treatment     <- factor(rep(c(1, 2), c(43, 41)),
                        levels = c(1, 2),
                        labels = c("placebo", "treated"))
improved      <- factor(rep(c(1, 2, 3, 1, 2, 3), c(29, 7, 7, 13, 7, 21)),
                        levels = c(1, 2, 3),
                        labels = c("none", "some", "marked"))
numberofdrugs <- rpois(84, 10) + 1
healthvalue   <- rpois(84, 5)
y             <- data.frame(healthvalue, numberofdrugs, treatment, improved)
test          <- glm(healthvalue~numberofdrugs+treatment+improved + treatment:improved, y, family=poisson)
summary(test)

> coef(test)
                    (Intercept)                   numberofdrugs                treatmenttreated
                    1.549172817                     0.004261529                     0.014634807
                   improvedsome                  improvedmarked   treatmenttreated:improvedsome
                    0.201150827                    -0.129251907                    -0.258841251
treatmenttreated:improvedmarked
                    0.051326071

coef.intercept=(1.5491)

coef.numberofdrugs=(0.00426)

coef.treatment=(0, 0.01463)

coef.improved=(0, 0.2011, -0.1292)

(0       0       0  )

(0  -0.2588  -0.2588)

library(effects)
allEffects(test)
 model: healthvalue ~ numberofdrugs + treatment + improved + treatment:improved

 numberofdrugs effect
numberofdrugs
       6        8       10       12       14       16       18       20
4.050962 4.322559 4.612365 4.921601 5.251570 5.603662 5.979360 6.380247

 treatment*improved effect
         improved
treatment     none     some   marked
  placebo 4.416773 3.713517 5.461153
  treated 4.596433 4.902746 5.309627