# for a multinomial treatment and binary outcome, what is more appropriate, ATC or ATE?

I need help to choose between ATC and ATE for my analysis with multinomial treatment and binary outcome.

In the example below taken from here, it seems that ATT does not sound well for multinomial treatments because I have several focal groups (treated groups), and my interest is in comparing each of these focal groups with the control group. For the binary case, the concept of ATT weight is straightforward, not certain here.

To deal with this, I think either ATC or ATE would probably be more appropriate for the case of multinomial treatments. I favour ATC over ATE because I see it as a generalization of ATT, which usually is deemed more desirable in observational studies. Also, I "might not have good overlap (common support) between the two treatment groups", making ATE less reasonable than ATT (and thus ATC).

Using ATC would mean making group 1 the focal group and I could do:

w_atc <- w*ps.mat[,"1"] #ATC

w[group == i] <- 1/ps.mat[group == i, i] #ATE

or

w_att <- w*ps.mat[,"2"] w_att <- w*ps.mat[,"3"] #ATT

sample data and code:

library("nnet")
library("cobalt")

set.seed(42)
group <- factor(sample(c(1,2,3), 100, #needs to be a factor
replace=TRUE))
demo1 <- rnorm(100,100,25)
demo2 <- rpois(100,10)
demo3 <- rbinom(100,1,0.67)

df <- data.frame(group, demo1, demo2,demo3)

fit <- multinom(group ~ demo1 + demo2 + demo3, data = df)
#> # weights:  15 (8 variable)
#> initial  value 109.861229
#> iter  10 value 107.354113
#> final  value 107.353911
#> converged

ps.mat <- predict(fit, type = 'probs')

w <- rep(0, nrow(df)) #inititalize weights

for (i in levels(group)) {
w[group == i] <- 1/ps.mat[group == i, i]
}

bal.tab(group ~ demo1 + demo2 + demo3, data = df,
weights = w, un = TRUE)


Thank you in advance for any help.