Weighted absolute mean difference (wAMD) of Shortreed and Ertefaie (2017)

Scores an arbitrary candidate propensity score on the exact wAMD balance criterion used by oal() to select its tuning parameters. This function is the package's single source of truth for the criterion: the internal grid search calls it verbatim, and exporting it lets any candidate score – from any package – be scored on the same yardstick (the mirror of psAve::psave_criteria()).

Usage

oal_wamd(
  ps,
  treat,
  covs,
  coef,
  estimand = c("ATE", "ATT"),
  clip = c(0.01, 0.99)
)

Arguments

ps: Numeric vector of propensity scores, strictly inside (0, 1) before clipping.
treat: Treatment vector: numeric 0/1, logical, or a two-level factor/character (second level = treated), as in oal().
covs: Numeric matrix of covariates, one row per unit; no missing values.
coef: Numeric vector of outcome-model coefficients, one per column of covs (matched by name when both are named, else by position). Absolute values are used as the balance weights.
estimand: "ATE" (default) or "ATT"; selects the IPW weight formula above.
clip: Length-2 numeric; the scores are clipped to [clip[1], clip[2]] before the weights are formed (default c(0.01, 0.99)).

Value

A list with elements

total: the wAMD, $\sum_j |\beta_j| d_j$;
by.covariate: named numeric vector of the per-covariate contributions $|\beta_j| d_j$ (they sum to total).

Details

The propensity scores are first clipped to clip; the inverse-probability weights at estimand are then (with $e_i$ the clipped score) $$ATE:\; w_i = A_i/e_i + (1 - A_i)/(1 - e_i), \qquad ATT:\; w_i = A_i + (1 - A_i)\, e_i/(1 - e_i).$$ For each covariate column $j$ the weighted absolute mean difference is $$d_j = \left| \frac{\sum_i w_i X_{ij} A_i}{\sum_i w_i A_i} - \frac{\sum_i w_i X_{ij} (1 - A_i)}{\sum_i w_i (1 - A_i)} \right|,$$ and the criterion is $\mathrm{wAMD} = \sum_j |\beta_j|\, d_j$, summed over all columns of covs (including any the propensity score model excluded), with $\beta_j$ the outcome-model coefficients supplied in coef (their absolute values are taken internally).

Inside oal(), covs is the standardized model matrix and coef the outcome coefficients on that same standardized scale (the wAMD, like the adaptive weights, is scale-dependent). The formula is implemented natively – never delegated to cobalt – so that it reproduces the published criterion exactly.

References

Shortreed SM, Ertefaie A (2017). Outcome-adaptive lasso: variable selection for causal inference. Biometrics, 73(4), 1111-1122. doi:10.1111/biom.12679

Examples

set.seed(7)
X <- matrix(rnorm(200), 100, 2, dimnames = list(NULL, c("x1", "x2")))
A <- rbinom(100, 1, plogis(X[, 1]))
ps <- plogis(0.8 * X[, 1])
oal_wamd(ps, A, X, coef = c(x1 = 0.5, x2 = 0.1), estimand = "ATE")
#> $total
#> [1] 0.2089005
#> 
#> $by.covariate
#>          x1          x2 
#> 0.207586166 0.001314295 
#>