Introduction

Generalized Estimating Equations (GEEs) are mainly used for modeling longitudinal binary or count endpoints from clinical trials. Within this package, a GEE is used to estimate the parameters of a generalized linear model that includes as fixed effects the variables: treatment arm, categorical visit, and other covariates for adjustment (e.g. age, sex, race). The covariance structure of the residuals can take on different forms. Often, an unstructured (i.e. saturated parameterization) covariance matrix is assumed which can be represented by random effects in the model.

This vignette shows the general purpose and syntax of the tern.gee R package which provides an interface for GEEs within the tern framework. This package builds upon some of the GEE functionality included in the geepack and geeasy R packages. Within this package, we have implemented GEEs in R in such a way that they can easily be embedded into a shiny application. See teal.modules.clinical::tm_a_gee() and the teal.modules.clinical package for more details about using this code inside a shiny application.

Example

Here we will demonstrate how the tern.gee package functionality can be used to fit a GEE model and tabulate its output.

Setup

Our sample dataset, fev_data, is available in the tern.gee package and consists of seven variables: subject ID (USUBJID), visit number (AVISIT), treatment (ARMCD = TRT or PBO), 3-category RACE, SEX, FEV1 at baseline (%) (FEV1_BL), and FEV1 at study visits (%) (FEV1). Additionally we create an arbitrary binary variable FEV1_BINARY for our analysis which takes a value of 1 where FEV1 > 30 and 0 otherwise. FEV1 (forced expired volume in one second) is a measure of how quickly the lungs can be emptied. Low levels of FEV1 may indicate chronic obstructive pulmonary disease (COPD). The scientific question at hand is whether treatment leads to an increase in FEV1 over time after adjusting for baseline covariates.

library(tern.gee)
fev_data$FEV1_BINARY <- as.integer(fev_data$FEV1 > 30)
head(fev_data)
#> # A tibble: 6 × 8
#>   USUBJID AVISIT ARMCD RACE                      SEX   FEV1_BL  FEV1 FEV1_BINARY
#>   <fct>   <fct>  <fct> <fct>                     <fct>   <dbl> <dbl>       <int>
#> 1 PT1     VIS1   TRT   Black or African American Fema…    25.3  NA            NA
#> 2 PT1     VIS2   TRT   Black or African American Fema…    25.3  40.0           1
#> 3 PT1     VIS3   TRT   Black or African American Fema…    25.3  NA            NA
#> 4 PT1     VIS4   TRT   Black or African American Fema…    25.3  20.5           0
#> 5 PT2     VIS1   PBO   Asian                     Male     45.0  NA            NA
#> 6 PT2     VIS2   PBO   Asian                     Male     45.0  31.5           1

Model Fitting

Fitting a GEE model is easy when you use tern.gee. By default, the model fitting function fit_gee() assumes unstructured correlation and proportional weights when calculating LS means, and fits a logistic regression model. Currently only logistic regression has been implemented as an available regression model when using fit_gee(). In future the package will be extended to include other models such as Poisson regression, etc. as alternative options.

fev_fit <- fit_gee(
  vars = list(
    response = "FEV1_BINARY",
    covariates = c("RACE", "SEX", "FEV1_BL"),
    arm = "ARMCD",
    id = "USUBJID",
    visit = "AVISIT"
  ),
  data = fev_data
)
#> Registered S3 methods overwritten by 'geeasy':
#>   method       from   
#>   drop1.geeglm MESS   
#>   drop1.geem   MESS   
#>   plot.geeglm  geepack
fev_fit
#> 
#> Call:
#> geeasy::geelm(formula = formula, id = .id, waves = .waves, data = data, 
#>     family = family$object, corstr = cor_details$str, Mv = cor_details$mv, 
#>     control = family$control)
#> 
#> Coefficients:
#>                   (Intercept)                      ARMCDTRT 
#>                   -0.20061892                    0.74524533 
#> RACEBlack or African American                     RACEWhite 
#>                    0.11627212                    1.38199917 
#>                     SEXFemale                       FEV1_BL 
#>                   -0.14521343                    0.05257141 
#> 
#> Degrees of Freedom: 537 Total (i.e. Null);  531 Residual
#> 
#> Scale is fixed.
#> 
#> Correlation:  Structure = unstructured    Link = identity 
#> Estimated Correlation Parameters:
#> [1] -0.046922366 -0.130175920  0.071402079 -0.126586549 -0.062642853
#> [6]  0.006795836
#> 
#> Number of clusters:   197   Maximum cluster size: 4

The resulting object consists of many pieces of information pertaining to the model such as the estimated coefficients, correlation parameters, etc. Additionally, the lsmeans() function from tern.gee can be used to extract the least squares means from any GEE model created using fit_gee().

fev_lsmeans <- lsmeans(fev_fit, data = fev_data)
fev_lsmeans
#>   ARMCD  prop_est prop_est_se prop_lower_cl prop_upper_cl   n   or_est
#> 1   PBO 0.9054200  0.01904206     0.8609409     0.9367178 420       NA
#> 2   TRT 0.9527634  0.01193578     0.9230409     0.9713629 380 2.106958
#>   or_lower_cl or_upper_cl log_or_est log_or_lower_cl log_or_upper_cl conf_level
#> 1          NA          NA         NA              NA              NA       0.95
#> 2    1.127384    3.937677  0.7452453       0.1198996        1.370591       0.95

Based on the output, there is evidence to support that treatment leads to an increase in FEV1 over placebo. The GEE model can be refined by using different correlation structures and weighting schemes.

Tabulation

After fitting a GEE model and extracting the LS means you may want to display your results in a table. The tern.gee package contains functionality to summarize the results of a lsmeans() object in an rtable structure, using additional functions from the rtables package.

fev_counts <- fev_data %>%
  dplyr::select(USUBJID, ARMCD) %>%
  unique()

fev_gee_table <- basic_table(show_colcounts = TRUE) %>%
  split_cols_by("ARMCD", ref_group = "PBO") %>%
  summarize_gee_logistic() %>%
  build_table(fev_lsmeans, alt_counts_df = fev_counts)

fev_gee_table
#>                                     PBO            TRT     
#>                                   (N=105)         (N=95)   
#> ———————————————————————————————————————————————————————————
#> n                                   420            380     
#> Adjusted Mean Proportion (SE)   0.91 (0.02)    0.95 (0.01) 
#>   95% CI                        (0.86, 0.94)   (0.92, 0.97)
#> Odds Ratio                                         2.11    
#>   95% CI                                       (1.13, 3.94)
#> Log Odds Ratio                                     0.75    
#>   95% CI                                       (0.12, 1.37)

First we create a table fev_counts to get the number of unique subjects receiving each treatment. These counts are displayed in the header of the table under each of the column names by specifying show_colcounts = TRUE when initializing the table via the basic_table() function. The table is split by arm (ARMCD), with PBO specified as the reference group to compare the TRT group to. Then the summarize_gee_logistic() function from tern.gee is applied. Finally, the build_table() function builds the rtable using our LS means dataset with fev_counts providing the counts of unique subjects in each arm.