# Propensity score stratification: standard errors and p-values

While there are many tutorials on how to perform propensity score stratification, I was unable to find any example that showed the calculation of standard errors and p-values for the final estimate.

In the original paper, Rosenbaum and Rubin (1984) cite Mosteller and Tukey (1977, Chap. 11c) for the calculation of the standard error. Regrettably, I do not have access to this.

What is the recommended way to calculate SEs and p-values today?

You may have a better chance to access to a more recent publication by Austin: http://www.ncbi.nlm.nih.gov/pubmed/20108233 (for example).

In the seconde page:

For example, with R:

library(plyr)
mod.strat <- dlply(.data = data, .variables = "strata",
.fun = function(DF) {
glm(Y ~ T, data = DF)
})

coefs <- mean(sapply(mod.strat, function(mod) mod$coef["T"])) sds <- sqrt(sum(((1/nlevels(data$strata))^2)*sapply(mod.strat, function(mod) vcov(mod)["T", "T"])))
ci <- coefs + qnorm(c(0.025, 0.975))*sds
p <- 2*(1-pnorm(abs(coefs/sds)))


where data is your data frame, strata is the name of your (PS-based) stratication variable, Y is your outcome, and T your binary exposure.

Note that in many simulations studies, stratification on PS has been shown to perform poorly compared to IPTW estimation or PS-matching.