Generating a union of overlapping intervals

This function takes a set of overlapping intervals and returns the union of the intervals.

Use case example

• calculate the total duration a patient has had any line in place
• your dataframe has:
  • one row per line
  • columns of start and end times for each line
• if two lines are in place at the same time, they should not be double-counted to contributing to duration
• so, you need to generate a non-overlapping set of intervals prior to calculating the total duration

########## Function to generate non-overlapping intervals ##########
# - dataframe with row of intervals, with column names 'start' and 'stop'
# - consolidates overlapping intervals and returns a dataframe with non-redundant, non-overlapping dataframes
# - logic of the if(elseif) -> if: works but might not be optimized

library(dplyr)                                         # for %>%, arrange, bind_rows

interval_union <- function(input) {
  if (nrow(input) == 1) {                              # if only 1 input interval, return it
    return(input)
  }
  input <- input %>% arrange(start)                    # sort inputs by start
  output = input[1, ]                                  # start off output with just the first (earliest) interval
  for (i in 2:nrow(input)) {                           # loop from 2nd to last input interval
    x <- input[i, ]                                    # the next interval to work on
    
    if (output$stop[nrow(output)] < x$start) {         # the next interval starts after the end of the last output interval...
      output <- bind_rows(output, x)                   # ... so add it as a NEW output interval; it will not be the last output interval
    } else if (output$stop[nrow(output)] == x$start) { # the next interval starts exactly at the end of the last output interval...
      output$stop[nrow(output)] <- x$stop              # ... so just extend the previous last output interval; it's still the last one
    }
    if (x$stop > output$stop[nrow(output)]) {          # the next interval ENDS after the end of the last output interval...
      output$stop[nrow(output)] <- x$stop              # ... so just extend the previous last output interval; it's still the last one
    }
  }
  return(output)
}

d <- data.frame(
    start = c('2005-01-01', '2000-01-01', '2001-01-01'),
    stop = c('2006-01-02', '2001-01-02', '2004-01-02'),
    stringsAsFactors = FALSE
  )
d

       start       stop
1 2005-01-01 2006-01-02
2 2000-01-01 2001-01-02
3 2001-01-01 2004-01-02

interval_union(d)

       start       stop
1 2000-01-01 2004-01-02
2 2005-01-01 2006-01-02

Note

It would definitely be possible to rewrite this using just base R, but because all my coding projects are in the tidyverse, I prefer to continue using its functions.