")
                
pan.ind <- GEE.var.pan(formula,id="subject",family=poisson,
         data_alt,corstr="independence")
         
gst.ind <- GEE.var.gst(formula,id="subject",family=poisson,
        data_alt,corstr="independence")
        
kc.ind <- GEE.var.kc(formula,id="subject",family=poisson,
         data_alt,corstr="independence") 
         
md.ind <- GEE.var.md(formula,id="subject",family=poisson,
        data_alt,corstr="independence")
        
fg.ind <- GEE.var.fg(formula,id="subject",family=poisson,data_alt,
                      corstr="independence",b=0.75) 
mbn.ind <- GEE.var.mbn(formula,id="subject",family=poisson,data_alt,
                      corstr="independence",d=2,r=1)                
wl.ind <- GEE.var.wl(formula,id="subject",family=poisson,
             data_alt,corstr="independence")

Get Summary Information of The Data.

Description

Get necessary information (i.e., the number of clusters, cluster sizes) of the data set.

Usage

cluster.size(id)

Arguments

id

The variable name of the cluster id in the data set.

Details

This function will get the number of clusters and cluster sizes of the data set.

Value

n

a vector of numbers denote the cluster sizes for different id.
m

the total number of clusters in the data set.

Author(s)

Ming Wang <[email protected]> Maintainer: Zheng Li <[email protected]>

Calculate variance estimator

Description

Being used to calculate variance estimator by the functions in this package. It cannot be directly used in other packages.

Calculate variance estimator

Description

Being used to calculate variance estimator by the functions in this package. It cannot be directly used in other packages.

Calculate variance estimator

Description

Being used to calculate variance estimator by the functions in this package. It cannot be directly used in other packages.

A Data Set of Orthodontic Measurements on Children

Description

The dental data consists of 27 subjects from the University of North Carolina Dental School.

Usage

dental

Format

  • subject:cluster id

  • gender:the sex of subject

  • age_8:the measurements at age 8

  • age_10:the measurements at age 10

  • age_12:the measurements at age 12

  • age_14:the measurements at age 14

Details

The data was collected by investigators at the University of North Carolina Dental School. It is a study of orthodontic measurements on children including 11 girls and 16 boys measured at ages 8, 10, 12, and 14.

Source

Pottho R. F. and Roy, S. W. A generalized multivariate analysis of variance model useful especially for growth curve problems. Biometrika 1964;51:313-326

A Modified GEE Variance Estimator Proposed by Fay and Graubard (2001)

Description

Calculate the modified GEE variance estimator proposed by Fay and Graubard (2001).

Usage

GEE.var.fg(formula,id,family=gaussian,data,corstr="independence",b=0.75)

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a formula expression as for other regression models to be fitted, of the form response ~ predictors. The details of formula specification can be seen in glm() and gee().

id

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

family

a family object: a list of functions and expressions for defining link and variance functions to be used in the model. This can be a character string naming a family function including "gaussian", "binomial", and "poisson". See family for details of family functions in glm() and gee().

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which glm is called.

corstr

a character string specifying working correlation structure: "independence", "AR-M","exchangeable", "unstructured" are possible.

b

adjustment factor in the proposed variance estimator, which is prespecfied subjectively to avoid extreme adjustments when the cluster size is close to 1. The default value is 0.75.

Details

Fit the model by GEE and calculate the variance estimator proposed by Fay and Graubard (2001).

Value

cov.beta

estimate of the variance for beta
cov.var

estimate of the variance-covariance matrix for the variance estimator

Author(s)

Ming Wang <[email protected]>

Maintainer: Zheng Li <[email protected]>

References

Fay MP and Graubard BI. Small-sample adjustments for Wald-type tests using sandwich estimators. Biometrics 2001;57: 1198-1206.

Examples

data(dental)
data_alt <- reshape(dental, direction="long", timevar="Time", 
          varying=names(dental)[3:6], v.names="response", times=c(8,10,12,14))
data_alt <- data_alt[order(data_alt$subject),]
data_alt$gender <- as.numeric(data_alt$gender)
data_alt$Time <- sqrt(data_alt$Time)
formula <- response~Time+gender
fg.ind <- GEE.var.fg(formula,id="subject",family=gaussian,
       data_alt,corstr="independence") ##Independence correlation structure;
fg.exch <- GEE.var.fg(formula,id="subject",family=gaussian,
        data_alt,corstr="exchangeable") ##Exchangeable correlation structure;
fg.ar1 <- GEE.var.fg(formula,id="subject",family=gaussian,
        data_alt,corstr="AR-M") ##AR-1 correlation structure;
fg.unstr <- GEE.var.fg(formula,id="subject",family=gaussian,
       data_alt,corstr="unstructured") ##Unstructured correlation structure;

A modified GEE Variance Estimator Proposed by Gosho et al.(2014)

Description

Calculate the modified GEE variance estimator proposed by Gosho et al. (2014).

Usage

GEE.var.gst(formula,id,family=gaussian,data,corstr="independence")

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a formula expression as for other regression models to be fitted, of the form response ~ predictors. The details of formula specification can be seen in glm() and gee().

id

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

family

a family object: a list of functions and expressions for defining link and variance functions to be used in the model. This can be a character string naming a family function including "gaussian", "binomial", and "poisson". See family for details of family functions in glm() and gee().

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula).

corstr

a character string specifying working correlation structure: "independence", "AR-M","exchangeable", "unstructured" are possible.

Details

Fit the model by GEE and provide the variance estimator based on Gosho et al.(2014). Gosho et al (2014) proposed to made an additional modification on Pan's estimator.

Value

cov.beta

estimate of the variance for beta
cov.var

estimate of the variance-covariance matrix for the variance estimator

Author(s)

Ming Wang <[email protected]>

Maintainer: Zheng Li <[email protected]>

References

Gosho, M., Sato, Y. and Takeuchi, H. Robust covariance estimator for small-sample adjustment in the generalized estimating equations: A simulation study. Science Journal of Applied Mathematics and Statistics 2014;2(1):20-25.

Examples

data(dental)
data_alt <- reshape(dental, direction="long", timevar="Time", 
         varying=names(dental)[3:6], v.names="response", times=c(8,10,12,14))
data_alt <- data_alt[order(data_alt$subject),]
data_alt$gender <- as.numeric(data_alt$gender)
data_alt$Time <- sqrt(data_alt$Time)
formula <- response~Time+gender
gst.ind <- GEE.var.gst(formula,id="subject",family=gaussian,
        data_alt,corstr="independence") ##Independence correlation structure;              
gst.exch <- GEE.var.gst(formula,id="subject",family=gaussian,
        data_alt,corstr="exchangeable") ##Exchangeable correlation structure;     
gst.ar1 <- GEE.var.gst(formula,id="subject",family=gaussian,
        data_alt,corstr="AR-M") ##AR-1 correlation structure;          
gst.unstr <- GEE.var.gst(formula,id="subject",family=gaussian,
         data_alt,corstr="unstructured") ##Unstructured correlation structure;

A Modified GEE Variance Estimator Proposed by Kauermann and Carroll (2001).

Description

Calculate the modified GEE variance estimator proposed by Kauermann and Carroll (2001).

Usage

GEE.var.kc(formula,id,family=gaussian,data,corstr="independence")

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a formula expression as for other regression models to be fitted, of the form response ~ predictors. The details of formula specification can be seen in glm() and gee().

id

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

family

a family object: a list of functions and expressions for defining link and variance functions to be used in the model. This can be a character string naming a family function including "gaussian", "binomial", and "poisson". See family for details of family functions in glm() and gee().

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which glm is called.

corstr

a character string specifying working correlation structure: "independence", "AR-M","exchangeable", "unstructured" are possible.

Details

Fit the model by GEE and calculate the bias-corrected sandwich variance estimator proposed by Kauermann and Carroll(2001).

Value

cov.beta

estimate of the variance for beta
cov.var

estimate of the variance-covariance matrix for the variance estimator

Author(s)

Ming Wang <[email protected]>

Maintainer: Zheng Li <[email protected]>

References

Kauermann G and Carroll RJ. A note on the efficiency of sandwich covariance matrix estimation. Journal of the American Statistical Association 2001;96: 1387-1398.

Examples

data(dental)
data_alt <- reshape(dental, direction="long", timevar="Time", 
        varying=names(dental)[3:6], v.names="response", times=c(8,10,12,14))
data_alt <- data_alt[order(data_alt$subject),]
data_alt$gender <- as.numeric(data_alt$gender)
data_alt$Time <- sqrt(data_alt$Time)
formula <- response~Time+gender
kc.ind <- GEE.var.kc(formula,id="subject",family=gaussian,
        data_alt,corstr="independence") ##Independence correlation structure;
kc.exch <- GEE.var.kc(formula,id="subject",family=gaussian,
        data_alt,corstr="exchangeable") ##Exchangeable correlation structure;                   
kc.ar1 <- GEE.var.kc(formula,id="subject",family=gaussian,
        data_alt,corstr="AR-M") ##AR-1 correlation structure;                   
kc.unstr <- GEE.var.kc(formula,id="subject",family=gaussian,
        data_alt,corstr="unstructured") ##Unstructured correlation structure;

GEE Sandwich Variance Estimator Proposed by Liang and Zeger (1986).

Description

Calculate the GEE original variance estimator proposed by Liang and Zeger (1986).

Usage

GEE.var.lz(formula,id="subject",family=gaussian,data,corstr="independence")

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a formula expression as for other regression models to be fitted, of the form response ~ predictors. The details of formula specification can be seen in glm() and gee().

id

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

family

a family object: a list of functions and expressions for defining link and variance functions to be used in the model. This can be a character string naming a family function including "gaussian", "binomial", and "poisson". See family for details of family functions in glm() and gee().

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which glm is called.

corstr

a character string specifying working correlation structure: "independence", "AR-M","exchangeable", "unstructured" are possible.

Details

Fit the model by GEE and calculate the original variance estimator proposed by Liang and Zeger (1986).

Value

cov.beta

estimate of the variance for beta
cov.var

estimate of the variance-covariance matrix for the variance estimator

Author(s)

Ming Wang <[email protected]>

Maintainer: Zheng Li <[email protected]>

References

Zeger SL and Liang KY. Longitudinal data analysis for discrete and continuous outcomes. Biometrics 1986: 121-130.

Examples

data(dental)
data_alt <- reshape(dental, direction="long", timevar="Time", 
        varying=names(dental)[3:6], v.names="response", times=c(8,10,12,14))
data_alt <- data_alt[order(data_alt$subject),]
data_alt$gender <- as.numeric(data_alt$gender)
data_alt$Time <- sqrt(data_alt$Time)
formula <- response~Time+gender
lz.ind <- GEE.var.lz(formula,id="subject",family=gaussian,
          data_alt,corstr="independence") ##Independence correlation structure;                   
lz.exch <- GEE.var.lz(formula,id="subject",family=gaussian,
         data_alt,corstr="exchangeable") ##Exchangeable correlation structure;                    
lz.ar1 <- GEE.var.lz(formula,id="subject",family=gaussian,
          data_alt,corstr="AR-M") ##AR-1 correlation structure;                     
lz.unstr <- GEE.var.lz(formula,id="subject",family=gaussian,
        data_alt,corstr="unstructured") ##Unstructured correlation structure;

A modified GEE Variance Estimator Proposed by Morel, Bokossa and Neerchal (2003).

Description

Calculate the modified GEE variance estimator proposed by Morel, Bokossa and Neerchal (2003).

Usage

GEE.var.mbn(formula,id,family=gaussian,data,corstr="independence",d=2,r=1)

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a formula expression as for other regression models to be fitted, of the form response ~ predictors. The details of formula specification can be seen in glm() and gee().

id

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

family

a family object: a list of functions and expressions for defining link and variance functions to be used in the model. This can be a character string naming a family function including "gaussian", "binomial", and "poisson". See family for details of family functions in glm() and gee().

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which glm is called.

corstr

a character string specifying working correlation structure: "independence", "AR-M","exchangeable", "unstructured" are possible.

d

adjustment factor in the variance estimator. The default value is 2. Details see Morel, Bokossa and Neerchal (2003).

r

adjustment factor in the variance estimator. The default value is 1. Details see Morel, Bokossa and Neerchal (2003).

Details

Fit the model by GEE and calculate the variance estimator proposed by Morel, Bokossa and Neerchal (2003).

Value

cov.beta

estimate of the variance for beta
cov.var

estimate of the variance-covariance matrix for the variance estimator

Author(s)

Ming Wang <[email protected]>

Maintainer: Zheng Li <[email protected]>

References

Morel JG, Bokossa MC, and Neerchal NK. Small sample correction for the variance of GEE estimators. Biometrical Journal 2003;45(4): 395-409.

Examples

data(dental)
data_alt <- reshape(dental, direction="long", timevar="Time", 
         varying=names(dental)[3:6], v.names="response", times=c(8,10,12,14))
data_alt <- data_alt[order(data_alt$subject),]
data_alt$gender <- as.numeric(data_alt$gender)
data_alt$Time <- sqrt(data_alt$Time)
formula <- response~Time+gender
mbn.ind <- GEE.var.mbn(formula,id="subject",family=gaussian,
       data_alt,corstr="independence",d=2,r=1) ##Independence correlation structure;            
mbn.exch <- GEE.var.mbn(formula,id="subject",family=gaussian,
      data_alt,corstr="exchangeable",d=2,r=1) ##Exchangeable correlation structure;             
mbn.ar1 <- GEE.var.mbn(formula,id="subject",family=gaussian,
       data_alt,corstr="AR-M",d=2,r=1) ##AR-1 correlation structure;                   
mbn.unstr <- GEE.var.mbn(formula,id="subject",family=gaussian,
       data_alt,corstr="unstructured",d=2,r=1) ##Unstructured correlation structur;

A Modified GEE Variance Estimator Proposed by Mancl and DeRouen (2001).

Description

Calculate the modified GEE variance estimator proposed by Mancl and DeRouen (2001).

Usage

GEE.var.md(formula,id,family=gaussian,data,corstr="independence")

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a formula expression as for other regression models to be fitted, of the form response ~ predictors. The details of formula specification can be seen in glm() and gee().

id

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

family

a family object: a list of functions and expressions for defining link and variance functions to be used in the model. This can be a character string naming a family function including "gaussian", "binomial", and "poisson". See family for details of family functions in glm() and gee().

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which glm is called.

corstr

a character string specifying working correlation structure: "independence", "AR-M","exchangeable", "unstructured" are possible.

Details

Fit the model by GEE and calculate the variance estimator proposed by Mancl and DeRouen (2001).

Value

cov.beta

estimate of the variance for beta
cov.var

estimate of the variance-covariance matrix for the variance estimator

Author(s)

Ming Wang <[email protected]>

Maintainer: Zheng Li <[email protected]>

References

Mancl LA and DeRouen TA. A Covariance Estimator for GEE with Improved Small- Sample Properties. Biometrics 2001;57: 126-134.

Examples

data(dental)
data_alt <- reshape(dental, direction="long", timevar="Time", 
            varying=names(dental)[3:6], v.names="response", times=c(8,10,12,14))
data_alt <- data_alt[order(data_alt$subject),]
data_alt$gender <- as.numeric(data_alt$gender)
data_alt$Time <- sqrt(data_alt$Time)
formula <- response~Time+gender
md.ind <- GEE.var.md(formula,id="subject",family=gaussian,
          data_alt,corstr="independence") ##Independence correlation structure;                    
md.exch <- GEE.var.md(formula,id="subject",family=gaussian,
         data_alt,corstr="exchangeable") ##Exchangeable correlation structure;                 
md.ar1 <- GEE.var.md(formula,id="subject",family=gaussian,
          data_alt,corstr="AR-M") ##AR-1 correlation structure;                     
md.unstr <- GEE.var.md(formula,id="subject",family=gaussian,
         data_alt,corstr="unstructured") ##Unstructured correlation structure;

A Modified GEE Variance Estimator Proposed by Mackinnon (1985).

Description

Calculate the variance estimators proposed by Mackinnon (1985).

Usage

GEE.var.mk(formula,id,family=gaussian,data,corstr="independence")

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a formula expression as for other regression models to be fitted, of the form response ~ predictors. The details of formula specification can be seen in glm() and gee().

id

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

family

a family object: a list of functions and expressions for defining link and variance functions to be used in the model. This can be a character string naming a family function including "gaussian", "binomial", and "poisson". See family for details of family functions in glm() and gee().

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which glm is called.

corstr

a character string specifying working correlation structure: "independence", "AR-M","exchangeable", "unstructured" are possible.

Details

Fit the model by GEE and calculate the variance estimator proposed by Mackinnon (1985). This estimator improved the sandwich variance estimator by ajusting the degree of freedom.

Value

cov.beta

estimate of the variance for beta
cov.var

estimate of the variance-covariance matrix for the variance estimator

Author(s)

Ming Wang <[email protected]>

Maintainer: Zheng Li <[email protected]>

References

MacKinnon JG. Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties. Journal of Econometrics 1985;29: 305-325.

Examples

data(dental)
data_alt <- reshape(dental, direction="long", timevar="Time", 
                   varying=names(dental)[3:6], v.names="response", times=c(8,10,12,14))
data_alt <- data_alt[order(data_alt$subject),]
data_alt$gender <- as.numeric(data_alt$gender)
data_alt$Time <- sqrt(data_alt$Time)
formula <- response~Time+gender
mk.ind <- GEE.var.mk(formula,id="subject",family=gaussian,
      data_alt,corstr="independence") ##Independence correlation structure;            
mk.exch <- GEE.var.mk(formula,id="subject",family=gaussian,
        data_alt,corstr="exchangeable") ##Exchangeable correlation structure;                
mk.ar1 <- GEE.var.mk(formula,id="subject",family=gaussian,
       data_alt,corstr="AR-M") ##AR-1 correlation structure;                         
mk.unstr <- GEE.var.mk(formula,id="subject",family=gaussian,
        data_alt,corstr="unstructured") ##Unstructured correlation structure;

A Modified GEE Variance Estimator Proposed by Pan (2001).

Description

Calculate the modified GEE variance estimator proposed by Pan (2001).

Usage

GEE.var.pan(formula,id,family=gaussian,data,corstr="independence")

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a formula expression as for other regression models to be fitted, of the form response ~ predictors. The details of formula specification can be seen in glm() and gee().

id

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

family

a family object: a list of functions and expressions for defining link and variance functions to be used in the model. This can be a character string naming a family function including "gaussian", "binomial", and "poisson". See family for details of family functions in glm() and gee().

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which glm is called.

corstr

a character string specifying working correlation structure: "independence", "AR-M","exchangeable", "unstructured" are possible.

Details

it the model by GEE and calculate the variance estimator proposed by Pan(2001). There are two assumptions for the model: 1) The conditional variance is correctly specified; 2) A common correlation structure exists across all subjects.

Value

cov.beta

estimate of the variance for beta
cov.var

estimate of the variance-covariance matrix for the variance estimator

Author(s)

Ming Wang <[email protected]>

Maintainer: Zheng Li <[email protected]>

References

Pan W. On the Robust Variance Estimator in Generalized Estimating Equations. Biometrika 2001;88: 901-906.

Examples

data(dental)
data_alt <- reshape(dental, direction="long", timevar="Time", 
         varying=names(dental)[3:6], v.names="response", times=c(8,10,12,14))
data_alt <- data_alt[order(data_alt$subject),]
data_alt$gender <- as.numeric(data_alt$gender)
data_alt$Time <- sqrt(data_alt$Time)
formula <- response~Time+gender
pan.ind <- GEE.var.pan(formula,id="subject",family=gaussian, 
          data_alt,corstr="independence") ##Independence correlation structure;                
pan.exch <- GEE.var.pan(formula,id="subject",family=gaussian,
          data_alt,corstr="exchangeable") ##Exchangeable correlation structure;                 
pan.ar1 <- GEE.var.pan(formula,id="subject",family=gaussian,
          data_alt,corstr="AR-M") ##AR-1 correlation structure;                   
pan.unstr <- GEE.var.pan(formula,id="subject",family=gaussian,
          data_alt,corstr="unstructured") ##Unstructured correlation structure;

A Modified GEE Variance Estimator Proposed by Wang and Long (2011).

Description

Calculate the modified GEE variance estimator proposed by Wang and Long (2011).

Usage

GEE.var.wl(formula,id,family=gaussian,data,corstr="independence")

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a formula expression as for other regression models to be fitted, of the form response ~ predictors. The details of formula specification can be seen in glm() and gee().

id

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

family

a family object: a list of functions and expressions for defining link and variance functions to be used in the model. This can be a character string naming a family function including "gaussian", "binomial", and "poisson". See family for details of family functions in glm() and gee().

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which glm is called.

corstr

a character string specifying working correlation structure: "independence", "AR-M","exchangeable", "unstructured" are possible.

Details

Fit the model by GEE and calculate the variance estimator proposed by Wang and Long (2011). Two assumptions need to be satisfied: 1) The conditional variance is correctly specified; 2) A common correlation structure exists across all subjects.

Value

cov.beta

estimate of the variance for beta
cov.var

estimate of the variance-covariance matrix for the variance estimator

Author(s)

Ming Wang <[email protected]>

Maintainer: Zheng Li <[email protected]>

References

Wang M and Long Q. Modified robust variance estimator for generalized estimating equations with improved small-sample performance. Statistics in Medicine 2011;30(11): 1278-1291.

Examples

data(dental)
data_alt <- reshape(dental, direction="long", timevar="Time", 
                   varying=names(dental)[3:6], v.names="response", times=c(8,10,12,14))
data_alt <- data_alt[order(data_alt$subject),]
data_alt$gender <- as.numeric(data_alt$gender)
data_alt$Time <- sqrt(data_alt$Time)
formula <- response~Time+gender
wl.ind <- GEE.var.wl(formula,id="subject",family=gaussian,
       data_alt,corstr="independence") ##Independence correlation structure;            
wl.exch <- GEE.var.wl(formula,id="subject",family=gaussian,
       data_alt,corstr="exchangeable") ##Exchangeable correlation structure;               
wl.ar1 <- GEE.var.wl(formula,id="subject",family=gaussian,
       data_alt,corstr="AR-M") ##AR-1 correlation structure;            
wl.unstr <- GEE.var.wl(formula,id="subject",family=gaussian,
         data_alt,corstr="unstructured") ##Unstructured correlation structure;

Calculate variance estimator

Description

Being used to calculate variance estimator by the functions in this package. It cannot be directly used in other packages.

Calculate variance estimator

Description

Being used to calculate variance estimator by the functions in this package. It cannot be directly used in other packages.

Calculate variance estimator

Description

Being used to calculate variance estimator by the functions in this package. It cannot be directly used in other packages.

Epiliptic seizure counts from the Randomized Progabide Trial

Description

The data consists of 59 subjects from the randomized progabide trial.

Usage

seizure

Format

  • base:baseline epiliptic seizure counts

  • trt:the indicator for treatment (1=progabide; 0=control)

  • age:baseline age for each subject

  • y1:epiliptic seizure counts in the first week

  • y2:epiliptic seizure counts in the second week

  • y3:epiliptic seizure counts in the third week

  • y4:epiliptic seizure counts in the forth week

Details

The outcome is the count number of epiliptic seizures in each of four consecutive two-week intervals, and the variables recorded include baseline epiliptic seizure counts in an eight-week interval prior to the treatment assignment, the indicator for treatment (1=progabide; 0=control), and baseline age.

Source

Thall PF, and Vail SC. Some covariance models for longitudinal count data with overdispersion. Biometrics 1990; 46: 657-671.

Toenail infection data from a multicenter study

Description

The data frame consists of 250 patients from a multicenter study comparing to treatments for toenail infection.

Usage

toenail

Format

  • ID: patient id. The variable for cluster id

  • Response: toenail infection status: 0=none or mild; 1=moderate or severe

  • Treatment: 1=oral treatment A; 0=oral treatment B

  • Month: the exact time point of measurement in month

  • Visit: the visit index

Details

In a randomized, double-blinded multicenter study, treatment A and B were compared to treat toenail infection disease. Patientes were evaluated for the degree of onycholysis. There are 1908 measurements in total.

Source

De Backer M, De Vroey C, Lesaffre E, Scheys I, De Keyser P. Twelve weeks of continuous oral therapy for toenail onychomycosis caused by dermatophytes: a double-blind comparative trial of terbinafine 250 mg/day versus itraconazole 200 mg/day. Journal of the American Academy of Dermatology 1998; 38: 57-63.