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 \(R <= 8\) 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 1.000 || 1.0000
#> control 0.466 |---------------------------| 3.5903
#>
#> - Units with 5 greatest weights by group:
#>
#> 1 2 3 4 5
#> treated 1 1 1 1 1
#> 221 228 188 185 174
#> control 2.9494 2.9494 3.006 3.0637 3.5903
#>
#> Ratio Coef of Var
#> treated 1.0000 0.0000
#> control 7.7042 0.4250
#> overall 7.7042 0.4616
#>
#> - Effective Sample Sizes:
#> Control Treated
#> Unweighted 87.000 156
#> Weighted 73.818 156
#>
#> - - - - - - - Subgroup race = hispan - - - - - - -
#> - Weight ranges:
#> Min Max
#> treated 1.0000 || 1.0000
#> control 0.0209 |------------| 0.5046
#>
#> - Units with 5 greatest weights by group:
#>
#> 1 2 3 4 5
#> treated 1 1 1 1 1
#> 56 54 49 48 47
#> control 0.4117 0.4767 0.4835 0.4968 0.5046
#>
#> Ratio Coef of Var
#> treated 1.0000 0.0000
#> control 24.1741 0.7143
#> overall 47.9120 1.0352
#>
#> - Effective Sample Sizes:
#> Control Treated
#> Unweighted 61.000 11
#> Weighted 40.616 11
#>
#> - - - - - - - Subgroup race = white - - - - - - -
#> - Weight ranges:
#> Min Max
#> treated 1.0000 || 1.000
#> control 0.0002 |---------| 0.385
#>
#> - Units with 5 greatest weights by group:
#>
#> 1 2 3 4 5
#> treated 1 1 1 1 1
#> 289 287 285 280 267
#> control 0.2393 0.2699 0.2937 0.2956 0.385
#>
#> Ratio Coef of Var
#> treated 1.000 0.0000
#> control 1825.568 1.1538
#> overall 4742.156 1.9499
#>
#> - Effective Sample Sizes:
#> Control Treated
#> Unweighted 281.000 18
#> Weighted 120.777 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
# 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 1.0000 || 1.0000
#> control 0.4654 |---------------------------| 3.5703
#>
#> - Units with 5 greatest weights by group:
#>
#> 1 3 4 6 7
#> treated 1 1 1 1 1
#> 221 228 188 185 174
#> control 2.9787 2.9787 3.0338 3.0899 3.5703
#>
#> Ratio Coef of Var
#> treated 1.0000 0.0000
#> control 7.6708 0.4264
#> overall 7.6708 0.4625
#>
#> - Effective Sample Sizes:
#> Control Treated
#> Unweighted 87.000 156
#> Weighted 73.744 156
#>
#> - - - - - - - Subgroup race = hispan - - - - - - -
#> - Weight ranges:
#> Min Max
#> treated 1.0000 || 1.0000
#> control 0.0254 |-----------| 0.4743
#>
#> - Units with 5 greatest weights by group:
#>
#> 1 2 3 4 7
#> treated 1 1 1 1 1
#> 56 54 48 47 28
#> control 0.3908 0.4496 0.4557 0.4704 0.4743
#>
#> Ratio Coef of Var
#> treated 1.0000 0.0000
#> control 18.6516 0.6795
#> overall 39.3245 1.0314
#>
#> - Effective Sample Sizes:
#> Control Treated
#> Unweighted 61.00 11
#> Weighted 41.95 11
#>
#> - - - - - - - Subgroup race = white - - - - - - -
#> - Weight ranges:
#> Min Max
#> treated 1.0000 || 1.000
#> control 0.0002 |---------| 0.385
#>
#> - Units with 5 greatest weights by group:
#>
#> 1 2 3 4 5
#> treated 1 1 1 1 1
#> 289 287 285 280 267
#> control 0.2393 0.2699 0.2937 0.2956 0.385
#>
#> Ratio Coef of Var
#> treated 1.000 0.0000
#> control 1825.568 1.1538
#> overall 4742.156 1.9499
#>
#> - Effective Sample Sizes:
#> Control Treated
#> Unweighted 281.000 18
#> Weighted 120.777 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
#> - - - - - - - - - - - - - -
#>