Balance summary / Variance

[kali-alex]

• How can we have the balance summary across each covariates for the propensity score ? (To calcul the Standardized Mean Difference for example)

• Which estimator is use to compute the variance (and thus 95%CI) ?

[yqzhong7]

How can we have the balance summary across each covariates for the propensity score ? (To calcul the Standardized Mean Difference for example)

You could extract the propensity scores and put them into other packages like cobalt. Please refer to cobalt for more details. I'll add cobalt support in the near future.

Here's a short example for using cobalt to example the balance.

library(AIPW)
library(cobalt)
library(SuperLearner)

set.seed(123)
data("eager_sim_obs")
cov = c("eligibility","loss_num","age", "time_try_pregnant","BMI","meanAP")

AIPW_SL <- AIPW$new(Y= eager_sim_obs$sim_Y,
                    A= eager_sim_obs$sim_A,
                    W= subset(eager_sim_obs,select=cov), 
                    Q.SL.library = c("SL.mean","SL.glm"),
                    g.SL.library = c("SL.mean","SL.glm"),
                    k_split = 10,
                    verbose=FALSE)$
  fit()$ #for ATT please use stratified_fit()
  summary(g.bound = c(0.025,0.975)) #Default truncation of propsensity scores


ate.weights <- function(aipw_obj,estimand = c("ATE","ATT")) {
  call <- match.call()
  out <- list(treat = aipw_obj$.__enclos_env__$private$A,
              covs = aipw_obj$.__enclos_env__$private$g.set,
              distance = aipw_obj$obs_est$p_score, #change this to `aipw_obj$obs_est$raw_p_score` for untruncated ps
              weights = aipw_obj$obs_est$ip_weights,
              estimand = estimand,
              call = call)
  return(out)
}

out <- ate.weights(AIPW_SL,"ATE")

bal.tab(out)

Which estimator is use to compute the variance (and thus 95%CI) ?

We used the delta method for variance estimations. You can find more in our manuscript (Derivations are in the Appendix 2)