How do I obtain rate estimates with 95% CIs for each level of a factor from a Poisson regression in R?

I am running a Poisson regression model in R structured the following way:

mod <- glm(outcome ~ X + A + B + C + offset(log(time)), data = dat, family = poisson(link = "log"))

Where X is my 2-level factor of interest and A, B, and C are additional covariates.

How can I extract rate estimates and 95% CIs for each level of X from mod?

My anticipated output would be: Estimated rate for X_level1 (95% CI) Estimated rate for X_level2 (95% CI)

Thank you in advance!

Solution

Presumably you mean the marginal effect of X on outcome, that is, the estimated value of outcome at each of the two levels of X when all the other covariates are held at their mean values. To do this you could use the emmeans package:

library(emmeans)

mod <- glm(outcome ~ X + A + B + C + offset(log(time)), 
           data = dat, family = poisson(link = "log"))

result <- as.data.frame(emmeans(mod, specs = 'X'))

result <- cbind(result[1], exp(result[2]), 
                CI = paste(round(exp(result[[5]]), 3),
                           round(exp(result[[6]]), 3), sep = '-'))

Giving you

result
#>        X   emmean              CI
#> 1 level1 107.5459 104.587-110.589
#> 2 level2 147.1999 143.957-150.516

Data used

set.seed(1)

dat <- data.frame(X = factor(sample(c('level1', 'level2'), 100, TRUE)),
                  A = sample(100)/5,
                  B = sample(100)/2, 
                  C = sample(100)/4, 
                  time = 1:100)

dat$outcome <- with(dat, rpois(100, 50 * as.numeric(X) - A + B - C + time))

head(dat)
#>        X   A    B     C time outcome
#> 1 level1 5.6 45.5 19.50    1      85
#> 2 level2 9.6 15.5  9.25    2      94
#> 3 level1 6.6 36.0 10.75    3      94
#> 4 level1 9.0 18.0 20.25    4      43
#> 5 level2 4.2 24.5  0.25    5     137
#> 6 level1 6.2 20.5 22.50    6      31

^{Created on 2023-03-23 with reprex v2.0.2}