17/02/06 18:18:03.12 fSw1iVag.net
pLH=TP/FP
nLH=(1-TP)/(1-FP)=FN/TN
DOR=pHL/nLH = (TP/FP)/(FN/TN)
# pr=Disese/Health : prevalance for actual number
PPV=TP/(TP+FP*pr)
(1-PPV)=FP/(TP+FP*pr)
NPV=TN/(TN+FN*pr)
(1-NPV)=FN/(TN+FN*pr)
PPV/(1-PPV) * NPV/(1-NPV) = TP/FP * TN/FN =DOR # for any prevalence
n=1000
set.seed(0)
TPR=runif(n)
set.seed(1)
FPR=runif(n)
pLH=TPR/FPR
nLH=(1-TPR)/(1-FPR)
DOR=pLH/nLH
logit = function(q) log(q/(1-q))
D=logit(TPR)-logit(FPR)
plot(log(DOR),D)
S=logit(TPR)+logit(FPR)
plot(D~S)
f=function(ab) sum((D-(ab[1]+ab[2]*S)^2))
optim(c(-0.1,-0.1),f) # Not Convergent
lm=lm(D~S) ; lm$coef
abline(lm)