`sbps.Rd`

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.

- 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.- x
a

`weightit.sbps`

or`summary.weightit.sbps`

object; the output of a call to`sbps()`

or`summary.weightit.sbps()`

.- object
a

`weightit.sbps`

object; the output of a call to`sbps()`

.- top
how many of the largest and smallest weights to display. Default is 5.

- ignore.s.weights
whether or not to ignore sampling weights when computing the weight summary. If

`FALSE`

, the default, the estimated weights will be multiplied by the sampling weights (if any) before values are computed.- ...
for

`print`

, arguments passed to`print()`

. Ignored otherwise.

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 multinomial treatments, the sum of the squared standardized mean differences within subgroups and overall, which are computed using `col_w_smd()`

in cobalt, and for continuous treatments, the sum of the squared correlations between each covariate and treatment within subgroups and overall, which are computed using `col_w_corr()`

in cobalt.

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()`

.

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 methods 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.

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

```
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 = "ps", estimand = "ATT"))
#> A weightit object
#> - method: "ps" (propensity score weighting)
#> - 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 = "ps", estimand = "ATT",
by = "race"))
#> A weightit object
#> - method: "ps" (propensity score weighting)
#> - 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: "ps" (propensity score weighting)
#> - 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:
#>
#> 2 3 4 5 7
#> 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")
#> Call
#> sbps(obj = W1, obj2 = W2)
#>
#> 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
#> Control Treated
#> 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
#> Control Treated
#> 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
#> Control Treated
#> 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: "ps" (propensity score weighting)
#> - 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:
#>
#> 2 3 4 5 6
#> 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:
#>
#> 2 3 4 6 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")
#> Call
#> sbps(obj = W1, obj2 = W2, smooth = TRUE)
#>
#> 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
#> Control Treated
#> 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
#> Control Treated
#> 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
#> Control Treated
#> Unadjusted 281. 18
#> Adjusted 120.78 18
#> - - - - - - - - - - - - - -
#>
```