Given a vector or matrix of propensity scores, outputs a vector of weights that target the provided estimand.

## Usage

```
get_w_from_ps(
ps,
treat,
estimand = "ATE",
focal = NULL,
treated = NULL,
subclass = NULL,
stabilize = FALSE
)
```

## Arguments

- ps
a vector, matrix, or data frame of propensity scores. See Details.

- treat
a vector of treatment status for each individual. See Details.

- estimand
the desired estimand that the weights should target. Current options include

`"ATE"`

(average treatment effect),`"ATT"`

(average treatment effect on the treated),`"ATC"`

(average treatment effect on the control),`"ATO"`

(average treatment effect in the overlap),`"ATM"`

(average treatment effect in the matched sample), and`"ATOS"`

(average treatment effect in the optimal subset). See Details.- focal
when

`estimand`

is`"ATT"`

or`"ATC"`

, which group should be consider the (focal) "treated" or "control" group, respectively. If not`NULL`

and`estimand`

is not`"ATT"`

or`"ATC"`

,`estimand`

will automatically be set to`"ATT"`

.- treated
when treatment is binary, the value of

`treat`

that is considered the "treated" group (i.e., the group for which the propensity scores are the probability of being in). If`NULL`

,`get_w_from_ps()`

will attempt to figure it out on its own using some heuristics. This really only matters when`treat`

has values other than 0 and 1 and when`ps`

is given as a vector or an unnamed single-column matrix or data frame.- subclass
`numeric`

; the number of subclasses to use when computing weights using marginal mean weighting through stratification (also known as fine stratification). If`NULL`

, standard inverse probability weights (and their extensions) will be computed; if a number greater than 1, subclasses will be formed and weights will be computed based on subclass membership.`estimand`

must be`"ATE"`

,`"ATT"`

, or`"ATC"`

if`subclass`

is non-`NULL`

. See Details.- stabilize
`logical`

; whether to compute stabilized weights or not. This simply involves multiplying each unit's weight by the proportion of units in their treatment group. For saturated outcome models and in balance checking, this won't make a difference; otherwise, this can improve performance.

## Value

A vector of weights. When `subclass`

is not `NULL`

, the
subclasses are returned as the `"subclass"`

attribute. When
`estimand = "ATOS"`

, the chosen value of `alpha`

(the smallest
propensity score allowed to remain in the sample) is returned in the
`"alpha"`

attribute.

## Details

`get_w_from_ps()`

applies the formula for computing weights from
propensity scores for the desired estimand. The formula for each estimand is below, with \(A_i\) the treatment value for unit \(i\) taking on values \(\mathcal{A} = (1, \ldots, g)\), \(p_{a, i}\) the probability of receiving treatment level \(a\) for unit \(i\), and \(f\) is the focal group (the treated group for the ATT and the control group for the ATC):

$$ \begin{aligned} w^{ATE}_i &= 1 / p_{A_i, i} \\ w^{ATT}_i &= w^{ATE}_i \times p_{f, i} \\ w^{ATO}_i &= w^{ATE}_i / \sum_{a \in \mathcal{A}}{1/p_{a, i}} \\ w^{ATM}_i &= w^{ATE}_i \times \min(p_{1, i}, \ldots, p_{g, i}) \\ w^{ATOS}_i &= w^{ATE}_i \times \mathbb{1}\left(\alpha < p_{2, i} < 1 - \alpha\right) \end{aligned} $$

`get_w_from_ps()`

can only be used with binary and multi-category treatments.

### Supplying the `ps`

argument

The `ps`

argument can be entered in two ways:

A numeric matrix with a row for each unit and a (named) column for each treatment level, with each cell corresponding to the probability of receiving the corresponding treatment level

A numeric vector with a value for each unit corresponding to the probability of being "treated" (only allowed for binary treatments)

When supplied as a vector, `get_w_from_ps()`

has to know which value of `treat`

corresponds to the "treated" group. For 0/1 variables, 1 will be considered
treated. For other types of variables, `get_w_from_ps()`

will try to
figure it out using heuristics, but it's safer to supply an argument to
`treated`

. When `estimand`

is `"ATT"`

or `"ATC"`

, supplying a value to
`focal`

is sufficient (for ATT, `focal`

is the treated group, and
for ATC, `focal`

is the control group).

When supplied as a matrix, the columns must be named with the levels of the treatment, and
it is assumed that each column corresponds to the probability of being in
that treatment group. This is the safest way to supply `ps`

unless
`treat`

is a 0/1 variable. When `estimand`

is `"ATT"`

or `"ATC"`

, a value for `focal`

must be specified.

### Marginal mean weighting through stratification (MMWS)

When `subclass`

is not `NULL`

, MMWS weights are computed. The implementation differs
slightly from that described in Hong (2010, 2012). First, subclasses are
formed by finding the quantiles of the propensity scores in the target group
(for the ATE, all units; for the ATT or ATC, just the units in the focal
group). Any subclasses lacking members of a treatment group will be filled
in with them from neighboring subclasses so each subclass will always have
at least one member of each treatment group. A new subclass-propensity score
matrix is formed, where each unit's subclass-propensity score for each
treatment value is computed as the proportion of units with that treatment
value in the unit's subclass. For example, if a subclass had 10 treated
units and 90 control units in it, the subclass-propensity score for being
treated would be .1 and the subclass-propensity score for being control
would be .9 for all units in the subclass.

For multi-category treatments, the propensity scores for each treatment are stratified separately as described in Hong (2012); for binary treatments, only one set of propensity scores are stratified and the subclass-propensity scores for the other treatment are computed as the complement of the propensity scores for the stratified treatment.

After the subclass-propensity scores have been
computed, the standard propensity score weighting formulas are used to
compute the unstabilized MMWS weights. To estimate MMWS weights equivalent
to those described in Hong (2010, 2012), `stabilize`

must be set to
`TRUE`

, but, as with standard propensity score weights, this is
optional. Note that MMWS weights are also known as fine stratification
weights and described by Desai et al. (2017).

## References

### Binary treatments

`estimand = "ATO"`

Li, F., Morgan, K. L., & Zaslavsky, A. M. (2018). Balancing covariates via propensity score weighting. Journal of the American Statistical Association, 113(521), 390–400. doi:10.1080/01621459.2016.1260466

`estimand = "ATM"`

Li, L., & Greene, T. (2013). A Weighting Analogue to Pair Matching in Propensity Score Analysis. The International Journal of Biostatistics, 9(2). doi:10.1515/ijb-2012-0030

`estimand = "ATOS"`

Crump, R. K., Hotz, V. J., Imbens, G. W., & Mitnik, O. A. (2009). Dealing with limited overlap in estimation of average treatment effects. Biometrika, 96(1), 187–199. doi:10.1093/biomet/asn055

Other estimands

Austin, P. C. (2011). An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies. Multivariate Behavioral Research, 46(3), 399–424. doi:10.1080/00273171.2011.568786

Marginal mean weighting through stratification (MMWS)

Hong, G. (2010). Marginal mean weighting through stratification: Adjustment for selection bias in multilevel data. Journal of Educational and Behavioral Statistics, 35(5), 499–531. doi:10.3102/1076998609359785

Desai, R. J., Rothman, K. J., Bateman, B. . T., Hernandez-Diaz, S., & Huybrechts, K. F. (2017). A Propensity-score-based Fine Stratification Approach for Confounding Adjustment When Exposure Is Infrequent: Epidemiology, 28(2), 249–257. doi:10.1097/EDE.0000000000000595

### Multi-Category Treatments

`estimand = "ATO"`

Li, F., & Li, F. (2019). Propensity score weighting for causal inference with multiple treatments. The Annals of Applied Statistics, 13(4), 2389–2415. doi:10.1214/19-AOAS1282

`estimand = "ATM"`

Yoshida, K., Hernández-Díaz, S., Solomon, D. H., Jackson, J. W., Gagne, J. J., Glynn, R. J., & Franklin, J. M. (2017). Matching weights to simultaneously compare three treatment groups: Comparison to three-way matching. Epidemiology (Cambridge, Mass.), 28(3), 387–395. doi:10.1097/EDE.0000000000000627

Other estimands

McCaffrey, D. F., Griffin, B. A., Almirall, D., Slaughter, M. E., Ramchand, R., & Burgette, L. F. (2013). A Tutorial on Propensity Score Estimation for Multiple Treatments Using Generalized Boosted Models. Statistics in Medicine, 32(19), 3388–3414. doi:10.1002/sim.5753

Marginal mean weighting through stratification

Hong, G. (2012). Marginal mean weighting through stratification: A
generalized method for evaluating multivalued and multiple treatments with
nonexperimental data. *Psychological Methods*, 17(1), 44–60. doi:10.1037/a0024918

## Examples

```
library("cobalt")
data("lalonde", package = "cobalt")
ps.fit <- glm(treat ~ age + educ + race + married +
nodegree + re74 + re75, data = lalonde,
family = binomial)
ps <- ps.fit$fitted.values
w1 <- get_w_from_ps(ps, treat = lalonde$treat,
estimand = "ATT")
treatAB <- factor(ifelse(lalonde$treat == 1, "A", "B"))
w2 <- get_w_from_ps(ps, treat = treatAB,
estimand = "ATT", focal = "A")
all.equal(w1, w2)
#> [1] TRUE
w3 <- get_w_from_ps(ps, treat = treatAB,
estimand = "ATT", treated = "A")
all.equal(w1, w3)
#> [1] TRUE
#Using MMWS
w4 <- get_w_from_ps(ps, treat = lalonde$treat,
estimand = "ATE", subclass = 20,
stabilize = TRUE)
#A multi-category example using GBM predicted probabilities
library(gbm)
#> Loaded gbm 2.2.2
#> This version of gbm is no longer under development. Consider transitioning to gbm3, https://github.com/gbm-developers/gbm3
T3 <- factor(sample(c("A", "B", "C"), nrow(lalonde), replace = TRUE))
gbm.fit <- gbm(T3 ~ age + educ + race + married +
nodegree + re74 + re75, data = lalonde,
distribution = "multinomial", n.trees = 200,
interaction.depth = 3)
#> Warning: Setting `distribution = "multinomial"` is ill-advised as it is currently broken. It exists only for backwards compatibility. Use at your own risk.
ps.multi <- drop(predict(gbm.fit, type = "response",
n.trees = 200))
w <- get_w_from_ps(ps.multi, T3, estimand = "ATE")
```