Odds ratio, distance and relative chance in contingency tables

odds.R

# Written by Gustavo A. Ballen (gaballench  at  gmail.com)
# https://github.com/gaballench

# The input for this function is a contingency table of class 'xtabs' or 'table' with exposure in rows and cases in columns.
# Internally it uses the 'pi' notation, or for those using ABCD notation there is an equivalence below:

## Model table is as follows
#                  illness
# exp          NO            YES
# NO        D(1-pi0)       C(1-pi1)
# YES        B(pi0)         A(pi1)

# The function presents two arguments. 'data' for the object to be analized, and outcome, a string with three posibilities:
# 'distance', 'relative' (default), and 'ratio'.
# For 'distance' the formula d = pi1 - pi0 is returned
# For 'relative' the quotient (i.e., relative risk) r = pi1/pi0 is returned
# For 'ratio' the odds ratio is returned
# For further details consult Szumilas, M (2010) available below:
# http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2938757/

odds <- function(data, outcome = "relative") {
    margins = apply(data, 1, FUN = sum)
    #marginsCol = apply(data, 2, FUN = sum)
    pi0 = data[2, 1]/margins[2]
    pi1 = data[2, 2]/margins[2]
    minuspi0 = data[1, 1]/margins[1] # 1 - pi0
    minuspi1 = data[1, 2]/margins[1] # 1 - pi1
    d = pi1 - pi0
    r = pi1/pi0
    omega0 = pi0/minuspi0
    omega1 = pi1/minuspi1
    omega = omega1/omega0
    prevalence = marginsCol[2]/sum(marginsCol)
    sensitivity = pi1/(pi1+minuspi1)
    specificity = minuspi0/(minuspi1+pi0)
    pos_pred_val = pi1/(pi1+pi0)
    neg_pred_val = minuspi0/(minuspi0+minuspi1)
    if(outcome == "ratio") {
        return(omega)
    }
    if(outcome == "distance"){
        return(d)
    }
    if(outcome == "relative") {
        return(r)
    }
}