Weighting from Supplied Propensity Scores

This page explains the details of computing weights from propensity scores that have already been estimated, requested by supplying them to the ps argument of weightit() or weightitMSM() instead of setting method. This can be used with binary, multi-category, and continuous treatments, as well as with censoring.

No model is fit; the supplied scores are converted to weights exactly as get_w_from_ps() would, and the result is a full weightit object rather than a bare vector of weights. formula must still contain the treatment variable, but the covariates on the right hand side play no role in the computation. Any method supplied alongside ps is ignored unless it is a user-supplied function.

Because nothing is estimated, no M-estimation components are produced, and glm_weightit() will treat the weights as fixed.

Binary Treatments

ps may be a numeric vector of the probability of being in the treated group, a one-column matrix or data frame of the same, or a two-column matrix or data frame with one column per treatment level. When two columns are supplied and their names match the treatment levels, those names determine which column is which; otherwise the columns are assumed to be in the order of the treatment levels. All estimands allowed by get_w_from_ps() are available: "ATE", "ATT", "ATC", "ATO", "ATM", and "ATOS".

Multi-Category Treatments

ps may be a matrix or data frame with one column per treatment level, or a numeric vector (or one-column matrix) giving each unit's probability of being in the treatment group it is actually in. The estimands "ATE", "ATT", "ATC", "ATO", and "ATM" are available.

Continuous Treatments

ps is interpreted as the conditional mean of the treatment (i.e., the fitted values of a treatment model) rather than as a probability. The generalized propensity score is formed by feeding the standardized residuals through the requested density, exactly as in method_glm.

Longitudinal Treatments

For longitudinal treatments, ps is supplied as a list with one entry per time point, and the weights are the product of the time-specific weights.

Censoring Weights

Wrapping the censoring indicator in .cens() requests inverse probability of censoring weights. ps is then the probability of being censored; the weights are 1/P(C = 0 | X) for the units still under observation and exactly 0 for the censored units.

Sampling Weights

Sampling weights are supported and are applied to the resulting weights, but they play no part in computing them, since no model is fit.

Additional Arguments

For binary and multi-category treatments, the following additional argument can be specified:

subclass: integer; the number of subclasses to use for computing weights using marginal mean weighting through stratification (MMWS). 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. See get_w_from_ps() for details and references.

For continuous treatments, the following additional arguments may be supplied:

density

A function corresponding to the conditional density of the treatment. The standardized residuals of the treatment will be fed through this function to produce the denominator of the generalized propensity score weights. If blank, dnorm() is used as recommended by Robins et al. (2000). This can also be supplied as a string containing the name of the function to be called. If the string contains underscores, the call will be split by the underscores and the latter splits will be supplied as arguments to the second argument and beyond. For example, if density = "dt_2" is specified, the density used will be that of a t-distribution with 2 degrees of freedom. Using a t-distribution can be useful when extreme treatment values are observed (Naimi et al., 2014).

Can also be "kernel" to use kernel density estimation, which calls density() to estimate the denominator density for the weights. (This used to be requested by setting use.kernel = TRUE, which is now deprecated.)

bw, adjust, kernel, n

If density = "kernel", the arguments to density(). The defaults are the same as those in density().

Additional Outputs

obj: No fit object is produced, since no model is fit; include.obj has no effect.

References

See get_w_from_ps() for references on each estimand and on marginal mean weighting through stratification.

Naimi, A. I., Moodie, E. E. M., Auger, N., & Kaufman, J. S. (2014). Constructing Inverse Probability Weights for Continuous Exposures: A Comparison of Methods. Epidemiology, 25(2), 292–299. doi:10.1097/EDE.0000000000000053

Robins, J. M., Hernán, M. Á., & Brumback, B. (2000). Marginal Structural Models and Causal Inference in Epidemiology. Epidemiology, 11(5), 550–560.

Examples

data("lalonde", package = "cobalt")

# Estimate the propensity score separately, then supply it
fit <- glm(treat ~ age + educ + married + nodegree + re74,
           data = lalonde, family = binomial)

(W1 <- weightit(treat ~ age + educ + married +
                  nodegree + re74, data = lalonde,
                ps = fitted(fit), 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, re74

summary(W1)
#>                   Summary of weights
#> 
#> ─ Weight ranges:
#> 
#>           Min                                 Max
#> Treated 1.                    │             1.   
#> Control 0.022 ╞═══════════════════════════╡ 2.044
#> 
#> ─ Units with the 5 most extreme weights by group:
#>                                    
#>             5     4   3     2     1
#>  Treated    1     1   1     1     1
#>           411   595 269   409   296
#>  Control 1.33 1.437 1.5 1.637 2.044
#> 
#> ─ Weight statistics:
#> 
#>         Coef of Var   MAD Entropy # Zeros
#> Treated       0.    0.       0.         0
#> Control       0.823 0.701    0.33       0
#> 
#> ─ Effective Sample Sizes:
#> 
#>            Control Treated
#> Unweighted  429.       185
#> Weighted    255.99     185

# Marginal mean weighting through stratification
(W2 <- weightit(treat ~ age + educ + married +
                  nodegree + re74, data = lalonde,
                ps = fitted(fit), estimand = "ATT",
                subclass = 20))
#> 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, re74

summary(W2)
#>                   Summary of weights
#> 
#> ─ Weight ranges:
#> 
#>           Min                               Max
#> Treated 1.          │                         1
#> Control 0.083 ╞═══════════════════════════╡   8
#> 
#> ─ Units with the 5 most extreme weights by group:
#>                             
#>            5   4   3   2   1
#>  Treated   1   1   1   1   1
#>          296 269 612 589 264
#>  Control 2.4 2.4   4   4   8
#> 
#> ─ Weight statistics:
#> 
#>         Coef of Var   MAD Entropy # Zeros
#> Treated       0.    0.      0.          0
#> Control       1.367 0.747   0.499       0
#> 
#> ─ Effective Sample Sizes:
#> 
#>            Control Treated
#> Unweighted  429.       185
#> Weighted    149.75     185