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.

Here we will demonstrate how the `tern.gee`

package
functionality can be used to fit a GEE model and tabulate its
output.

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
```

tern-gee.R

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
```

tern-gee.R

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 0.8608217 0.9367768 420 NA
#> 2 TRT 0.9527634 0.01193578 0.9229565 0.9713959 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 1.125774 3.943307 0.7452453 0.118471 1.37202 0.95
```

tern-gee.R

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.

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.