Count active observations by week - r

Question

I have a data frame of observations with a start and end date for each observation indicating the period it was active.
The duration active varies by observation, and can spread across multiple weeks.
Some observations are still active and do not have an end date.
For a given date range, how can I count the number of observations that were active during a week within that date range, including those still active?
I have a crude method that works, but is pretty slow. It seems like there has to be a more efficient and simpler way to do this.
EDIT: My first approach was similar to Ronak's solution, which is definitely better than mine for smaller data sets, but my real data set has more observations and longer date ranges, so I run into memory constraints.
#I'm primarily using tidyverse/lubridate, but definitely open to other solutions.
library(tidyverse)
library(lubridate)
# sample data frame of observations with start and end dates:
df_obs <- tibble(
observation = c(1:10),
date_start = as_date(c("2020-03-17", "2020-01-20", "2020-02-06", "2020-01-04", "2020-01-06", "2020-01-24", "2020-01-09", "2020-02-11", "2020-03-13", "2020-02-07")),
date_end = as_date(c("2020-03-27", "2020-03-20", NA, "2020-03-04", "2020-01-16", "2020-02-24", NA, "2020-02-19", NA, "2020-02-27"))
)
# to account for observations that are still active, NAs are converted to today's date:
df_obs <- mutate(df_obs, date_end = if_else(is.na(date_end), Sys.Date(), date_end))
# create a data frame of weeks by start and end date to count the active observations in a given week
# for this example I'm just using date ranges from the sample data:
df_weeks <-
seq(min(df_obs$date_start), max(df_obs$date_start), by = 'day') %>%
enframe(NULL, 'week_start') %>%
mutate(week_start = as_date(cut(week_start, "week"))) %>%
mutate(week_end = week_start + 6) %>%
distinct()
# create a function that filters the observations data frame based on start and end dates:
check_active <- function(d, s, e){
d %>%
filter(date_start <= e) %>%
filter(date_end >= s) %>%
nrow()
}
# applying that function to each week in the date range data frame gives the expected results:
df_weeks %>%
rowwise() %>%
mutate(total_active = check_active(df_obs, week_start, week_end)) %>%
select(-week_end) %>%
ungroup()
# A tibble: 12 x 2
week_start total_active
<date> <int>
1 2019-12-30 1
2 2020-01-06 3
3 2020-01-13 3
4 2020-01-20 4
5 2020-01-27 4
6 2020-02-03 6
7 2020-02-10 7
8 2020-02-17 7
9 2020-02-24 6
10 2020-03-02 4
11 2020-03-09 4
12 2020-03-16 5

Answer 1

Here is one way :
library(tidyverse)
df_obs %>%
#Replace NA with today's date
#Create sequence between start and end date
mutate(date_end = replace(date_end, is.na(date_end), Sys.Date()),
date = map2(date_start, date_end, seq, "day")) %>%
#Get data in long format
unnest(date) %>%
#Unselect start an end date
select(-date_start, -date_end) %>%
#Cut data by week
mutate(date = cut(date, "week")) %>%
#Get unique rows for observation and date
distinct(observation, date) %>%
#Count number of observation in each week
count(date)
which returns :
# A tibble: 14 x 2
# value n
# <fct> <int>
# 1 2019-12-30 1
# 2 2020-01-06 3
# 3 2020-01-13 3
# 4 2020-01-20 4
# 5 2020-01-27 4
# 6 2020-02-03 6
# 7 2020-02-10 7
# 8 2020-02-17 7
# 9 2020-02-24 6
#10 2020-03-02 4
#11 2020-03-09 4
#12 2020-03-16 5
#13 2020-03-23 4
#14 2020-03-30 3