sbps: Subgroup Balancing Propensity Score

In WeightIt: Weighting for Covariate Balance in Observational Studies

Subgroup Balancing Propensity Score

Description

Implements the subgroup balancing propensity score (SBPS), which is an algorithm that attempts to achieve balance in subgroups by sharing information from the overall sample and subgroups (Dong, Zhang, Zeng, & Li, 2020; DZZL). Each subgroup can use either weights estimated using the whole sample, weights estimated using just that subgroup, or a combination of the two. The optimal combination is chosen as that which minimizes an imbalance criterion that includes subgroup as well as overall balance.

Usage

sbps(
  obj,
  obj2 = NULL,
  moderator = NULL,
  formula = NULL,
  data = NULL,
  smooth = FALSE,
  full.search
)

Arguments

obj	a weightit object containing weights estimated in the overall sample.
obj2	a weightit object containing weights estimated in the subgroups. Typically this has been estimated by including by in the call to weightit(). Either obj2 or moderator must be specified.
moderator	optional; a string containing the name of the variable in data for which weighting is to be done within subgroups or a one-sided formula with the subgrouping variable on the right-hand side. This argument is analogous to the by argument in weightit(), and in fact it is passed on to by. Either obj2 or moderator must be specified.
formula	an optional formula with the covariates for which balance is to be optimized. If not specified, the formula in obj$call will be used.
data	an optional data set in the form of a data frame that contains the variables in formula or moderator.
smooth	logical; whether the smooth version of the SBPS should be used. This is only compatible with weightit methods that return a propensity score.
full.search	logical; when smooth = FALSE, whether every combination of subgroup and overall weights should be evaluated. If FALSE, a stochastic search as described in DZZL will be used instead. If TRUE, all 2^R combinations will be checked, where R is the number of subgroups, which can take a long time with many subgroups. If unspecified, will default to TRUE if R <= 8 and FALSE otherwise.

Details

The SBPS relies on two sets of weights: one estimated in the overall sample and one estimated within each subgroup. The algorithm decides whether each subgroup should use the weights estimated in the overall sample or those estimated in the subgroup. There are 2^R permutations of overall and subgroup weights, where R is the number of subgroups. The optimal permutation is chosen as that which minimizes a balance criterion as described in DZZL. The balance criterion used here is, for binary and multi-category treatments, the sum of the squared standardized mean differences within subgroups and overall, which are computed using cobalt::col_w_smd(), and for continuous treatments, the sum of the squared correlations between each covariate and treatment within subgroups and overall, which are computed using cobalt::col_w_corr().

The smooth version estimates weights that determine the relative contribution of the overall and subgroup propensity scores to a weighted average propensity score for each subgroup. If P_O are the propensity scores estimated in the overall sample and P_S are the propensity scores estimated in each subgroup, the smooth SBPS finds R coefficients C so that for each subgroup, the ultimate propensity score is C*P_S + (1-C)*P_O, and weights are computed from this propensity score. The coefficients are estimated using optim() with method = "L-BFGS-B". When C is estimated to be 1 or 0 for each subgroup, the smooth SBPS coincides with the standard SBPS.

If obj2 is not specified and moderator is, sbps() will attempt to refit the model specified in obj with the moderator in the by argument. This relies on the environment in which obj was created to be intact and can take some time if obj was hard to fit. It's safer to estimate obj and obj2 (the latter simply by including the moderator in the by argument) and supply these to sbps().

Value

A weightit.sbps object, which inherits from weightit. This contains all the information in obj with the weights, propensity scores, call, and possibly covariates updated from sbps(). In addition, the prop.subgroup component contains the values of the coefficients C for the subgroups (which are either 0 or 1 for the standard SBPS), and the moderator component contains a data.frame with the moderator.

This object has its own summary method and is compatible with cobalt functions. The cluster argument should be used with cobalt functions to accurately reflect the performance of the weights in balancing the subgroups.

References

Dong, J., Zhang, J. L., Zeng, S., & Li, F. (2020). Subgroup balancing propensity score. Statistical Methods in Medical Research, 29(3), 659–676. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/0962280219870836")}

See Also

weightit(), summary.weightit()

Examples

library("cobalt")
data("lalonde", package = "cobalt")

#Balancing covariates between treatment groups within races
(W1 <- weightit(treat ~ age + educ + married +
                nodegree + race + re74, data = lalonde,
                method = "glm", estimand = "ATT"))

(W2 <- weightit(treat ~ age + educ + married +
                nodegree + race + re74, data = lalonde,
                method = "glm", estimand = "ATT",
                by = "race"))
S <- sbps(W1, W2)
print(S)
summary(S)
bal.tab(S, cluster = "race")

#Could also have run
#  sbps(W1, moderator = "race")

S_ <- sbps(W1, W2, smooth = TRUE)
print(S_)
summary(S_)
bal.tab(S_, cluster = "race")

WeightIt documentation built on Oct. 4, 2024, 9:07 a.m.