Define periods/episodes of exposition with overlaping and concatenated intervals of time - r

Question

I'm trying to identify periods/episodes of exposition to a drug with prescriptions. If those prescriptions are separated for 30 days it's considered a new period/episode of exposition. Prescriptions can overlap during certain time or be consecutive. If the sum of separated days of two consecutive prescripction is greater than 30 days it's not considered a new episode.
I have data like this:
id = c(rep(1,3), rep(2,6), rep(3,5))
start = as.Date(c("2017-05-10", "2017-07-28", "2017-11-23", "2017-01-27", "2017-10-02", "2018-05-14", "2018-05-25", "2018-11-26", "2018-12-28", "2016-01-01", "2016-03-02", "2016-03-20", "2016-04-25", "2016-06-29"))
end = as.Date(c("2017-07-27", "2018-01-28", "2018-03-03", "2017-04-27", "2018-05-13", "2018-11-14", "2018-11-25", "2018-12-27", "2019-06-28", "2016-02-15", "2016-03-05", "2016-03-24", "2016-04-29", "2016-11-01"))
DT = data.table(id, start, end)
DT
id start end
1: 1 2017-05-10 2017-07-27
2: 1 2017-07-28 2018-01-28
3: 1 2017-11-23 2018-03-03
4: 2 2017-01-27 2017-04-27
5: 2 2017-10-02 2018-05-13
6: 2 2018-05-14 2018-11-14
7: 2 2018-05-25 2018-11-25
8: 2 2018-11-26 2018-12-27
9: 2 2018-12-28 2019-06-28
10: 3 2016-01-01 2016-02-15
11: 3 2016-03-02 2016-03-05
12: 3 2016-03-20 2016-03-24
13: 3 2016-04-25 2016-04-29
14: 3 2016-06-29 2016-11-01
I calculated the difference of start and last end observation (last_diffdays)
DT[, last_diffdays := start-shift(end, n=1L), by = .(id)][is.na(last_diffdays), last_diffdays := 0][]
id start end last_diffdays
1: 1 2017-05-10 2017-07-27 0 days
2: 1 2017-07-28 2018-01-28 1 days
3: 1 2017-11-23 2018-03-03 -66 days
4: 2 2017-01-27 2017-04-27 0 days
5: 2 2017-10-02 2018-05-13 158 days
6: 2 2018-05-14 2018-11-14 1 days
7: 2 2018-05-25 2018-11-25 -173 days
8: 2 2018-11-26 2018-12-27 1 days
9: 2 2018-12-28 2019-06-28 1 days
10: 3 2016-01-01 2016-02-15 0 days
11: 3 2016-03-02 2016-03-05 16 days
12: 3 2016-03-20 2016-03-24 15 days
13: 3 2016-04-25 2016-04-29 32 days
14: 3 2016-06-29 2016-11-01 61 days
This shows when an overlap happens (negative values) or not (positive values). I think an ifelse/fcase statement here would be a bad idea and I'm not comfortable doing it.
I think a good output for this job would be something like:
id start end last_diffdays noexp_days period
1: 1 2017-05-10 2017-07-27 0 days 0 1
2: 1 2017-07-28 2018-01-28 1 days 1 1
3: 1 2017-11-23 2018-03-03 -66 days 0 1
4: 2 2017-01-27 2017-04-27 0 days 0 1
5: 2 2017-10-02 2018-05-13 158 days 158 2
6: 2 2018-05-14 2018-11-14 1 days 1 2
7: 2 2018-05-25 2018-11-25 -173 days 0 2
8: 2 2018-11-26 2018-12-27 1 days 1 2
9: 2 2018-12-28 2019-06-28 1 days 1 2
10: 3 2016-01-01 2016-02-15 0 days 0 1
11: 3 2016-03-02 2016-03-05 16 days 16 1
12: 3 2016-03-20 2016-03-24 15 days 15 1
13: 3 2016-04-25 2016-04-29 32 days 32 2
14: 3 2016-06-29 2016-11-01 61 days 61 3
I manually calculated the days without exposition (noexp_days) of the before prescription.
I dunno If I'm the right path but I think I need to calculate noexp_days variable and then make a cumsum((noexp_days)>30)+1.
If there is a much better solution I don't see or any other possibility I haven't considered I will appreciate to read about them.
Thanks in advance for any help! :)

Answer 1

Try :
library(data.table)
DT[, noexp_days := pmax(as.integer(last_diffdays), 0)]
DT[, period := cumsum(noexp_days > 30) + 1, id]
DT
# id start end last_diffdays noexp_days period
# 1: 1 2017-05-10 2017-07-27 0 days 0 1
# 2: 1 2017-07-28 2018-01-28 1 days 1 1
# 3: 1 2017-11-23 2018-03-03 -66 days 0 1
# 4: 2 2017-01-27 2017-04-27 0 days 0 1
# 5: 2 2017-10-02 2018-05-13 158 days 158 2
# 6: 2 2018-05-14 2018-11-14 1 days 1 2
# 7: 2 2018-05-25 2018-11-25 -173 days 0 2
# 8: 2 2018-11-26 2018-12-27 1 days 1 2
# 9: 2 2018-12-28 2019-06-28 1 days 1 2
#10: 3 2016-01-01 2016-02-15 0 days 0 1
#11: 3 2016-03-02 2016-03-05 16 days 16 1
#12: 3 2016-03-20 2016-03-24 15 days 15 1
#13: 3 2016-04-25 2016-04-29 32 days 32 2
#14: 3 2016-06-29 2016-11-01 61 days 61 3