#Dan Heitjan  dheitjan@biostats.hmc.psu.edu
#
ftupwr <- function(p1,p2,bign,r,alpha) {
## Compute the power of a two-sided level alpha test of the
## hypothesis that pi1=pi2, when pi1=p1, pi2=p2, and there are
## bign observations, bign/(1+r) in group 1 and r*bign/(1+r) in
## group 2.  This is based on the two-tailed test version of
## formula (6) in Fleiss, Tytun and Ury (1980 Bcs 36, 343--346).
## This may be used for del not too small (del>=0.1) and r not
## too big or small (0.33<=r<=3).
##   Daniel F. Heitjan, 30 April 1991
 mstar <- bign/(r+1)
 del <- abs(p2-p1)
 rp1 <- r+1
 zalp <- qnorm(1-alpha/2)
 pbar <- (p1+r*p2)/(1+r)
 qbar <- 1-pbar
 num <- (r*del^2*mstar-rp1*del)^0.5-zalp*(rp1*pbar*qbar)^0.5
 den <- (r*p1*(1-p1)+p2*(1-p2))^0.5
 zbet <- num/den
 pnorm(zbet) }
##
ftuss <- function(p1,p2,r,alpha,beta) {
## Compute the approximate sample size needed to have power 1-beta
## for detecting significance in a two-tailed level alpha test of
## the hypothesis that pi1=pi2, when pi1=p1, pi2=p2, and there
## are to be m in group 1 and rm in group 2.  The calculation is
## based on equations (3) and (4) of Fleiss, Tytun and Ury (1980
## Bcs 36, 343--346).  This is accurate to within 1% for
## moderately large values of del(p2-p1) (del>=0.1) and sample
## sizes that are not too disproportionate (0.5<=r<=2).
##   Daniel F. Heitjan, 30 April 1991
 zalp <- qnorm(1-alpha/2)
 zbet <- qnorm(1-beta)
 rp1 <- (r+1)
 pbar <- (p1+r*p2)/rp1
 qbar <- 1-pbar
 q1 <- 1-p1
 q2 <- 1-p2
 del <- abs(p2-p1)
 num <- (zalp*(rp1*pbar*qbar)^0.5+zbet*(r*p1*q1+p2*q2)^0.5)^2
 den <- r*del^2
 mp <- num/den
 m <- 0.25*mp*(1+(1+2*rp1/(r*mp*del))^0.5)^2
 list(n1=floor(m+1),n2=floor(m*r+1)) }