Find lag in group matching a condition - r

Question

I need for each group of ID's to find the last (lag) of another column, but not just the last, but the last matching the condition.
My problem is, I don't know how to add the condition to the row.
My data and desired output:
I've tried
df %>%
group_by(ID) %>%
arrange(activity_nr) %>%
mutate(desired_output = if_else(is.na(matched) &
lag(event) != "hospital",
lag(event), NA)) `
But the condition of lag(event) != "hospital" is not correct, since it only matches if event is not hospital - what I want is for it to find the last non-hospital event.
I've also tried
df %>%
group_by(ID) %>%
arrange(activity_nr) %>%
mutate(desired_output = if_else(is.na(matched) &
str_detect(event, "1"),
lag(event), NA))
and
df %>%
group_by(ID) %>%
arrange(activity_nr) %>%
mutate(desired_output = if_else(is.na(matched),
lag(str_detect(event, "1")), NA))
Data:
df <- structure(list(ID = c(1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2,
2, 3, 3, 3, 3, 3, 3), event = c("108", "hospital", "hospital",
"hospital", "hospital", "108", "110", "hospital", "hospital",
"110", "hospital", "hospital", "107", "107", "105", "105", "hospital",
"hospital", "110", "110"), event_type = c("start", "start", "end",
"start", "end", "end", "start", "start", "end", "end", "start",
"end", "start", "end", "start", "end", "start", "end", "start",
"end"), activity_nr = c(1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7,
8, 1, 2, 3, 4, 6, 7), activity_id = c(1, 1, 1, 2, 2, 1, 1, 1,
1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2), activity_type = c("housing",
"hospital", "hospital", "hospital", "hospital", "housing", "housing",
"hospital", "hospital", "housing", "hospital", "hospital", "housing",
"housing", "housing", "housing", "hospital", "hospital", "housing",
"housing"), matched = c(NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, 107, NA, NA, NA, NA, NA, 110, NA, NA), `Desired output` = c(NA,
NA, 108, NA, 108, NA, NA, NA, 110, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA)), class = c("tbl_df", "tbl", "data.frame"), row.names = c(NA,
-20L))

Answer 1

Ok so I actually found the solution.
Here you go:
df %>%
group_by(ID) %>%
arrange(activity_nr) %>%
mutate(temp = event,
temp = ifelse(temp == "hospital", NA, temp)) %>%
fill(temp, .direction = "down") %>%
mutate(desired_output = case_when(is.na(matched)
~ temp,
TRUE ~ desired_output))