rbw: Residual Balancing Weights for Marginal Structural Models

Residual balancing is a method of constructing weights for marginal structural models, which can be used to estimate marginal effects of time-varying treatments and controlled direct/mediator effects in causal mediation analysis. Compared with inverse probability-of-treatment weights (IPW), residual balancing weights tend to be more robust and more efficient, and are easier to use with continuous exposures. This package provides two main functions, rbwPanel() and rbwMed(), that produce residual balancing weights for analyzing time-varying treatments and causal mediation, respectively.

Reference

• Zhou, Xiang and Geoffrey T Wodtke. 2020. “Residual Balancing: A Method of Constructing Weights for Marginal Structural Models” Political Analysis.

Installation

You can install the released version of rbw from CRAN with:

install.packages("rbw")

And the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("xiangzhou09/rbw")

Estimating Marginal Effects of Time-varying Treatments

The rbwPanel() function constructs residual balancing weights for estimating marginal effects of time-varying treatments. The following example illustrates its use by estimating the effect of negative campaign advertising (d.gone.neg) on election outcomes (demprcnt) for 113 Democratic candidates in US Senate and Gubernatorial elections.

library(rbw)
# install.packages("survey")
library(survey)

# models for time-varying confounders
m1 <- lm(dem.polls ~ (d.gone.neg.l1 + dem.polls.l1 + undother.l1) * factor(week), data = campaign_long)
m2 <- lm(undother ~ (d.gone.neg.l1 + dem.polls.l1 + undother.l1) * factor(week), data = campaign_long)
xmodels <- list(m1, m2)

# residual balancing weights
rbwPanel_fit <- rbwPanel(exposure = d.gone.neg, xmodels = xmodels, id = id, time = week, data = campaign_long)
#> Entropy minimization converged within tolerance level

# merge weights into wide-format data
campaign_wide2 <- merge(campaign_wide, rbwPanel_fit$weights, by = "id")

# fit a marginal structural model (adjusting for baseline confounders)
rbw_design <- svydesign(ids = ~ 1, weights = ~ rbw, data = campaign_wide2)
msm_rbw <- svyglm(demprcnt ~ cum_neg * deminc + camp.length + factor(year) + office, design = rbw_design)
summary(msm_rbw)
#> 
#> Call:
#> svyglm(formula = demprcnt ~ cum_neg * deminc + camp.length + 
#>     factor(year) + office, design = rbw_design)
#> 
#> Survey design:
#> svydesign(ids = ~1, weights = ~rbw, data = campaign_wide2)
#> 
#> Coefficients:
#>                  Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)      49.18066    2.84225  17.303  < 2e-16 ***
#> cum_neg           0.98164    0.54222   1.810 0.073122 .  
#> deminc           16.23583    2.97437   5.459 3.28e-07 ***
#> camp.length      -0.05905    0.06775  -0.872 0.385451    
#> factor(year)2002 -5.48633    1.62291  -3.381 0.001020 ** 
#> factor(year)2004 -6.15855    1.72409  -3.572 0.000538 ***
#> factor(year)2006 -1.30567    2.11142  -0.618 0.537674    
#> office            0.60034    1.28520   0.467 0.641391    
#> cum_neg:deminc   -2.65044    0.77025  -3.441 0.000836 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> (Dispersion parameter for gaussian family taken to be 28.21637)
#> 
#> Number of Fisher Scoring iterations: 2

Estimating Controlled Direct Effects (CDE)

In causal mediation analysis, the rbwMed() function can be used to construct residual balancing weights for estimating the controlled direct effect or the controlled mediator effect with a marginal structural model. The following example illustrates its use by estimating the controlled direct effect of college education (college) on depression at age 40 (cesd40) at different levels of socioeconomic status (ses) for a subsample of respondents in the National Longitudinal Survey of Youth, 1979.

# models for post-treatment confounders
m1 <- lm(cesd92 ~ female + race + momedu + parinc + afqt3 +
  educexp + college, data = education)
m2 <- lm(prmarr98 ~ female + race + momedu + parinc + afqt3 +
  educexp + college, data = education)
m3 <- lm(transitions98 ~ female + race + momedu + parinc + afqt3 +
  educexp + college, data = education)

# residual balancing weights
rbwMed_fit <- rbwMed(treatment = college, mediator = ses,
  zmodels = list(m1, m2, m3), baseline_x = female:educexp,
  interact = TRUE, base_weights = weights, data = education)
#> Entropy minimization converged within tolerance level

# attach residual balancing weights to data
education$rbw <- rbwMed_fit$weights

# fit marginal structural model
rbw_design <- svydesign(ids = ~ 1, weights = ~ rbw, data = education)
msm_rbw <- svyglm(cesd40 ~ college * ses, design = rbw_design)
summary(msm_rbw)
#> 
#> Call:
#> svyglm(formula = cesd40 ~ college * ses, design = rbw_design)
#> 
#> Survey design:
#> svydesign(ids = ~1, weights = ~rbw, data = education)
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)   3.8267     0.2836  13.491  < 2e-16 ***
#> college      -1.0916     0.9801  -1.114 0.265462    
#> ses          -1.7313     0.4508  -3.841 0.000125 ***
#> college:ses   1.3929     1.5022   0.927 0.353881    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> (Dispersion parameter for gaussian family taken to be 13.02137)
#> 
#> Number of Fisher Scoring iterations: 2