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zRRscore <- function(dat, conf.level){
N. <- 1 - ((1 - conf.level) / 2)
z <- qnorm(N., mean = 0, sd = 1)
# See https://users.stat.ufl.edu/~aa/cda/R/two-sample/R2/index.html and function PropCIs::riskscoreci
# a <- as.numeric(dat[1])
# b <- as.numeric(dat[3])
# c <- as.numeric(dat[2])
# d <- as.numeric(dat[4])
a <- as.numeric(dat[1])
b <- as.numeric(dat[2])
c <- as.numeric(dat[3])
d <- as.numeric(dat[4])
N1 <- a + b
N0 <- c + d
scRR.p <- (a / N1) / (c / N0)
if ((c == 0) && (a == 0)){
scRR.ll = 0
scRR.ul = Inf
}
else{
a1 <- N0 * (N0 * (N0 + N1) * a + N1 * (N0 + a) * (z^2))
a2 <- -N0 * (N0 * N1 * (c + a) + 2 * (N0 + N1) * c * a + N1 * (N0 + c + 2 * a) * (z^2))
a3 <- 2 * N0 * N1 * c * (c + a) + (N0 + N1) * (c^2) * a + N0 * N1 * (c + a) * (z^2)
a4 <- -N1 * (c ^ 2) * (c + a)
b1 <- a2 / a1
b2 <- a3 / a1
b3 <- a4 / a1
c1 <- b2 - (b1^2) / 3
c2 <- b3 - b1 * b2 / 3 + 2 * (b1^3) / 27
# Argument x for acos must be between -1 and +1. Changed 280722.
acos.x <- sqrt(27) * c2 / (2 * c1 * sqrt(-c1))
acos.x <- ifelse(acos.x <= -1 | acos.x >= 1, 0, acos.x)
ceta <- acos(acos.x)
t1 <- -2 * sqrt(-c1 / 3) * cos(pi / 3 - ceta / 3)
t2 <- -2 * sqrt(-c1 / 3) * cos(pi / 3 + ceta / 3)
t3 <- 2 * sqrt(-c1 / 3) * cos(ceta / 3)
p01 <- t1 - b1 / 3
p02 <- t2 - b1 / 3
p03 <- t3 - b1 / 3
p0sum <- p01 + p02 + p03
p0up <- min(p01, p02, p03)
p0low <- p0sum - p0up - max(p01, p02, p03)
if((c == 0) && (a != 0)){
scRR.ll <- (1 - (N1 - a) * (1 - p0low) / (c + N1 - (N0 + N1) * p0low)) / p0low
scRR.ul <- Inf
}
else if((c != N0) && (a == 0)){
scRR.ll <- 0
scRR.ul <- (1 - (N1 - a) * (1 - p0up) / (c + N1 - (N0 + N1) * p0up)) / p0up
}
else if((c == N0) && (a == N1)){
scRR.ll <- N1 / (N1 + z^2)
scRR.ul <- (N0 + z^2) / N0
}
else if((a == N1) || (c == N0)){
if((c == N0) && (a == 0)) {
scRR.ll <- 0
}
if((c == N0) && (a != 0)) {
x1 <- a
n1 <- N1
x2 <- c
n2 <- N0
phat1 <- x2 / n2
phat2 <- x1 / n1
phihat <- phat2 / phat1
phil <- conf.level * phihat
chi2 <- 0
while (chi2 <= z){
a. <- (n2 + n1) * phil
b. <- -((x2 + n1) * phil + x1 + n2)
c. <- x2 + x1
p1hat <- (-b. - sqrt(b.^2 - 4 * a. * c.)) / (2 * a.)
p2hat <- p1hat * phil
q2hat <- 1 - p2hat
var <- (n2 * n1 * p2hat) / (n1 * (phil - p2hat) + n2 * q2hat)
chi2 <- ((x1 - n1 * p2hat) / q2hat) / sqrt(var)
scRR.ll <- phil
phil <- scRR.ll / 1.0001}
}
i <- c
j <- a
ni <- N0
nj <- N1
if(a == N1){
i <- a
j <- c
ni <- N1
nj <- N0
}
phat1 <- i / ni
phat2 <- j / nj
phihat <- phat2 / phat1
phiu <- 1.1 * phihat
if((c == N0) && (a == 0)) {
if(N0 < 100) {
phiu = 0.01
}
else {phiu = 0.001
}
}
chi1 <- 0
while (chi1 >= -z){
a. <- (ni + nj) * phiu
b. <- -((i + nj) * phiu + j + ni)
c. <- i + j
p1hat <- (-b. - sqrt(b.^2 - 4 * a. * c.)) / (2 * a.)
p2hat <- p1hat * phiu
q2hat <- 1 - p2hat
var <- (ni * nj * p2hat) / (nj * (phiu - p2hat) + ni * q2hat)
chi1 <- ((j - nj * p2hat) / q2hat) / sqrt(var)
phiu1 <- phiu
phiu <- 1.0001 * phiu1
}
if(a == N1) {
scRR.ll <- 1 / phiu1
scRR.ul <- (1 - (N1 - a) * (1 - p0up) / (c + N1 - (N0 + N1) * p0up)) / p0up
}
else{scRR.ul <- phiu1}
}
else{
scRR.ll <- (1 - (N1 - a) * (1 - p0low) / (c + N1 - (N0 + N1) * p0low)) / p0low
scRR.ul <- (1 - (N1 - a) * (1 - p0up) / (c + N1 - (N0 + N1) * p0up)) /p0up
}
}
c(scRR.p, scRR.ll, scRR.ul)
}
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