This package implements the estimators proposed in Barkley et al. (2017), Causal Inference from Observational Studies with Clustered Interference for estimating the causal effects of different treatment policies in the presence of partial or clustered interference. The package is available on CRAN with a companion website

In causal inference, when one individual’s treatment may affect another individual’s outcome, it’s often called interference. In most applications, it is assumed that there is no interference whatsoever. In some applications this must be relaxed - e.g., as in infectious disease research.

A relaxation of the assumption of “no interference” is to assume that individuals may be partitioned into distinct clusters of individuals (e.g., households, or classrooms, etc.) such that there may be interference within the clusters, but not between the clusters. Historically, this assumption has been referred to as partial interference after Sobel (2006).

Barkley et al. (2017) introduces the terminology clustered interference to refer to this same assumption. This phrase may be sufficiently descriptive of the underlying assumption, and perhaps clarifies the presumed restriction of interference to clusters.

Barkley et al. (2017) proposes new causal estimands for defining treatment effects in the context of observational studies when there may be interference or spillover effects between units in the same cluster. The manuscript also introduces IPTW estimators for thos estimands, which are implemented in ‘clusteredinterference’.

A version of this manuscript is available on arXiv at 1711.04834:

Barkley, B. G., Hudgens, M. G., Clemens, J. D., Ali, M., and Emch, M. E. (2017). Causal inference from observational studies with clustered interference. arXiv preprint arXiv:1711.04834. URL https://arxiv.org/abs/1711.04834.

This package is now on CRAN!

install.packages("clusteredinterference")

Or, visit the GitHub repo:

# devtools::install_github("BarkleyBG/clusteredinterference")

library(clusteredinterference)

data("toy_data")
head(toy_data)
#>   Outcome Treatment Cluster_ID      Age Distance
#> 1       1         0          1 37.62826 6.485258
#> 2       0         1          1 36.61508 6.928957
#> 3       1         1          1 31.74776 6.659470
#> 4       1         0          2 34.79259 8.138802
#> 5       0         0          2 48.05607 7.736209
#> 6       0         0          2 42.21215 8.023865

Estimation is carried out with one function:

set.seed(1113)
causal_fx <- policyFX(
  data = toy_data,
  formula = Outcome | Treatment ~ Age + Distance + (1 | Cluster_ID) | Cluster_ID,
  alphas = c(.15, .25), 
  k_samps = 1
)

The estimates of causal estimands are printed in a tidy dataframe:

causal_fx
#> ------------- causal estimates --------------
#>       estimand estimate     se     LCI    UCI
#>       mu(0.15)   0.6985 0.0893  0.5234 0.8736
#>       mu(0.25)   0.6664 0.0702  0.5287 0.8041
#>      mu0(0.15)   0.7157 0.0917  0.5360 0.8954
#>      mu0(0.25)   0.6869 0.0775  0.5350 0.8388
#>      mu1(0.15)   0.1619 0.0429  0.0779 0.2460
#>      mu1(0.25)   0.2440 0.0536  0.1389 0.3491
#>  OE(0.25,0.15)  -0.0321 0.0275 -0.0861 0.0219
#>  OE(0.15,0.25)   0.0321 0.0275 -0.0219 0.0861
#>           ... and 4 more rows ... 
#> ---------------------------------------------

Use summary() for a little more information:

summary(causal_fx)
#> ------------- causal estimates --------------
#>       estimand estimate     se     LCI    UCI
#>       mu(0.15)   0.6985 0.0893  0.5234 0.8736
#>       mu(0.25)   0.6664 0.0702  0.5287 0.8041
#>      mu0(0.15)   0.7157 0.0917  0.5360 0.8954
#>      mu0(0.25)   0.6869 0.0775  0.5350 0.8388
#>      mu1(0.15)   0.1619 0.0429  0.0779 0.2460
#>      mu1(0.25)   0.2440 0.0536  0.1389 0.3491
#>  OE(0.25,0.15)  -0.0321 0.0275 -0.0861 0.0219
#>  OE(0.15,0.25)   0.0321 0.0275 -0.0219 0.0861
#> 
#>           ... and 4 more rows ... 
#> 
#> -------------- treatment model -------------
#> Generalized linear mixed model fit by maximum likelihood (Adaptive
#>   Gauss-Hermite Quadrature, nAGQ = 2) [glmerMod]
#>  Family: binomial  ( logit )
#> Formula: Treatment ~ Age + Distance + (1 | Cluster_ID)
#>    Data: data
#>      AIC      BIC   logLik deviance df.resid 
#> 137.0345 147.3743 -64.5172 129.0345       94 
#> Random effects:
#>  Groups     Name        Std.Dev.
#>  Cluster_ID (Intercept) 1.18    
#> Number of obs: 98, groups:  Cluster_ID, 30
#> Fixed Effects:
#> (Intercept)          Age     Distance  
#>    -1.44609     -0.00851      0.26097  
#> 
#> ------------- propensity scores -------------
#>      1      2      3      4      5      6      7      8      9     10 
#>  0.105  0.162  0.086  0.102  0.167  0.045  0.244 0.0934 0.0765  0.197 
#>     11     12     13     14     15     16     17     18     19     20 
#> 0.0653  0.281  0.104  0.365 0.0867  0.198  0.207  0.106 0.0847  0.134 
#>     21     22     23     24     25     26     27     28     29     30 
#>  0.103  0.111  0.105  0.302 0.0434 0.0943 0.0443 0.0512   0.13  0.263 
#> ---------------------------------------------

Note that Treatment ~ Age + Distance + (1 | Cluster_ID) in the the middle of the formula argument is sent to lme4::glmer() to specify the form of the (logit-link binomial) treatment model.

The policyFX() output list includes an element, formula, for the Formula object:

causal_fx$formula
#> Outcome | Treatment ~ Age + Distance + (1 | Cluster_ID) | Cluster_ID

The output list also includes an element, model, which is the fitted glmerMod S4 model object. Here we can see that the middle of formula was passed into the glmer() logit-link binomial mixed model:

causal_fx$model@call
#> lme4::glmer(formula = Treatment ~ Age + Distance + (1 | Cluster_ID), 
#>     data = data, family = stats::binomial, nAGQ = nAGQ)

The fitted model estimates three fixed effects (intercept, a term for Age and a term for Distance) and one random effect (for Cluster_ID):

lme4::getME(causal_fx$model, c("beta", "theta"))
#> $beta
#> [1] -1.446087049 -0.008509771  0.260968952
#> 
#> $theta
#> Cluster_ID.(Intercept) 
#>               1.180325

The vignette provides more information on the formal arguments:

vignette("estimate-policyFX")

A changelog is found in the NEWS.md file. Version history is also tracked by the release tags for this GitHub repo.

• The manuscript introducing the methods in ‘clusteredinterference’ is:
  • Barkley, B. G., Hudgens, M. G., Clemens, J. D., Ali, M., and Emch, M. E. (2017). Causal inference from observational studies with clustered interference. arXiv preprint arXiv:1711.04834. URL https://arxiv.org/abs/1711.04834.
• The terminology of partial interference is attributed to Sobel (2006):
  • Sobel, M. E. (2006). What do randomized studies of housing mobility demonstrate? Causal inference in the face of interference. Journal of the American Statistical Association, 101(476), 1398-1407. doi: 10.1198/016214506000000636
• Please see the inferference package for related estimators from the following articles:
  • Perez‐Heydrich, C., Hudgens, M. G., Halloran, M. E., Clemens, J. D., Ali, M., & Emch, M. E. (2014). Assessing effects of cholera vaccination in the presence of interference. Biometrics, 70(3), 731-741. doi: 10.1111/biom.12184
  • Tchetgen, E. J. T., & VanderWeele, T. J. (2012). On causal inference in the presence of interference. Statistical Methods in Medical Research, 21(1), 55-75. doi: 10.1177/0962280210386779
• An earlier version of the methods implemented in ‘clusteredinterference’ was implemented using the geex package for estimating equations.
• Thanks to Bradley Saul for inferference, geex, and for comments and suggestions that were helpful in the creation of ‘clusteredinterference’.