dplyr::case_when() + lag to iterate through a column

[sm127]

Ideally, I would like to fill a variable, period, based on the difference of two, changing, dates.

Say my df looks like this:

id	index_date	test_date	period
1	1/1/2006	1/1/2006
1	1/1/2006	3/4/2007
1	1/1/2006	3/5/2007
1	1/1/2006	6/18/2012
2	2/16/2016	2/16/2016
2	2/16/2016	5/1/2018
2	2/16/2016	9/6/2018
3	9/10/2008	9/10/2008
3	9/10/2008	7/5/2013
4	6/8/2014	6/8/2014
4	6/8/2014	6/28/2014
4	6/8/2014	7/13/2014
4	6/8/2014	5/24/2017
4	6/8/2014	12/4/2020
4	6/8/2014	12/10/2020

period is a factor that corresponds to a calculation based on previous test dates. Here is what I would like to do in

df %>%
    group_by(id) %>%
    arrange(test_date, .by_group = T) %>%
    mutate(
        period =
            case_when(
                test_date[2] - test_date[1] >= 45 ~ 1,
                test_date[3] - test_date[2] >= 45 ~ 2
...
            )
    )

While this would work if there were few test_date/participant, some ids have over 300 test_dates. I'm thinking I could use lag here but not sure how to implement. The final df should look something like this:

id	index_date	test_date	period
1	1/1/2006	1/1/2006	NA
1	1/1/2006	3/4/2007	1
1	1/1/2006	3/5/2007	NA
1	1/1/2006	6/18/2012	2
2	2/16/2016	2/16/2016	NA
2	2/16/2016	5/1/2018	1
2	2/16/2016	9/6/2018	2
3	9/10/2008	9/10/2008	NA
3	9/10/2008	7/5/2013	1
4	6/8/2014	6/8/2014	NA
4	6/8/2014	6/28/2014	1
4	6/8/2014	7/13/2014	1
4	6/8/2014	5/24/2017	2
4	6/8/2014	12/4/2020	3
4	6/8/2014	12/10/2020	3

[HanOostdijk]

What do you mean by test_date[2] ?
As I understand it, this would be the value of the column test_date for the second observation.
This would imply that whatever the calculation in the case_when clause the result period for all observations would be the same.
How could then the value for the first observation be NA ?

Please indicate exactly in words how you would like to calculate period.
And please provide you input as described e.g. in
https://forum.posit.co/t/faq-whats-a-reproducible-example-reprex-and-how-do-i-do-one/5219