Estimate marginal treatment effects using a GLM working model

Estimates the marginal treatment effect from a logistic regression working model using a specified choice of variance estimator and contrast.

Usage

get_marginal_effect(
  object,
  trt,
  strata = NULL,
  method = "Ge",
  type = "HC0",
  contrast = "diff",
  reference,
  mod = FALSE
)

Arguments

object: a fitted glm object.
trt: a string specifying the name of the treatment variable in the model formula. It must be one of the linear predictor variables used in fitting the object.
strata: an optional string or vector of strings specifying the names of stratification variables. Relevant only for Ye's method and used to adjust the variance-covariance estimation for stratification. If provided, each specified variable must be present in the model.
method: a string indicating the chosen method for variance estimation. Supported methods are Ge and Ye. The default method is Ge based on Ge et al (2011) which is suitable for the variance estimation of conditional average treatment effect. The method Ye is based on Ye et al (2023) and is suitable for the variance estimation of population average treatment effect. For more details, see Magirr et al. (2024).
type: a string indicating the type of variance estimator to use (only applicable for Ge's method). Supported types include HC0 (default), model-based, HC3, HC, HC1, HC2, HC4, HC4m, and HC5. See vcovHC for heteroscedasticity-consistent estimators.
contrast: a string indicating choice of contrast. Defaults to 'diff' for a risk difference. See apply_contrast.
reference: a string indicating which treatment group should be considered as the reference level. Accepted values are one of the levels in the treatment variable. Default to the first level used in the glm object. This parameter influences the calculation of treatment effects relative to the chosen reference group.
mod: for Ye's method, the implementation of open-source RobinCar package has an additional variance decomposition step when estimating the robust variance, which then utilizes different counterfactual outcomes than the original reference. Set mod = TRUE to use exactly the implementation method described in Ye et al (2022), default to FALSE to use the modified implementation in RobinCar and Bannick et al (2023) which improves stability.

Value

an updated glm object appended with marginal estimate components: counterfactual.predictions (see predict_counterfactuals), counterfactual.means (see average_predictions), robust_varcov (see estimate_varcov), marginal_est, marginal_se (see apply_contrast) and marginal_results. A summary is shown below

counterfactual.predictions	Counterfactual predictions based on the working model. For each subject in the input glm data, the potential outcomes are obtained by assigning subjects to each of the possible treatment variable levels. Each prediction is associated with a descriptive label explaining the counterfactual scenario.
counterfactual.means	Average of the counterfactual predictions for each level of the treatment variable.
robust_varcov	Variance-covariance matrix of the marginal effect estimate for each level of treatment variable, with estimation method indicated in the attributes.
marginal_est	Marginal treatment effect estimate for a given contrast.
marginal_se	Standard error estimate of the marginal treatment effect estimate.
marginal_results	Analysis results data (ARD) containing a summary of the analysis for subsequent reporting.

Details

The get_marginal_effect function is a wrapper that facilitates advanced variance estimation techniques for GLM models with covariate adjustment targeting a population average treatment effect. It is particularly useful in clinical trial analysis and other fields requiring robust statistical inference. It allows researchers to account for complex study designs, including stratification and treatment contrasts, by providing a flexible interface for variance-covariance estimation.

Examples

trial01$trtp <- factor(trial01$trtp)
fit1 <- glm(aval ~ trtp + bl_cov, family = "binomial", data = trial01) |>
  get_marginal_effect(trt = "trtp", method = "Ye", contrast = "diff", reference = "0")
#> Warning: There is 1 record omitted from the original data due to missing values, please check if they should be imputed prior to model fitting.
fit1$marginal_results
#> # A tibble: 12 × 8
#>    TRTVAR TRTVAL    PARAM ANALTYP1    STAT     STATVAL ANALMETH      ANALDESC   
#>    <chr>  <chr>     <chr> <chr>       <chr>      <dbl> <chr>         <chr>      
#>  1 trtp   1         aval  DESCRIPTIVE N       134      count         Computed u…
#>  2 trtp   1         aval  DESCRIPTIVE n        56      count         Computed u…
#>  3 trtp   1         aval  DESCRIPTIVE %        41.8    percentage    Computed u…
#>  4 trtp   1         aval  INFERENTIAL risk      0.419  g-computation Computed u…
#>  5 trtp   1         aval  INFERENTIAL risk_se   0.0427 Ye            Computed u…
#>  6 trtp   0         aval  DESCRIPTIVE N       133      count         Computed u…
#>  7 trtp   0         aval  DESCRIPTIVE n        65      count         Computed u…
#>  8 trtp   0         aval  DESCRIPTIVE %        48.9    percentage    Computed u…
#>  9 trtp   0         aval  INFERENTIAL risk      0.487  g-computation Computed u…
#> 10 trtp   0         aval  INFERENTIAL risk_se   0.0435 Ye            Computed u…
#> 11 trtp   diff: 1-0 aval  INFERENTIAL diff     -0.0684 g-computation Computed u…
#> 12 trtp   diff: 1-0 aval  INFERENTIAL diff_se   0.0609 Ye            Computed u…