I am using the CausalImpact package in R to calculate the impact of a marketing intervention using Bayesian Structural Time Series. This methodology and package is explained in Broderson et al. 2015 found at https://research.google.com/pubs/pub41854.html (direct PDF link here).
I calculated the impact of a marketing intervention in 18 clinics (the "test" subjects). Using the package, I calculated the causal impact of the intervention compared with the respective synthetic control in each of the 18 clinics.
A replicable example of one sample intervention is available from Google's Github page on CausalImpact and the code is provided below:
library(CausalImpact) #code from Google's Github page on CausalImpact package set.seed(1) x1 <- 100 + arima.sim(model = list(ar = 0.999), n = 100) y <- 1.2 * x1 + rnorm(100) y[71:100] <- y[71:100] + 10 data <- cbind(y, x1) pre.period <- c(1, 70) post.period <- c(71, 100) impact <- CausalImpact(data, pre.period, post.period) summary(impact)
For this example, one can pull out the "Relative Effect" (effect size), along with the lower 95% CI, upper 95% CI, and SD values for this one example intervention.
impact$summary$RelEffect impact$summary$RelEffect.lower impact$summary$RelEffect.upper impact$summary$RelEffect.sd
I have done this for 18 different "test" clinics. For each one, I have the effect size along with the corresponding 95% CI and SD.
My question is this: In what way can I summarize the intervention in one single, summary metric while taking into account variance for each result?
I believe this involves a random effects Meta-Analysis approach by inverse weighing of the variance, but I am not certain. I tried looking into the Metafor package in R (http://www.metafor-project.org/doku.php/analyses), but I cannot seem to find an appropriate analysis or code. Most of the examples I have seen require a sample size for multiple studies. The best I can think of is that my results are analogous to 18 different studies with a sample size of n=1, though I do not think that is a valid interpretation. As the CausalImpact methodology is based on a Bayesian approach, the CI are also not necessarily symmetrical (as seen in the example above). I am also uncertain how to present these results in an appropriate forest plot.
Any help on getting one summary metric is hugely appreciated. I apologize for any errors I may have made. Thank you.