Filter numbers that are closest to target values and eliminate duplicated observations

I have this dataframe:

data_a <- read.csv(text = "
date,treatment,stage
1,a,1
2,a,10
3,a,20
4,a,30
5,a,60
6,a,70
7,a,89
8,a,91
9,a,92
1,b,1
2,b,10
3,b,20
4,b,30
5,b,59.8
6,b,60.2
7,b,88.8
8,b,90.2
9,b,92
1,c,1
2,c,10
3,c,20
4,c,60
5,c,66
6,c,70
7,c,80
8,c,85
9,c,85")

I need to filter within each treatment the observations matching stage 10, 60, and 89 (or the observation closest to those target values). The code I have is this:

filtered_data <- data_a %>%
  group_by(treatment) %>%
  filter(abs(stage - 10) == min(abs(stage - 10)) |
         abs(stage - 60) == min(abs(stage - 60)) |
         abs(stage - 89) == min(abs(stage - 89)))

This code partially does the trick, but there are problems for treatment b and c.

In b, two observations have the same difference from the target. So, both observations are filtered in, which is not desired.

In c, two observations have the same value and are closest to the target, and therefore both observations are selected, which is not desired.

The desired output is this:

filtered_data <- read.csv(text = "
date,treatment,stage
2,a,10
5,a,60
7,a,89
2,b,10
5,b,59.8
7,b,88.8
2,c,10
4,c,60
8,c,85")

I would do it thusly

library(tidyverse)

crossing(
  data_a,
  target_stage = c(10, 60, 89)
  ) %>% 
  group_by(treatment, target_stage) %>% 
  slice_min(
    abs(stage-target_stage),
    with_ties = F
    )
#> # A tibble: 9 × 4
#> # Groups:   treatment, target_stage [9]
#>    date treatment stage target_stage
#>   <int> <chr>     <dbl>        <dbl>
#> 1     2 a          10             10
#> 2     5 a          60             60
#> 3     7 a          89             89
#> 4     2 b          10             10
#> 5     5 b          59.8           60
#> 6     7 b          88.8           89
#> 7     2 c          10             10
#> 8     4 c          60             60
#> 9     8 c          85             89

^{Created on 2023-05-22 with reprex v2.0.2}

If you expand the grid using crossing you can then group by this and find the smallest whilst also removing ties

Using dplyr and purrr:

library(dplyr)
library(purrr)

map_dfr(c(10, 60, 89),
        ~ data_a %>%
          filter(abs(stage - .x) == min(abs(stage - .x)),
                 .by = treatment) %>% 
          slice_min(stage, n = 1, with_ties = FALSE, by = treatment)) %>% 
  arrange(treatment, date)

#>   date treatment stage
#> 1    2         a  10.0
#> 2    5         a  60.0
#> 3    7         a  89.0
#> 4    2         b  10.0
#> 5    5         b  59.8
#> 6    7         b  88.8
#> 7    2         c  10.0
#> 8    4         c  60.0
#> 9    8         c  85.0

Using data.table:

library(data.table)

setDT(data_a)[
  data_a[CJ(stage = c(10, 60, 89), treatment = unique(data_a$treatment)), 
                on = .(treatment, stage), 
                roll = "nearest", 
                .(date, treatment)], 
  on = .(treatment, date)][
    order(treatment, date)]

#>    date treatment stage
#> 1:    2         a  10.0
#> 2:    5         a  60.0
#> 3:    7         a  89.0
#> 4:    2         b  10.0
#> 5:    5         b  59.8
#> 6:    7         b  88.8
#> 7:    2         c  10.0
#> 8:    4         c  60.0
#> 9:    9         c  85.0

You can use outer() + max.col() to find the closest or farthest values from 10, 60, 89.

library(dplyr)

data_a %>%
  slice({
    mat <- abs(outer(c(10, 60, 89), stage, '-'))
    max.col(-mat, "first")
  }, .by = treatment)

#   date treatment stage
# 1    2         a  10.0
# 2    5         a  60.0
# 3    7         a  89.0
# 4    2         b  10.0
# 5    5         b  59.8
# 6    7         b  88.8
# 7    2         c  10.0
# 8    4         c  60.0
# 9    8         c  85.0