Common Odds Ratio - R Udf

Question

[zx8754]

If you kindly paste SNP1,5220,26,0,810,30,1 as input on this website, it gives out Armitage's trend test common odds ratio of Odds_ratio=8.568. At the bottom of the page they explain what it means as below:

Common odds ratio:    (Case_12*Control_11/N01 + Case_22*Control_12/N12 + 4*(Case_22*Control_11/N02))/
(Case_11*Control_12/N01 + Case_12*Control_22/N12 + 4*(Case_22*Control_11*Case_11*Control_22)**0.5/N02)

Question: I am trying to make an R function, but not sure what N01, N12, N02 mean? Or do you know of an existing R function that would give the same result?

So far, before making it into a function, I am trying to break down the formula so I can get the same result as in the website:

d <- structure(c(5220L, 810L, 26L, 30L, 0L, 1L),
               .Dim = 2:3,
               .Dimnames = structure(
                 list(
                   caco = c("0", "1"), 
                   snp1 = c("CC", "CT", "TT")),
                 .Names = c("caco","snp1")),
               class = "table")
# snp1
# caco   CC   CT   TT
# 0 5220   26    0
# 1  810   30    1

#Assign Variables
Control_11 <- d[1,1]
Control_12 <- d[1,2]
Control_22 <- d[1,3]
Case_11 <- d[2,1]
Case_12 <- d[2,2]
Case_22 <- d[2,3]

#Doesn't work - OR=5986.03
# N01 <- Control_11 + Case_11
# N12 <- Control_12 + Case_12
# N02 <- Control_22 + Case_22

#Doesn't work - OR=214.8141
# N01 <- (Control_11 + Case_11)*2 + Control_12 + Case_12
# N12 <- Control_12 + Case_12
# N02 <- (Control_22 + Case_22)*2 + Control_12 + Case_12

#Return OR - Correct OR should be 8.568
(Case_12*Control_11/N01
 + Case_22*Control_12/N12
 + 4*(Case_22*Control_11/N02))/
  (Case_11*Control_12/N01
   + Case_12*Control_22/N12
   + 4*(Case_22*Control_11*Case_11*Control_22)**0.5/N02)

EDIT: Tried following, close but not the same result:

#Doesn't work - OR=7.59501 - Probably rounding?
N01 <- Case_11 + Case_12 + Case_22 
N02 <- Control_11 + Control_12 + Control_22
N12 <- N01 + N02

[Alex Reynolds]

Have you contacted the developers to ask for source or at least a top-level description of their work? If their research is reproducible, they should be able to provide (pseudo) code to show how the analysis works.

[zx8754]

Contacted them today to explain what N01, N02, N12 variables mean. If I hear anything I will update this post.

Answer 1

[zx8754]

Found the solution, the formula was adopted from Peter D. Sasieni - "From Genotypes to Genes: Doubling the Sample Size" (Biometrics 1997). There was inconsistency how the variables were named on the paper and on the adopted website.

Here is the working R function:

udf_CommonOddsRatio <- function(d) 
{ 
  # Armitage's trend test - common odds ratio
  # http://ihg.gsf.de/cgi-bin/hw/hwa2.pl
  # 
  # Peter D. Sasieni - "From Genotypes to Genes: Doubling the Sample Size"
  # (Biometrics 1997)
  # 
  # Example data - class=table
  # d <- structure(c(5220L, 810L, 26L, 30L, 0L, 1L),
  #                .Dim = 2:3,
  #                .Dimnames = structure(
  #                  list(
  #                    caco = c("0", "1"), 
  #                    snp1 = c("CC", "CT", "TT")),
  #                  .Names = c("caco","snp1")),
  #                class = "table")
  # snp1
  # caco   CC   CT   TT
  # 0 5220   26    0
  # 1  810   30    1

  #Assign Variables
  Control_11 <- d[1,1]
  Control_12 <- d[1,2]
  Control_22 <- d[1,3]
  Case_11 <- d[2,1]
  Case_12 <- d[2,2]
  Case_22 <- d[2,3]

  N01 <- Case_11 + Control_11 + Case_12 + Control_12
  N02 <- Case_11 + Control_11 + Case_22 + Control_22
  N12 <- Case_12 + Control_12 + Case_22 + Control_22

  #Return OR
  return(
    (Case_12*Control_11/N01
     + Case_22*Control_12/N12
     + 4*(Case_22*Control_11/N02))/
      (Case_11*Control_12/N01
       + Case_12*Control_22/N12
       + 4*(Case_22*Control_11*Case_11*Control_22)**0.5/N02)
  )
}