4 Advanced treatment assignments

So far, we have focused on estimation for a fixed treatment assignment: assign to treatment 1 with probability 1.

We might also want to know about the gap-closing estimand

• if we assigned people to treatment stochastically
• if each person’s assignment were individualized

4.1 Stochastic treatments

We may want to study a counterfactual where treatment is assigned with some probability between 0 and 1. The counterfactual_assignments argument can handle this possibility.

For example, consider the gap-closing estimand if assigned to treatment 1 with each probability .75.

estimate_stochastic <- gapclosing(
  data = simulated_data,
  counterfactual_assignments = .75,
  outcome_formula = formula(outcome ~ confounder + category*treatment),
  treatment_formula = formula(treatment ~ confounder + category),
  category_name = "category"
)

The disparity between categories A and B under that stochastic intervention (0.75 probability of treatment = 1) is estimated to be 0.44, whereas under the previous deterministic intervention to assign treatment to the value 1 the disparity would be 0.14. This illustrates an important point: the gap-closing estimand can be different depending on the counterfactual assignment rule, as the figure below shows for counterfactuals in which treatment is assigned with probabilities ranging from 0 to 1.

4.2 Individualized treatments

Treatment may also be different (and possibly stochastic) for each unit in the counterfactual world of interest.

For example, suppose we assign those in Category A to treatment 1 with probability .5, those in Category B to treatment with probability .4, and those in Category C to treatment with probability .3. In this case, counterfactual_assignments will be set to a vector of length nrow(data).

our_assignments <- case_when(simulated_data$category == "A" ~ .5,
                             simulated_data$category == "B" ~ .4, 
                             simulated_data$category == "C" ~ .3)
estimate_stochastic <- gapclosing(
  data = simulated_data,
  counterfactual_assignments = our_assignments,
  outcome_formula = formula(outcome ~ confounder + category*treatment),
  treatment_formula = formula(treatment ~ confounder + category),
  category_name = "category"
)

That intervention would close the B - A gap by 31%.