Estimating causal policyFX with clusteredinterference

2019-03-17

First, load the clusteredinterference package

library(clusteredinterference)

Now load a quick data example that’s included in the package

data("toy_data")

Estimation

Estimation is implemented with the policyFX() function:

suppressWarnings(RNGversion("3.5.0")) ## For backwards compatibility
set.seed(1113)
causal_fx <- policyFX(
data = toy_data,
formula = Outcome | Treatment ~ Age + Distance + (1 | Cluster_ID) | Cluster_ID,
alphas = c(.3, .5),
k_samps = 1
)

The policyFX() function outputs a "policyFX" object, which works well with a few methods, including:

summary(causal_fx)
#> ------------- causal estimates --------------
#>     estimand estimate     se     LCI    UCI
#>      mu(0.3)   0.6523 0.0635  0.5279 0.7767
#>      mu(0.5)   0.6075 0.0505  0.5086 0.7063
#>     mu0(0.3)   0.6707 0.0736  0.5264 0.8151
#>     mu0(0.5)   0.5849 0.0728  0.4422 0.7276
#>     mu1(0.3)   0.2799 0.0563  0.1695 0.3902
#>     mu1(0.5)   0.3974 0.0577  0.2842 0.5105
#>  OE(0.5,0.3)  -0.0449 0.0366 -0.1165 0.0268
#>  OE(0.3,0.5)   0.0449 0.0366 -0.0268 0.1165
#>
#>           ... 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
#> ---------------------------------------------

Necessary arguments

data

A data.frame. At present, tibbles are coerced back to standard data.frames. I also recommend against using factors in the columns.

alphas

A numeric vector of probabilities corresponding the the policies of interest. Each must be between 0 and 1.

k_samps

The user must specify the number of sum-sampled vectors for estimating the counterfactual probabilities (nuisance parameters). It is recommended to choose k_samps <=5. To avoid the sub-sampling approximation and use all possible vectors, set k_samps=0.

formula

The formula may be the trickiest, and it has plenty of information. It provides:

outcome | treatment ~ predictors and random intercept | clustering specification

Note that the middle section is passed to glmer() to fit the mixed effects model, so this is how to specify the modeling formula.

Treatment ~ Age + Distance + (1 | Cluster_ID)

See below for the model output.

Formal arguments with defaults

root_options = NULL

This is for rootSolve::multiroot() used in the point estimation procedure. E.g., this will be passed in:

root_options = list(atol = 1e-7)

nAGQ=2

This is for lme4::glmer(). The default in glmer() is nAGQ=1, which indicates a Laplace approximation to the log-likelihood. Instead, in this package the default is nAGQ=2, which indicates that n=2 Adaptive Gaussian Quadrature points will be used. This is slightly slower but is a more accurate calculation. In limited testing, it seems that nAGQ=2 was almost as accurate as higher values, so 2 was chosen as the default. See their documentation for more details.

return_matrices = FALSE

If TRUE, this will return the “bread” and “meat” matrices in the variance calculations. The default is FALSE as these matrices can be quite large.

Dots tricks

In the event you’re only interested in a subset of contrasts, you can pass a customized grid into the function.

my_grid <- makeTargetGrid(alphas = (3:8)/20, small_grid = TRUE)
#>   alpha1_num alpha2_num trt alpha1 alpha2 estimand effect_type estVar
#> 1          1         NA  NA   0.15     NA       mu     outcome   TRUE
#> 2          2         NA  NA   0.20     NA       mu     outcome   TRUE
#> 3          3         NA  NA   0.25     NA       mu     outcome   TRUE
#> 4          4         NA  NA   0.30     NA       mu     outcome   TRUE
#> 5          5         NA  NA   0.35     NA       mu     outcome   TRUE
#> 6          6         NA  NA   0.40     NA       mu     outcome   TRUE

This can be particularly useful for plotting, as you can “turn off” the variance estimates

my_grid$estVar <- FALSE This is available through the dots argument. Note that when supplying a custom target_grid, it’s not necessary to specify the alphas argument, as that is taken directly from target_grid. causal_fx2 <- policyFX( data = toy_data, formula = Outcome | Treatment ~ Age + Distance + (1 | Cluster_ID) | Cluster_ID, # alphas = c(.3, .5), target_grid = my_grid, k_samps = 5, verbose = FALSE, root_options = list(atol=1e-4) ) print(causal_fx, nrows = 9) #> ------------- causal estimates -------------- #> estimand estimate se LCI UCI #> mu(0.3) 0.6523 0.0635 0.5279 0.77667 #> mu(0.5) 0.6075 0.0505 0.5086 0.70633 #> mu0(0.3) 0.6707 0.0736 0.5264 0.81506 #> mu0(0.5) 0.5849 0.0728 0.4422 0.72760 #> mu1(0.3) 0.2799 0.0563 0.1695 0.39020 #> mu1(0.5) 0.3974 0.0577 0.2842 0.51055 #> OE(0.5,0.3) -0.0449 0.0366 -0.1165 0.02681 #> OE(0.3,0.5) 0.0449 0.0366 -0.0268 0.11651 #> SE0(0.5,0.3) -0.0858 0.0403 -0.1648 -0.00677 #> ... and 3 more rows ... #> --------------------------------------------- Plotting The tidy dataframe estimates can be easily used for plotting: plotdat <- causal_fx2$estimates[causal_fx2$estimates$estimand_type=="mu",]
plot(x = plotdat$alpha1, y = plotdat$estimate, main = "Estimated Population Means") Treatment model

As mentioned above, the treatment model is specified via the formula argument. For example, compare:

# Returns the specified formula, coerced to a Formula object
causal_fx$formula #> Outcome | Treatment ~ Age + Distance + (1 | Cluster_ID) | Cluster_ID # causal_fx$model is a glmerMod S4 object
causal_fx$model@call #> lme4::glmer(formula = Treatment ~ Age + Distance + (1 | Cluster_ID), #> data = data, family = stats::binomial, nAGQ = nAGQ) lme4::getME(causal_fx$model, c("beta", "theta"))
#> $beta #>  -1.446087049 -0.008509771 0.260968952 #> #>$theta
#> Cluster_ID.(Intercept)
#>               1.180325