Use prognostic covariate adjustment when fitting an rctglm

The procedure uses fit_best_learner to fit a prognostic model to historical data and uses the model to produce counterfactual predictions as a prognostic score that is then adjusted for as a covariate in the rctglm procedure. See Powering RCTs for marginal effects with GLMs using prognostic score adjustment by Højbjerre-Frandsen et. al (2025) for more details.

Usage

rctglm_with_prognosticscore(
  formula,
  exposure_indicator,
  exposure_prob,
  data,
  family = gaussian,
  estimand_fun = "ate",
  estimand_fun_deriv0 = NULL,
  estimand_fun_deriv1 = NULL,
  cv_variance = FALSE,
  cv_variance_folds = 10,
  ...,
  data_hist,
  prog_formula = NULL,
  cv_prog_folds = 5,
  learners = default_learners(),
  verbose = options::opt("verbose")
)

Arguments

formula: an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under ‘Details’ in the glm documentation.
exposure_indicator: (name of) the binary variable in data that identifies randomisation groups. The variable is required to be binary to make the "orientation" of the estimand_fun clear.
exposure_prob: a numeric with the probability of being in "group 1" (rather than group 0) in groups defined by exposure_indicator.
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 the function is called.
family: a description of the error distribution and link function to be used in the model. For glm this can be a character string naming a family function, a family function or the result of a call to a family function. For glm.fit only the third option is supported. (See family for details of family functions.)
estimand_fun: a function with arguments psi1 and psi0 specifying the estimand. Alternative, specify "ate" or "rate_ratio" as a character to use one of the default estimand functions. See more details in the "Estimand" section of rctglm.
estimand_fun_deriv0: a function specifying the derivative of estimand_fun wrt. psi0. As a default the algorithm will use symbolic differentiation to automatically find the derivative from estimand_fun
estimand_fun_deriv1: a function specifying the derivative of estimand_fun wrt. psi1. As a default the algorithm will use symbolic differentiation to automatically find the derivative from estimand_fun
cv_variance: a logical determining whether to estimate the variance using cross-validation (see details of rctglm).
cv_variance_folds: a numeric with the number of folds to use for cross validation if cv_variance is TRUE.
...: Additional arguments passed to stats::glm()
data_hist: a data.frame with historical data on which to fit a prognostic model
prog_formula: an object of class "formula" (or one that can be coerced to that class): a symbolic description of the prognostic model to be fitted to data_hist. Passed in a list as the preproc argument in fit_best_learner(). As a default, the formula is created by modelling the response (assumed to have the same name as in formula) using all columns in data_hist.
cv_prog_folds: a numeric with the number of cross-validation folds used when fitting and evaluating models
learners: a list (preferably named) containing named lists of elements model and optionally grid. The model element should be a parsnip model specification, which is passed to workflowsets::workflow_set as the model argument, while the grid element is passed as the grid argument of workflowsets::option_add
verbose: numeric verbosity level. Higher values means more information is printed in console. A value of 0 means nothing is printed to console during execution (Defaults to 2, overwritable using option 'postcard.verbose' or environment variable 'R_POSTCARD_VERBOSE')

Value

rctglm_with_prognosticscore returns an object of class rctglm_prog, which inherits from rctglm.

An rctglm_prog object is a list with the same components as an rctglm object (see the Value section of rctglm for a breakdown of the structure), but with an additional list element of:

prognostic_info: List with information about the fitted prognostic model on historical data. It has components:
- formula: The formula with symbolic description of how the response is modelled as function of covariates in the models
- model_fit: A trained workflow - the result of fit_best_learner
- learners: A list of learners used for the discrete super learner
- cv_folds: The amount of folds used for cross validation
- data: The historical data used for cross validation when fitting and testing models

Details

Prognostic covariate adjustment involves training a prognostic model (using fit_best_learner) on historical data (data_hist) to predict the response in that data.

Assuming that the historical data is representative of the comparator group in a “new” data set (group 0 of the binary exposure_indicator in data), we can use the prognostic model to predict the counterfactual outcome of all observations (including the ones in the comparator group for which the prediction of counterfactual outcome coincides with a prediction of actual outcome).

This prediction, which is called the prognostic score, is then used as an adjustment covariate in the GLM (the prognostic score is added to formula before calling rctglm with the modified formula).

See much more details in the reference in the description.

Examples

# Generate some data
n <- 100
b0 <- 1
b1 <- 1.5
b2 <- 2
W1 <- runif(n, min = -2, max = 2)
exp_prob <- .5

dat_treat <- glm_data(
  Y ~ b0+b1*abs(sin(W1))+b2*A,
  W1 = W1,
  A = rbinom (n, 1, exp_prob)
)

dat_notreat <- glm_data(
  Y ~ b0+b1*abs(sin(W1)),
  W1 = W1
)

learners <- list(
  mars = list(
    model = parsnip::set_engine(
      parsnip::mars(
        mode = "regression", prod_degree = 3
      ),
      "earth"
    )
 ),
    lm = list(
      model = parsnip::set_engine(
        parsnip::linear_reg(),
        "lm"
      )
    )
)
ate <- rctglm_with_prognosticscore(
  formula = Y ~ .,
  exposure_indicator = A,
  exposure_prob = exp_prob,
  data = dat_treat,
  family = gaussian(),
  estimand_fun = "ate",
  data_hist = dat_notreat,
  learners = learners)
#> 
#> ── Fitting prognostic model ──
#> 
#> ℹ Created formula for fitting prognostic model as: Y ~ .
#> ℹ Fitting learners
#> • mod_mars
#> • mod_lm
#> i	No tuning parameters. `fit_resamples()` will be attempted
#> i 1 of 2 resampling: mod_mars
#> ✔ 1 of 2 resampling: mod_mars (125ms)
#> i	No tuning parameters. `fit_resamples()` will be attempted
#> i 2 of 2 resampling: mod_lm
#> ✔ 2 of 2 resampling: mod_lm (92ms)
#> ℹ Model with lowest RMSE: mod_mars
#> ℹ Investigate trained learners and fitted model in `prognostic_info` list element
#> 
#> ── Symbolic differentiation of estimand function ──
#> 
#> ℹ Symbolically deriving partial derivative of the function 'psi1 - psi0' with respect to 'psi0' as: '-1'.
#> • Alternatively, specify the derivative through the argument
#> `estimand_fun_deriv0`
#> ℹ Symbolically deriving partial derivative of the function 'psi1 - psi0' with respect to 'psi1' as: '1'.
#> • Alternatively, specify the derivative through the argument
#> `estimand_fun_deriv1`

# Pull information on estimand
estimand(ate)
#>   Estimate Std. Error
#> 1 2.043516  0.1911481

Usage

Arguments

Value

Details

See also

Examples