How can I test statistic difference/comparability between these two specific study groups?

Question

I have two groups stored in the covariate dose - which are coded as either 0 or 1 corresponding to a specific drug. However, each group consist of multiple patients with individually different stages of their cancer disease - defined in the covariate WHO. There are four different WHO stages ranging from 1 to 4, with 1 being the most benign and 4 the most malignant.

I am conducting survival analyses. However, as one intuitively may suspect, a group of higher WHO-stages might confound the overall probability of survival in the study group.

Can I test (and how in R) whether there is a significant difference between the dose==0 and dose==1 study group, when it comes to WHO-gradings? Are the two groups comparable?

My data
p <- structure(list(WHO = c(1L, 2L, 2L, 3L, 2L, 3L, 1L, 2L, 3L, 3L, 
3L, 1L, 2L, 1L, 2L, 3L, 3L, 1L, 2L, 1L, 3L, 1L, 1L, 1L, 1L, 1L, 
1L, 2L, 4L, 4L, 1L, 4L, 1L, 2L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 3L, 
3L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 2L, 1L, 2L, 2L, 4L, 4L, 4L, 2L, 
4L, 1L, 4L, 4L, 2L, 4L, 4L, 3L, 4L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 4L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
3L, 2L, 2L, 3L, 3L, 3L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L), dose = structure(c(1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 
0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 
0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 
0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1), class = "AsIs")), .Names = c("WHO", 
"dose"), class = "data.frame", row.names = c(1L, 4L, 5L, 6L, 
7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 16L, 17L, 18L, 19L, 
20L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 31L, 32L, 
33L, 34L, 35L, 36L, 37L, 38L, 39L, 40L, 41L, 42L, 43L, 44L, 45L, 
46L, 47L, 48L, 49L, 50L, 51L, 52L, 53L, 54L, 55L, 56L, 57L, 58L, 
59L, 60L, 61L, 62L, 63L, 64L, 65L, 66L, 67L, 68L, 69L, 70L, 71L, 
72L, 73L, 74L, 75L, 76L, 77L, 78L, 79L, 80L, 81L, 82L, 83L, 84L, 
85L, 86L, 87L, 88L, 89L, 90L, 91L, 92L, 93L, 94L, 95L, 96L, 97L, 
98L, 99L, 100L, 101L, 102L, 103L, 104L, 105L, 106L))

Answer 1

You could do a basic regression with dose as a dummy, see that it is insignificant. You get equivalent results if you do a probit, and flip dose to the dependent variable. To be more robust though, you can do a test for independence between the two. Looking at the distance correlation, you can see that they are independent. The R code for that is simply: library(energy) dcor.ttest(p$\$$WHO,p$\$$dose, distance = FALSE)