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Compute weights from propensity scores

Source: R/get_w_from_ps.R
get_w_from_ps.Rd

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

See also

method_glm

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 predicted probabilities
# from multinomial logistic regression
T3 <- factor(sample(c("A", "B", "C"), nrow(lalonde),
                    replace = TRUE))

multi.fit <- multinom_weightit(
  T3 ~ age + educ + race + married +
    nodegree + re74 + re75, data = lalonde,
  vcov = "none"
)

ps.multi <- fitted(multi.fit)
head(ps.multi)
#>           A         B         C
#> 1 0.3275345 0.2714686 0.4009970
#> 2 0.3110696 0.3349112 0.3540192
#> 3 0.3261981 0.3602605 0.3135413
#> 4 0.3176130 0.3061721 0.3762149
#> 5 0.3214072 0.3244588 0.3541339
#> 6 0.3294088 0.3469696 0.3236216

w5 <- get_w_from_ps(ps.multi, treat = T3,
                    estimand = "ATE")