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epi.ssxsectn <- function(N = NA, pdexp1, pdexp0, pexp = NA, n, power, r = 1, design = 1, sided.test = 2, nfractional = FALSE, conf.level = 0.95){
alpha.new <- (1 - conf.level) / sided.test
z.alpha <- qnorm(1 - alpha.new, mean = 0, sd = 1)
if (!is.na(pdexp1) & !is.na(n) & !is.na(power)){
stop("Error: at least one of exposed, n and power must be NA.")
}
# Sample size:
if(!is.na(pdexp1) & !is.na(pdexp0) & is.na(n) & !is.na(power)){
# Sample size estimate. From Woodward p 405:
z.beta <- qnorm(power, mean = 0, sd = 1)
# Prevalence ratio:
lambda <- pdexp1 / pdexp0
# Odds ratio:
psi <- (pdexp1 / (1 - pdexp1)) / (pdexp0 / (1 - pdexp0))
pi <- pdexp0
pc <- (pi * ((r * lambda) + 1)) / (r + 1)
p1 <- (r + 1) / (r * (lambda - 1)^2 * pi^2)
p2 <- z.alpha * sqrt((r + 1) * pc * (1 - pc))
p3 <- z.beta * sqrt((lambda * pi * (1 - (lambda * pi))) + (r * pi * (1 - pi)))
n0 <- p1 * (p2 + p3)^2
# Account for the design effect:
n0 <- n0 * design
# Finite population correction:
n <- ifelse(is.na(N), n0, (n0 * N) / (n0 + (N - 1)))
n.exp1 <- ifelse(nfractional == TRUE, n / (r + 1) * r, ceiling(n / (r + 1) * r))
n.exp0 <- ifelse(nfractional == TRUE, n / (r + 1) * 1, ceiling(n / (r + 1) * 1))
n.total <- n.exp1 + n.exp0
rval <- list(n.total = n.total, n.exp1 = n.exp1, n.exp0 = n.exp0, power = power, pr = lambda, or = psi)
}
# Power:
else
if(!is.na(pdexp1) & !is.na(pdexp0) & !is.na(n) & is.na(power)){
# Study power. From Woodward p 409:
# Prevalence ratio:
lambda <- pdexp1 / pdexp0
# Odds ratio:
psi <- (pdexp1 / (1 - pdexp1)) / (pdexp0 / (1 - pdexp0))
pi <- pdexp0
pc <- (pi * ((r * lambda) + 1)) / (r + 1)
if(nfractional == TRUE){
n.exp1 <- n / (r + 1) * r
n.exp0 <- n / (r + 1) * 1
n.total <- n.exp1 + n.exp0
}
if(nfractional == FALSE){
n.exp1 <- ceiling(n / (r + 1) * r)
n.exp0 <- ceiling(n / (r + 1) * 1)
n.total <- n.exp1 + n.exp0
}
# Convert n (finite corrected sample size) to n0:
n0 <- ifelse(!is.na(N), (n * N - n) / (N - n), n)
t1 <- ifelse(lambda >= 1,
(pi * (lambda - 1) * sqrt(n0 * r)),
(pi * (1 - lambda) * sqrt(n0 * r)))
t2 <- z.alpha * (r + 1) * sqrt(pc * (1 - pc))
t3 <- (r + 1) * (lambda * pi * (1 - lambda * pi) + r * pi * (1 - pi))
z.beta <- (t1 - t2) / sqrt(t3)
power <- pnorm(z.beta, mean = 0, sd = 1)
rval <- list(n.total = n.total, n.exp1 = n.exp1, n.exp0 = n.exp0, power = power, pr = lambda, or = psi)
}
# Lambda:
else
if(is.na(pdexp1) & !is.na(pdexp0) & !is.na(n) & !is.na(power)){
# Risk ratio to be detected - requires an estimate of prevalence of exposure in the unexposed.
# From Woodward p 409:
z.beta <- qnorm(power, mean = 0, sd = 1)
pi <- pdexp0
if(nfractional == TRUE){
n.exp1 <- n / (r + 1) * r
n.exp0 <- n / (r + 1) * 1
n.total <- n.exp1 + n.exp0
}
if(nfractional == FALSE){
n.exp1 <- ceiling(n / (r + 1) * r)
n.exp0 <- ceiling(n / (r + 1) * 1)
n.total <- n.exp1 + n.exp0
}
# Convert n (finite corrected sample size) to n0:
n0 <- ifelse(!is.na(N), (n * N - n) / (N - n), n)
Y <- r * n0 * pi^2
Z <- (r + 1) * pi * (z.alpha + z.beta)^2
a <- Y + (pi * Z)
b <- (2 * Y) + Z
c <- Y - (r * (1 - pi) * Z)
# Risk ratio:
lambda.pos <- (1 / (2 * a)) * (b + sqrt(b^2 - 4 * a * c))
lambda.neg <- (1 / (2 * a)) * (b - sqrt(b^2 - 4 * a * c))
rlambda.pos <- lambda.pos
rlambda.neg <- ifelse(lambda.neg < 0, 0, lambda.neg)
# From http://www.epigear.com/index_files/or2rr.html:
# s = prevalence of disease in the population
# p = prevalence of exposure in the population
# Prevalence of disease in the exposed, unexposed and population:
pdexp1.pos <- lambda.pos * pdexp0
pdexp0.pos <- pdexp0
s.pos <- (pdexp1.pos + pdexp0.pos) / 2
p.pos <- pexp
pdexp1.neg <- lambda.neg * pdexp0
pdexp0.neg <- pdexp0
s.neg <- (pdexp1.neg + pdexp0.neg) / 2
p.neg <- pexp
# Odds ratio:
psi.pos <- (lambda.pos * (1 - (s.pos / (p.pos * lambda.pos + 1 - p.pos)))) /
(1 - ((lambda.pos * s.pos) / (p.pos * lambda.pos + 1 - p.pos)))
psi.neg <- (lambda.neg * (1 - (s.neg / (p.neg * lambda.neg + 1 - p.neg)))) /
(1 - ((lambda.neg * s.neg) / (p.neg * lambda.neg + 1 - p.neg)))
rpsi.pos <- psi.pos
rpsi.neg <- ifelse(psi.neg < 0, 0, psi.neg)
rval <- list(n.total = n.total, n.exp1 = n.exp1, n.exp0 = n.exp0, power = power, pr = sort(c(rlambda.neg, rlambda.pos)), or = sort(c(rpsi.neg, rpsi.pos)))
}
rval
}
# epi.ssxsection(pdexp1 = 0.25, pdexp0 = 0.10, pexp = 0.05, n = NA, power = 0.80, r = 1, design = 1, sided.test = 2, conf.level = 0.95)
# epi.ssxsection(pdexp1 = 0.25, pdexp0 = 0.10, pexp = 0.05, n = 200, power = NA, r = 1, design = 1, sided.test = 2, conf.level = 0.95)
# epi.ssxsection(pdexp1 = NA, pdexp0 = 0.10, pexp = 0.05, n = 200, power = 0.80, r = 1, design = 1, sided.test = 2, conf.level = 0.95)
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