I'm using offset for the first time (as per a recommendation from a colleague) and have a couple questions about interpreting my results. Our ultimate goal is to look at the effect of some population level treatment on disease incidence (cases/population). We've decided to use poisson models, but there are surely a variety of ways to look at our data. My data look like this:
cases <- c(6216128, 3341110, 855105, 359371, 417393, 640434, 528914, 377166, 401556, 252832, 128458)
population <- c(54703334, 54252430, 55976643, 56630708, 57373529, 58025577, 58617708, 58921850, 59695818, 60466585, 60223458)
treat.count <- c(13389482, 17746954, 27974966, 27329972, 16534356, 10591797, 12740820, 11787687, 6780603, 5503181, 4446687)
treat.percent <- c(0.24476537, 0.32711814, 0.49976141, 0.48259986, 0.28818789, 0.18253669, 0.21735446, 0.20005629, 0.11358590, 0.09101194, 0.07383646)
data <- cbind(cases, population, treat.count, treat.percent)
mydata <- as.data.frame(data)
I have two overarching questions:
- the interpretation of offset in these poisson models and
- the interpretation of the poisson model with offset and covariates added.
1) with the inclusion of offset and no covariates:
f1 <- glm(cases ~ offset(population), data=mydata, family=poisson)
is that the expected value of cases
, divided by pop
, is exp(intercept)
...correct?
2) with the inclusion of offset and covariates:
f2 <- glm(cases ~ offset(population)+log(treat.percent), data=mydata, family=poisson)
is that the expected value of cases
, divided by pop
, is exp(intercept)
...as the treat.percent
increases?
There were similar questions posted before, but not quite this situation.