I would like to calculate the number of cases following the initial record in a data panel (detect dropout). Could someone assist me with the methodology or provide guidance on how to achieve this?

Data

dt <- tibble(
  `id` = c("id1", "id2","id3"),
  `2018` = c(NA,NA,"id3"),
  `2019` = c(NA,"id2","id3"),
  `2020` = c(NA, "id2",NA),
  `2021` = c("id1", NA,"id3"),
  `2022` = c("id1", NA,"id3"),
  `2023` = c(NA, "id2","id3")
) %>% as.data.table(); dt

       id   2018   2019   2020   2021   2022   2023
   <char> <char> <char> <char> <char> <char> <char>
1:    id1   <NA>   <NA>   <NA>    id1    id1   <NA> ---> 1st record 2021
2:    id2   <NA>    id2    id2   <NA>   <NA>    id2 ---> 1st record 2019
3:    id3    id3    id3   <NA>    id3    id3    id3 ---> 1st record 2018

Expected Output

dt <- dt[, .(
  `2018` = ifelse(is.na(`2018`), 1, 0),
  `2019` = ifelse(is.na(`2019`), 1, 0),
  `2020` = ifelse(is.na(`2020`), 1, 0),
  `2021` = ifelse(is.na(`2021`), 1, 0),
  `2022` = ifelse(is.na(`2022`), 1, 0),
  `2023` = ifelse(is.na(`2023`), 1, 0)), by = c("id")]
dt

output <- tibble(
  `id` = c("id1", "id2","id3"),
  `2018` = c(0,0,0),
  `2019` = c(0,0,0),
  `2020` = c(0, 0,1),
  `2021` = c(0, 1,0),
  `2022` = c(0, 1,0),
  `2023` = c(1, 0,0),
  n = c(1,2,1)
) %>% as.data.table(); output

       id  2018  2019  2020  2021  2022  2023 n_dropOut
   <char> <num> <num> <num> <num> <num> <num>     <num>
1:    id1     0     0     0     0     0     1         1
2:    id2     0     0     0     1     1     0         2
3:    id3     0     0     1     0     0     0         1

I've tried this code but it is incorrect

dt[, n_dropOut := 
                 `2018` + 
                 `2019` + 
                 `2020` + 
                 `2021` + 
                 `2022` + 
                 `2023`
, by = c("id")]

       id  2018  2019  2020  2021  2022  2023 n_dropOut
   <char> <num> <num> <num> <num> <num> <num>     <num>
1:    id1     1     1     1     0     0     1         4
2:    id2     1     0     0     1     1     0         3
3:    id3     0     0     1     0     0     0         1

helper <- function(x) {
  i <- Position(\(x) !is.na(x), x) # i is the position of first non-NA
  if (is.na(i)) return(0L)         # If not found return 0 
  j <- length(x)                   # Otherwise sum number of NAs from i to the end
  sum(is.na(x[i:j]))
}

dt[, n_dropout := helper(unlist(.SD)), .SDcols = `2018`:`2023`, by = id]


       id   2018   2019   2020   2021   2022   2023 n_dropout
   <char> <char> <char> <char> <char> <char> <char>     <int>
1:    id1   <NA>   <NA>   <NA>    id1    id1   <NA>         1
2:    id2   <NA>    id2    id2   <NA>   <NA>    id2         2
3:    id3    id3    id3   <NA>    id3    id3    id3         1