Finding cumulative second max per group in R - r

Question

I have a dataset where I would like to create a new variable that is the cumulative second largest value of another variable, and I would like to perform this function per group.
Let's say I create the following example data frame:
(df1 <- data.frame(patient = rep(1:5, each=8), visit = rep(1:2,each=4,5), trial = rep(1:4,10), var1 = sample(1:50,20,replace=TRUE)))
This is pretend data that represents 5 patients who each had 2 study visits, and each visit had 4 trials with a measurement taken (var1).
> head(df1,n=20)
patient visit trial var1
1 1 1 1 25
2 1 1 2 23
3 1 1 3 48
4 1 1 4 37
5 1 2 1 41
6 1 2 2 45
7 1 2 3 8
8 1 2 4 9
9 2 1 1 26
10 2 1 2 14
11 2 1 3 41
12 2 1 4 35
13 2 2 1 37
14 2 2 2 30
15 2 2 3 14
16 2 2 4 28
17 3 1 1 34
18 3 1 2 19
19 3 1 3 28
20 3 1 4 10
I would like to create a new variable, cum2ndmax, that is the cumulative 2nd largest value of var1 and I would like to group this variable by patient # and visit #.
I figured out how to calculate the cumulative 2nd max number like so:
df1$cum2ndmax <- sapply(seq_along(df1$var1),function(x){sort(df1$var1[seq(x)],decreasing=TRUE)[2]})
df1
However, this calculates the cumulative 2nd max across the whole dataset, not for each group. I have attempted to calculate this variable using grouped data like so after installing and loading package dplyr:
library(dplyr)
df2 <- df1 %>%
group_by(patient,visit) %>%
mutate(cum2ndmax = sapply(seq_along(df1$var1),function(x){sort(df1$var1[seq(x)],decreasing=TRUE)[2]}))
But I get an error: Error: Problem with mutate() input cum2ndmax. x Input cum2ndmax can't be recycled to size 4.
Ideally, my result would look something like this:
patient visit trial var1 cum2ndmax
1 1 1 25 NA
1 1 2 23 23
1 1 3 48 25
1 1 4 37 37
1 2 1 41 NA
1 2 2 45 41
1 2 3 8 41
1 2 4 9 41
2 1 1 26 NA
2 1 2 14 14
2 1 3 41 26
2 1 4 35 35
… … … … …
Any help in getting this to work in R would be much appreciated! Thank you!

Answer 1

One dplyr and purrr option could be:
df1 %>%
group_by(patient, visit) %>%
mutate(cum_second_max = map_dbl(.x = seq_along(var1),
~ ifelse(.x == 1, NA, var1[dense_rank(-var1[1:.x]) == 2])))
patient visit trial var1 cum_second_max
<int> <int> <int> <int> <dbl>
1 1 1 1 25 NA
2 1 1 2 23 23
3 1 1 3 48 25
4 1 1 4 37 37
5 1 2 1 41 NA
6 1 2 2 45 41
7 1 2 3 8 41
8 1 2 4 9 41
9 2 1 1 26 NA
10 2 1 2 14 14
11 2 1 3 41 26
12 2 1 4 35 35
13 2 2 1 37 NA
14 2 2 2 30 30
15 2 2 3 14 30
16 2 2 4 28 30
17 3 1 1 34 NA
18 3 1 2 19 19
19 3 1 3 28 28
20 3 1 4 10 28

Answer 2

Here is an Rcpp solution.
cum_second_max is a modification of cummax which keeps track of the second maximum.
library(tidyverse)
Rcpp::cppFunction("
NumericVector cum_second_max(NumericVector x) {
double max_value = R_NegInf, max_value2 = NA_REAL;
NumericVector result(x.length());
for (int i = 0 ; i < x.length() ; ++i) {
if (x[i] > max_value) {
max_value2 = max_value;
max_value = x[i];
}
else if (x[i] < max_value && x[i] > max_value2) {
max_value2 = x[i];
}
result[i] = isinf(max_value2) ? NA_REAL : max_value2;
}
return result;
}
")
df1 %>%
group_by(patient, visit) %>%
mutate(
c2max = cum_second_max(var1)
)
#> # A tibble: 20 x 5
#> # Groups: patient, visit [5]
#> patient visit trial var1 c2max
#> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 1 1 25 NA
#> 2 1 1 2 23 23
#> 3 1 1 3 48 25
#> 4 1 1 4 37 37
#> 5 1 2 1 41 NA
#> 6 1 2 2 45 41
#> 7 1 2 3 8 41
#> 8 1 2 4 9 41
#> 9 2 1 1 26 NA
#> 10 2 1 2 14 14
#> 11 2 1 3 41 26
#> 12 2 1 4 35 35
#> 13 2 2 1 37 NA
#> 14 2 2 2 30 30
#> 15 2 2 3 14 30
#> 16 2 2 4 28 30
#> 17 3 1 1 34 NA
#> 18 3 1 2 19 19
#> 19 3 1 3 28 28
#> 20 3 1 4 10 28

Answer 3

Thanks so much everyone! I really appreciate it and could not have solved this without your help! In the end, I ended up using a similar approach suggested by tmfmnk since I was already using dplyr. I found an interesting result with the code suggested by tmkmnk where for some reason it gave me a column of values that just repeated the first row's number. With a small tweak to change dense_rank to order, I got exactly what I wanted like this:
df1 %>%
group_by(patient, visit) %>%
mutate(cum_second_max = map_dbl(.x = seq_along(var1),
~ ifelse(.x == 1, NA, var1[order(-var1[1:.x])[2])))