在 group_by 中，改变一个新列，该列根据列的出现顺序获取列的值

我在争论一个有交叉试验设计的数据集.下面是一个 struct 类似的玩具示例:

df <- structure(list(subject = c("a", "a", "a", "a", "a", "a", "b", 
"b", "b", "b", "c", "c", "c", "c", "c", "c"), treatment = c("none", 
"placebo", "placebo", "drug", "drug", "drug", "none", "drug", 
"placebo", "placebo", "none", "placebo", "drug", "drug", "drug", 
"drug"), day = c(0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 0, 1, 2, 3, 4, 
5)), row.names = c(NA, -16L), class = c("tbl_df", "tbl", "data.frame"
))

# A tibble: 16 × 3
   subject treatment   day
   <chr>   <chr>     <dbl>
 1 a       none          0
 2 a       placebo       1
 3 a       placebo       2
 4 a       drug          3
 5 a       drug          4
 6 a       drug          5
 7 b       none          0
 8 b       drug          1
 9 b       placebo       2
10 b       placebo       3
11 c       none          0
12 c       placebo       1
13 c       drug          2
14 c       drug          3
15 c       drug          4
16 c       drug          5

因此，每个受试者都从treatment中的"无"值开始，然后进行几天的placebo或drug治疗，然后再进行几天的其他治疗.

所以我想要的输出是这样的:

# A tibble: 16 × 4
   subject treatment   day stage 
   <chr>   <chr>     <dbl> <chr> 
 1 a       none          0 first 
 2 a       placebo       1 second
 3 a       placebo       2 second
 4 a       drug          3 third 
 5 a       drug          4 third 
 6 a       drug          5 third 
 7 b       none          0 first 
 8 b       drug          1 second
 9 b       placebo       2 third 
10 b       placebo       3 third 
11 c       none          0 first 
12 c       placebo       1 second
13 c       drug          2 third 
14 c       drug          3 third 
15 c       drug          4 third 
16 c       drug          5 third  

对我来说有意义的是使用group_by和mutate的组合以及treatment中的factor，这是不起作用的

#my failed attempt
df %>% 
  arrange(subject, day) %>% #needed for my actual dataset
  group_by(subject) %>% 
  mutate(stage=factor(treatment, levels=c("first", "second", "third"))) %>% 
  ungroup(

它给出:

# A tibble: 16 × 4
   subject treatment   day stage 
   <chr>   <chr>     <dbl> <fct> 
 1 a       none          0 second
 2 a       placebo       1 third 
 3 a       placebo       2 third 
 4 a       drug          3 first 
 5 a       drug          4 first 
 6 a       drug          5 first 
 7 b       none          0 second
 8 b       drug          1 first 
 9 b       placebo       2 third 
10 b       placebo       3 third 
11 c       none          0 second
12 c       placebo       1 third 
13 c       drug          2 first 
14 c       drug          3 first 
15 c       drug          4 first 
16 c       drug          5 first

问题是标签是根据"治疗"值的字母顺序显示的，但我希望它们按照每个受试者内treatment个值的出现顺序显示.我也试过用levels而不是labels，我只得到了全部NA.

任何帮助都将不胜感激.dplyr解决方案是首选，但很乐意与任何其他解决方案合作.