Exploring Lift and Relative Risk

gistfile1.txt

# lift:  p(x,y) /  ( p(x)*p(y)   == ratio of 'overage' compared to independence

# rr = relative risk  ==   p(x+|y+)  /  p(x-|y-)   

rr_more <- function(n){
	m <- matrix(rmultinom(1,n,c(1,2,3,4)),c(2,2))
	rownames(m) <- colnames(m) <- c(T,F)
	R <- rowSums(m) 
 	C <- colSums(m)
	lift <- m[1,1] / (R[1] * C[1] / n) 
	rr <- (m[1,1] / R[1]) / (m[2,1] / R[2])
	pred <- rowSums(m) %*% t(colSums(m)) / (n)
	save <- m[1,1] - pred[1,1]
	return (list(obs=m, pred=pred, lift=lift, rr=rr, save=save, R=R, C=C))
}

# suggested call:  rr_more(100)

# Assertion:
# "number of people we would save by fixing factor"
# is  p(outcome) * p(factor) * (1 - lift) * N
# because:
# if outcome and factor were independent, you would have
# p(o) * p(f) * N  people.  (i.e., lift of 1)