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
weightitobject containing weights estimated in the overall sample.- obj2
a
weightitobject containing weights estimated in the subgroups. Typically this has been estimated by includingbyin the call toweightit(). Eitherobj2ormoderatormust be specified.- moderator
optional; a string containing the name of the variable in
datafor 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 thebyargument inweightit(), and in fact it is passed on toby. Eitherobj2ormoderatormust be specified.- formula
an optional formula with the covariates for which balance is to be optimized. If not specified, the formula in
obj$callwill be used.- data
an optional data set in the form of a data frame that contains the variables in
formulaormoderator.- smooth
logical; whether the smooth version of the SBPS should be used. This is only compatible withweightitmethods that return a propensity score.- full.search
logical; whensmooth = FALSE, whether every combination of subgroup and overall weights should be evaluated. IfFALSE, a stochastic search as described in DZZL will be used instead. IfTRUE, 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 toTRUEif \(R \le 8\) andFALSEotherwise.
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.
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().
References
Dong, J., Zhang, J. L., Zeng, S., & Li, F. (2020). Subgroup balancing propensity score. Statistical Methods in Medical Research, 29(3), 659–676. doi:10.1177/0962280219870836
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"))
#> A weightit object
#> - method: "glm" (propensity score weighting with GLM)
#> - number of obs.: 614
#> - sampling weights: none
#> - treatment: 2-category
#> - estimand: ATT (focal: 1)
#> - covariates: age, educ, married, nodegree, race, re74
(W2 <- weightit(treat ~ age + educ + married +
nodegree + race + re74, data = lalonde,
method = "glm", estimand = "ATT",
by = "race"))
#> A weightit object
#> - method: "glm" (propensity score weighting with GLM)
#> - number of obs.: 614
#> - sampling weights: none
#> - treatment: 2-category
#> - estimand: ATT (focal: 1)
#> - covariates: age, educ, married, nodegree, race, re74
#> - by: race
S <- sbps(W1, W2)
print(S)
#> A weightit.sbps object
#> - method: "glm" (propensity score weighting with GLM)
#> - number of obs.: 614
#> - sampling weights: none
#> - treatment: 2-category
#> - estimand: ATT (focal: 1)
#> - covariates: age, educ, married, nodegree, race, re74
#> - moderator: race (3 subgroups)
summary(S)
#> Summary of weights
#>
#> - Overall vs. subgroup proportion contribution:
#>
#> race = "black" race = "hispan" race = "white"
#> Overall 0 0 0
#> Subgroup 1 1 1
#>
#> Subgroup: race = "black"
#>
#> - Weight ranges:
#>
#> Min Max
#> treated 1. || 1.
#> control 0.466 |---------------------------| 3.59
#>
#> - Units with the 5 most extreme weights by group:
#>
#> 6 5 4 3 1
#> treated 1 1 1 1 1
#> 559 381 573 303 411
#> control 2.949 2.949 3.006 3.064 3.59
#>
#> - Weight statistics:
#>
#> Coef of Var MAD Entropy # Zeros
#> treated 0. 0. 0. 0
#> control 0.425 0.366 0.093 0
#>
#> - Effective Sample Sizes:
#>
#> Control Treated
#> Unweighted 87. 156
#> Weighted 73.82 156
#>
#> Subgroup: race = "hispan"
#>
#> - Weight ranges:
#>
#> Min Max
#> treated 1. || 1.
#> control 0.021 |------------| 0.505
#>
#> - Units with the 5 most extreme weights by group:
#>
#> 100 87 44 28 2
#> treated 1 1 1 1 1
#> 425 456 480 424 412
#> control 0.412 0.477 0.484 0.497 0.505
#>
#> - Weight statistics:
#>
#> Coef of Var MAD Entropy # Zeros
#> treated 0. 0. 0. 0
#> control 0.714 0.579 0.246 0
#>
#> - Effective Sample Sizes:
#>
#> Control Treated
#> Unweighted 61. 11
#> Weighted 40.62 11
#>
#> Subgroup: race = "white"
#>
#> - Weight ranges:
#>
#> Min Max
#> treated 1 || 1.
#> control 0 |---------| 0.385
#>
#> - Units with the 5 most extreme weights by group:
#>
#> 60 42 23 22 10
#> treated 1 1 1 1 1
#> 592 589 595 546 580
#> control 0.239 0.27 0.294 0.296 0.385
#>
#> - Weight statistics:
#>
#> Coef of Var MAD Entropy # Zeros
#> treated 0. 0. 0. 0
#> control 1.154 0.952 0.619 0
#>
#> - Effective Sample Sizes:
#>
#> Control Treated
#> Unweighted 281. 18
#> Weighted 120.78 18
bal.tab(S, cluster = "race")
#> Balance by cluster
#>
#> - - - Cluster: black - - -
#> Balance Measures
#> Type Diff.Adj
#> prop.score Distance 0.0016
#> age Contin. 0.0126
#> educ Contin. -0.0332
#> married Binary 0.0030
#> nodegree Binary 0.0062
#> re74 Contin. -0.0826
#>
#> Effective sample sizes
#> 0 1
#> Unadjusted 87. 156
#> Adjusted 73.82 156
#>
#> - - - Cluster: hispan - - -
#> Balance Measures
#> Type Diff.Adj
#> prop.score Distance -0.2678
#> age Contin. 0.1196
#> educ Contin. -0.0756
#> married Binary 0.0217
#> nodegree Binary 0.0018
#> re74 Contin. 0.0114
#>
#> Effective sample sizes
#> 0 1
#> Unadjusted 61. 11
#> Adjusted 40.62 11
#>
#> - - - Cluster: white - - -
#> Balance Measures
#> Type Diff.Adj
#> prop.score Distance 0.0652
#> age Contin. 0.0191
#> educ Contin. -0.0185
#> married Binary -0.0015
#> nodegree Binary 0.0039
#> re74 Contin. -0.0117
#>
#> Effective sample sizes
#> 0 1
#> Unadjusted 281. 18
#> Adjusted 120.78 18
#> - - - - - - - - - - - - - -
#>
#Could also have run
#S <- sbps(W1, moderator = "race")
S_ <- sbps(W1, W2, smooth = TRUE)
print(S_)
#> A weightit.sbps object
#> - method: "glm" (propensity score weighting with GLM)
#> - number of obs.: 614
#> - sampling weights: none
#> - treatment: 2-category
#> - estimand: ATT (focal: 1)
#> - covariates: age, educ, married, nodegree, race, re74
#> - moderator: race (3 subgroups)
summary(S_)
#> Summary of weights
#>
#> - Overall vs. subgroup proportion contribution:
#>
#> race = "black" race = "hispan" race = "white"
#> Overall 0.17 0.25 0
#> Subgroup 0.83 0.75 1
#>
#> Subgroup: race = "black"
#>
#> - Weight ranges:
#>
#> Min Max
#> treated 1. || 1.
#> control 0.465 |---------------------------| 3.57
#>
#> - Units with the 5 most extreme weights by group:
#>
#> 6 5 4 3 1
#> treated 1 1 1 1 1
#> 559 381 573 303 411
#> control 2.979 2.979 3.034 3.09 3.57
#>
#> - Weight statistics:
#>
#> Coef of Var MAD Entropy # Zeros
#> treated 0. 0. 0. 0
#> control 0.426 0.366 0.094 0
#>
#> - Effective Sample Sizes:
#>
#> Control Treated
#> Unweighted 87. 156
#> Weighted 73.74 156
#>
#> Subgroup: race = "hispan"
#>
#> - Weight ranges:
#>
#> Min Max
#> treated 1. || 1.
#> control 0.025 |-----------| 0.474
#>
#> - Units with the 5 most extreme weights by group:
#>
#> 100 87 44 28 2
#> treated 1 1 1 1 1
#> 269 456 480 424 412
#> control 0.391 0.45 0.456 0.47 0.474
#>
#> - Weight statistics:
#>
#> Coef of Var MAD Entropy # Zeros
#> treated 0. 0. 0. 0
#> control 0.679 0.553 0.225 0
#>
#> - Effective Sample Sizes:
#>
#> Control Treated
#> Unweighted 61. 11
#> Weighted 41.95 11
#>
#> Subgroup: race = "white"
#>
#> - Weight ranges:
#>
#> Min Max
#> treated 1 || 1.
#> control 0 |---------| 0.385
#>
#> - Units with the 5 most extreme weights by group:
#>
#> 60 42 23 22 10
#> treated 1 1 1 1 1
#> 592 589 595 546 580
#> control 0.239 0.27 0.294 0.296 0.385
#>
#> - Weight statistics:
#>
#> Coef of Var MAD Entropy # Zeros
#> treated 0. 0. 0. 0
#> control 1.154 0.952 0.619 0
#>
#> - Effective Sample Sizes:
#>
#> Control Treated
#> Unweighted 281. 18
#> Weighted 120.78 18
bal.tab(S_, cluster = "race")
#> Balance by cluster
#>
#> - - - Cluster: black - - -
#> Balance Measures
#> Type Diff.Adj
#> prop.score Distance 0.0019
#> age Contin. 0.0388
#> educ Contin. -0.0305
#> married Binary 0.0096
#> nodegree Binary 0.0086
#> re74 Contin. -0.0561
#>
#> Effective sample sizes
#> 0 1
#> Unadjusted 87. 156
#> Adjusted 73.74 156
#>
#> - - - Cluster: hispan - - -
#> Balance Measures
#> Type Diff.Adj
#> prop.score Distance -0.1909
#> age Contin. 0.0167
#> educ Contin. -0.0654
#> married Binary 0.0314
#> nodegree Binary 0.0084
#> re74 Contin. -0.0175
#>
#> Effective sample sizes
#> 0 1
#> Unadjusted 61. 11
#> Adjusted 41.95 11
#>
#> - - - Cluster: white - - -
#> Balance Measures
#> Type Diff.Adj
#> prop.score Distance 0.0652
#> age Contin. 0.0191
#> educ Contin. -0.0185
#> married Binary -0.0015
#> nodegree Binary 0.0039
#> re74 Contin. -0.0117
#>
#> Effective sample sizes
#> 0 1
#> Unadjusted 281. 18
#> Adjusted 120.78 18
#> - - - - - - - - - - - - - -
#>