WeightIt: Weighting for Covariate Balance in Observational Studies

Overview

WeightIt is a one-stop package to generate balancing weights and censoring weights for point and longitudinal treatments in observational studies. Support is included for binary, multi-category, and continuous treatments; a variety of estimands including the ATE, ATT, ATC, ATO, and others; and for a wide variety of weighting methods, including those that rely on parametric modeling, machine learning, or optimization. WeightIt also provides functionality for fitting regression models in weighted samples that account for estimation of the weights in quantifying uncertainty. WeightIt uses a familiar formula interface and is meant to complement MatchIt as a package that provides a unified interface to basic and advanced weighting methods.

For a complete vignette, see the website for WeightIt or vignette("WeightIt"). Other vignettes describe the weighting methods and how to choose among them (vignette("weighting-methods")), how to estimate effects after weighting (vignette("estimating-effects")), how to weight for longitudinal treatments with censoring (vignette("longitudinal-treatments")), and how to install the packages some methods require (vignette("installing-packages")).

To install and load WeightIt, use the code below:

#CRAN version
install.packages("WeightIt")

#Development version
pak::pak("ngreifer/WeightIt")

library("WeightIt")

The workhorse function of WeightIt is weightit(), which generates weights from a given formula and data input according to methods and other parameters specified by the user. Below is an example of the use of weightit() to generate propensity score weights for estimating the ATT:

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

W <- weightit(treat ~ age + educ + nodegree + 
                married + race + re74 + re75, 
              data = lalonde, method = "glm", 
              estimand = "ATT")
W

## 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, nodegree, married, race, re74, re75

Evaluating weights has two components: evaluating the covariate balance produced by the weights, and evaluating whether the weights will allow for sufficient precision in the eventual effect estimate. For the first goal, functions in the cobalt package, which are fully compatible with WeightIt, can be used, as demonstrated below:

library("cobalt")

bal.tab(W, un = TRUE)

## Balance Measures
##                 Type Diff.Un Diff.Adj
## prop.score  Distance  1.7941  -0.0205
## age          Contin. -0.3094   0.1188
## educ         Contin.  0.0550  -0.0284
## nodegree      Binary  0.1114   0.0184
## married       Binary -0.3236   0.0186
## race_black    Binary  0.6404  -0.0022
## race_hispan   Binary -0.0827   0.0002
## race_white    Binary -0.5577   0.0021
## re74         Contin. -0.7211  -0.0021
## re75         Contin. -0.2903   0.0110
## 
## Effective sample sizes
##            Control Treated
## Unadjusted  429.       185
## Adjusted     99.82     185

For the second goal, qualities of the distributions of weights can be assessed using summary(), as demonstrated below.

summary(W)

##                   Summary of weights
## 
## ─ Weight ranges:
## 
##           Min                                 Max
## Treated 1.              │                   1.   
## Control 0.009 ╞═══════════════════════════╡ 3.743
## 
## ─ Units with the 5 most extreme weights by group:
##                                     
##             5     4    3     2     1
##  Treated    1     1    1     1     1
##           597   573  381   411   303
##  Control 3.03 3.059 3.24 3.523 3.743
## 
## ─ Weight statistics:
## 
##         Coef of Var   MAD Entropy # Zeros
## Treated       0.    0.      0.          0
## Control       1.818 1.289   1.098       0
## 
## ─ Effective Sample Sizes:
## 
##            Control Treated
## Unweighted  429.       185
## Weighted     99.82     185

Large effective sample sizes imply low variability in the weights, and therefore increased precision in estimating the treatment effect.

Finally, we can estimate the effect of the treatment using a weighted outcome model, accounting for estimation of the weights in the standard error of the effect estimate:

fit <- lm_weightit(re78 ~ treat, data = lalonde,
                   weightit = W)

summary(fit, ci = TRUE)

## 
## Call:
## lm_weightit(formula = re78 ~ treat, data = lalonde, weightit = W)
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)  2.5 % 97.5 %    
## (Intercept)   5135.1      583.8   8.797   <1e-06 3990.9 6279.2 ***
## treat         1214.1      798.2   1.521    0.128 -350.3 2778.4    
## Standard error: HC0 robust (adjusted for estimation of weights)

The table below contains the available methods in WeightIt for estimating weights, and which treatment types each supports. Some of these methods require installing other packages to use; see vignette("installing-packages") for information on how to install them, and vignette("weighting-methods") for descriptions of the methods and guidance on choosing among them.

Method	method	Binary	Multi-category	Continuous	Censoring
Generalized linear model PS	"glm"	✓	✓	✓	✓
Generalized boosted modeling PS	"gbm"	✓	✓	✓	✓
Covariate balancing PS	"cbps"	✓	✓	✓	✓
Non-parametric covariate balancing PS	"npcbps"	✓	✓	✓
Entropy balancing	"ebal"	✓	✓	✓	✓
Inverse probability tilting	"ipt"	✓	✓

PS = propensity score; for continuous treatments, the generalized propensity score (GPS). †With a continuous treatment, "energy" performs distance covariance optimal weighting.

In addition, WeightIt implements the subgroup balancing propensity score using the function sbps(). Inverse probability of censoring weights, which account for units dropping out before the outcome is measured, are requested by wrapping a censoring indicator in .cens() on the left side of a model formula. Weights for longitudinal treatments are estimated with weightitMSM(); see vignette("longitudinal-treatments") for a guide. Several other tools and utilities are available, including trim() to trim or truncate weights, calibrate() to calibrate propensity scores, and get_w_from_ps() to compute weights from propensity scores.

WeightIt provides functions to fit weighted models that account for the uncertainty in estimating the weights. These include glm_weightit() for fitting generalized linear models, ordinal_weightit() for ordinal regression models, multinom_weightit() for multinomial regression models, and coxph_weightit() for Cox proportional hazards models. Several methods are available for computing the parameter variances, including asymptotically correct M-estimation-based variances, robust variances that treat the weights as fixed, and traditional and fractional weighted bootstrap variances. Clustered variances are supported. See vignette("estimating-effects") for information on how to use these after weighting to estimate treatment effects.

Please submit bug reports, questions, comments, or other issues to https://github.com/ngreifer/WeightIt/issues. If you would like to see your package or method integrated into WeightIt, please contact the author. Fan mail is greatly appreciated.

Citing WeightIt

To generate a citation for WeightIt, please use the following:

citation("WeightIt")