How to add an offset to mixed model - r

Question

I have a data set containing the step count of cows from a 4 week trial where each animal was exposed to treatment A or treatment B at the beginning of week 2, and want to know how the step rate of the two treatment groups changed each week compared to week 1.
How do I add an offset to my model to do this?
The model I am running before adding the offset is this:
mod.1 <- glmmTMB(Step.count ~ Week*Treatment + (1|Cow.ID), data = data.df, family = poisson)
Here is an example of my data
data.1 <- data.frame(Cow.ID = rep(1, 20),
Week = sample(c(1,2,3,4), 20, replace = TRUE),
Treatment = sample(c("infected"), 20, replace = TRUE),
Step.count = rpois(20, 60.1))
data.2 <- data.frame(Cow.ID = rep(2, 20),
Week = sample(c(1,2,3,4), 20, replace = TRUE),
Treatment = sample(c("infected"), 20, replace = TRUE),
Step.count = rpois(20, 60.1))
data.3 <- data.frame(Cow.ID = rep(3, 20),
Week = sample(c(1,2,3,4), 20, replace = TRUE),
Treatment = sample(c("non-infected"), 20, replace = TRUE),
Step.count = rpois(20, 60.1))
data.4 <- data.frame(Cow.ID = rep(4, 20),
Week = sample(c(1,2,3,4), 20, replace = TRUE),
Treatment = sample(c("non-infected"), 20, replace = TRUE),
Step.count = rpois(20, 60.1))
sample.df <- rbind(data.1, data.2, data.3, data.4)

Answer 1

Hard to say without an example of your data, but assuming that you have a datafame something like this
library(dplyr)
cows <- tibble(
Cow.Id = rep(1:4, times = 5),
Week = rep(1:5, each = 4),
Step.count = floor(runif(20, 100,200)),
Treatment = rep(c('A','B','A','B'), times = 5),
)
Then, you can easily calculate a column of Step.count.offset for each cow like this:
cows.clean <- cows %>%
group_by(Cow.Id) %>%
arrange(Week) %>%
mutate(
Step.count.offset = Step.count - first(Step.count)
) %>%
ungroup()