multgee: GEE Solver for Correlated Nominal or Ordinal Multinomial Responses

Installation

You can install the release version of multgee:

install.packages("multgee")

The source code for the release version of multgee is available on CRAN at:

• https://CRAN.R-project.org/package=multgee

Or you can install the development version of multgee:

# install.packages('devtools')
devtools::install_github("AnestisTouloumis/multgee")

The source code for the development version of multgee is available on github at:

• https://github.com/AnestisTouloumis/multgee

To use multgee, you should load the package as follows:

library("multgee")
#> Loading required package: gnm

Usage

This package provides a generalized estimating equations (GEE) solver for fitting marginal regression models with correlated nominal or ordinal multinomial responses based on a local odds ratios parameterization for the association structure (see Touloumis, Agresti and Kateri, 2013).

There are two core functions to fit GEE models for correlated multinomial responses:

• ordLORgee for an ordinal response scale. Options for the marginal model include cumulative link models or an adjacent categories logit model,
• nomLORgee for a nominal response scale. Currently, the only option is a marginal baseline category logit model.

The main arguments in both functions are:

• an optional data frame (data),
• a model formula (formula),
• a cluster identifier variable (id),
• an optional vector that identifies the order of the observations within each cluster (repeated).

The association structure among the correlated multinomial responses is expressed via marginalized local odds ratios (Touloumis et al., 2013). The estimating procedure for the local odds ratios can be summarized as follows: For each level pair of the repeated variable, the available responses are aggregated across clusters to form a square marginalized contingency table. Treating these tables as independent, an RC-G(1) type model is fitted in order to estimate the marginalized local odds ratios. The LORstr argument determines the form of the marginalized local odds ratios structure. Since the general RC-G(1) model is closely related to the family of association models, one can instead fit an association model to each of the marginalized contingency tables by setting LORem = "2way" in the core functions.

There are also four utility functions:

• confint for obtaining Wald–type confidence intervals for the regression parameters using the standard errors of the sandwich (method = "robust") or of the model–based (method = "naive") covariance matrix estimator. The default option is using the sandwich covariance matrix estimator (method = "robust"),
• waldts for assessing the goodness-of-fit of two nested GEE models based on a Wald test statistic,
• intrinsic.pars for assessing whether the underlying association structure does not change dramatically across the level pairs of repeated,
• vcov for obtaining the sandwich (method = "robust") or the model–based (method = "naive") estimate of the covariance matrix of the regression parameters.

Example

The following R code replicates the GEE analysis presented in Touloumis et al. (2013).

data("arthritis")
intrinsic.pars(y, arthritis, id, time, rscale = "ordinal")
#> [1] 0.6517843 0.9097341 0.9022272

The intrinsic parameters do not differ much. This suggests that the uniform local odds ratios structure might be a good approximation for the association pattern.

fitord <- ordLORgee(formula = y ~ factor(time) + factor(trt) + factor(baseline), 
    data = arthritis, id = id, repeated = time)
summary(fitord)
#> GEE FOR ORDINAL MULTINOMIAL RESPONSES 
#> version 1.6.0 modified 2017-07-10 
#> 
#> Link : Cumulative logit 
#> 
#> Local Odds Ratios:
#> Structure:         category.exch
#> Model:             3way
#> 
#> call:
#> ordLORgee(formula = y ~ factor(time) + factor(trt) + factor(baseline), 
#>     data = arthritis, id = id, repeated = time)
#> 
#> Summary of residuals:
#>       Min.    1st Qu.     Median       Mean    3rd Qu.       Max. 
#> -0.5176739 -0.2380475 -0.0737290 -0.0001443 -0.0066846  0.9933154 
#> 
#> Number of Iterations: 6 
#> 
#> Coefficients:
#>                   Estimate   san.se   san.z Pr(>|san.z|)    
#> beta10            -1.84003  0.38735 -4.7504      < 2e-16 ***
#> beta20             0.27712  0.34841  0.7954      0.42639    
#> beta30             2.24779  0.36509  6.1568      < 2e-16 ***
#> beta40             4.54824  0.41994 10.8307      < 2e-16 ***
#> factor(time)3     -0.00079  0.12178 -0.0065      0.99485    
#> factor(time)5     -0.36050  0.11413 -3.1586      0.00159 ** 
#> factor(trt)2      -0.50463  0.16725 -3.0173      0.00255 ** 
#> factor(baseline)2 -0.70291  0.37861 -1.8565      0.06338 .  
#> factor(baseline)3 -1.27558  0.35066 -3.6376      0.00028 ***
#> factor(baseline)4 -2.65579  0.41039 -6.4714      < 2e-16 ***
#> factor(baseline)5 -3.99555  0.53246 -7.5040      < 2e-16 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Local Odds Ratios Estimates:
#>        [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10] [,11] [,12]
#>  [1,] 0.000 0.000 0.000 0.000 1.919 1.919 1.919 1.919 2.484 2.484 2.484 2.484
#>  [2,] 0.000 0.000 0.000 0.000 1.919 1.919 1.919 1.919 2.484 2.484 2.484 2.484
#>  [3,] 0.000 0.000 0.000 0.000 1.919 1.919 1.919 1.919 2.484 2.484 2.484 2.484
#>  [4,] 0.000 0.000 0.000 0.000 1.919 1.919 1.919 1.919 2.484 2.484 2.484 2.484
#>  [5,] 1.919 1.919 1.919 1.919 0.000 0.000 0.000 0.000 2.465 2.465 2.465 2.465
#>  [6,] 1.919 1.919 1.919 1.919 0.000 0.000 0.000 0.000 2.465 2.465 2.465 2.465
#>  [7,] 1.919 1.919 1.919 1.919 0.000 0.000 0.000 0.000 2.465 2.465 2.465 2.465
#>  [8,] 1.919 1.919 1.919 1.919 0.000 0.000 0.000 0.000 2.465 2.465 2.465 2.465
#>  [9,] 2.484 2.484 2.484 2.484 2.465 2.465 2.465 2.465 0.000 0.000 0.000 0.000
#> [10,] 2.484 2.484 2.484 2.484 2.465 2.465 2.465 2.465 0.000 0.000 0.000 0.000
#> [11,] 2.484 2.484 2.484 2.484 2.465 2.465 2.465 2.465 0.000 0.000 0.000 0.000
#> [12,] 2.484 2.484 2.484 2.484 2.465 2.465 2.465 2.465 0.000 0.000 0.000 0.000
#> 
#> pvalue of Null model: <0.0001

The 95% Wald confidence intervals for the regression parameters are

confint(fitord)
#>                        2.5 %      97.5 %
#> beta10            -2.5992134 -1.08084855
#> beta20            -0.4057572  0.95999854
#> beta30             1.5322296  2.96335073
#> beta40             3.7251701  5.37130863
#> factor(time)3     -0.2394781  0.23790571
#> factor(time)5     -0.5841988 -0.13680277
#> factor(trt)2      -0.8324304 -0.17683500
#> factor(baseline)2 -1.4449754  0.03916401
#> factor(baseline)3 -1.9628588 -0.58829522
#> factor(baseline)4 -3.4601391 -1.85143755
#> factor(baseline)5 -5.0391534 -2.95195213

Getting help

The statistical methods implemented in multgee are described in Touloumis et al. (2013). A detailed description of the functionality of multgee can be found in Touloumis (2015). Note that an updated version of this paper also serves as a vignette:

browseVignettes("multgee")

How to cite

To cite multgee in publications use:

  Anestis Touloumis (2015). R Package multgee: A Generalized Estimating
  Equations Solver for Multinomial Responses. Journal of Statistical
  Software, 64(8), 1-14. URL http://www.jstatsoft.org/v64/i08/.

A BibTeX entry for LaTeX users is

  @Article{,
    title = {{R} Package {multgee}: A Generalized Estimating Equations Solver for Multinomial Responses},
    author = {Anestis Touloumis},
    journal = {Journal of Statistical Software},
    year = {2015},
    volume = {64},
    number = {8},
    pages = {1--14},
    url = {http://www.jstatsoft.org/v64/i08/},
  }

To cite the methodology implemented in multgee in publications use:

  Anestis Touloumis, Alan Agresti and Maria Kateri (2013). R Package
  multgee: A Generalized Estimating Equations Solver for Multinomial
  Responses. Biometrics, 69(3), 633-640. URL
  http://onlinelibrary.wiley.com/enhanced/doi/10.1111/biom.12054/.

A BibTeX entry for LaTeX users is

  @Article{,
    title = {GEE for multinomial responses using a local odds ratios parameterization},
    author = {Anestis Touloumis and Alan Agresti and Maria Kateri},
    journal = {Biometrics},
    year = {2013},
    volume = {69},
    number = {3},
    pages = {633--640},
    url = {http://onlinelibrary.wiley.com/enhanced/doi/10.1111/biom.12054/},
  }

References

Touloumis, A. (2015) R Package multgee: A Generalized Estimating Equations Solver for Multinomial Responses. Journal of Statistical Software, 64, 1–14.

Touloumis, A., Agresti, A. and Kateri, M. (2013) GEE for Multinomial Responses Using a Local Odds Ratios Parameterization. Biometrics, 69, 633–640.