### B. Balgooyen
### 08/16/01
###
### COMPARISON OF INCIDENCE RATES -- EXACT TEST (2-sided)
###
### This test appears in the text: FUNDAMENTALS OF BIOSTATISTICS By Bernard Rosner (pg. 686)
###
###
### Let P = true proportion of events in group 1.
### To test the hypothesis  Ho: ID(1) = ID(2)       (or equivalently, P=Po) 
###                         H1: ID(1) not(=) ID(2)  (or equivalently, P not(=) Po)
###		Where:
### 		ID(1) = true incidence density in group 1
###			ID(2) = true incidence density in group 2
###			Po    = t1/(t1+t2),  Qo=1-Po
 




a1 <- 5					# Let a1 = the observed number of events in group 1
a2 <- 2					# Let a2 = the observed number of events in group 2

t1 <- 85424    			# let t1 = total event time in group 1 
t2 <- 264579				# let t2 = total event time in group 2


Po <- t1/(t1 + t2)
Qo <- 1-Po

if (a1 < (a1+a2)*Po)
	low.limit <- 0
	
if (a1 < (a1+a2)*Po)
	up.limit <- a1
	
if (a1 >= (a1 + a2)*Po)
	low.limit <- a1
	
if (a1 >= (a1 + a2)*Po)
	up.limit <- a1+a2

	
sum.vector<-c()			# Set sum.vector to empty set


for (i in low.limit:up.limit){
	one.sum <- choose(a1+a2,i)*Po^i*Qo^((a1+a2)-i)
	sum.vector <- c(sum.vector,one.sum)
}

binom.result <- sum(sum.vector)
p.value <- 2*binom.result
print(p.value)			# The result for the 2-sided p-value