# NOT RUN {
# Reproduce Table 1 in Bacchetti (2010). This involves planning a study with
# n1 = n2 = 935 subjects per group, where Group 1 is the control group and
# Group 2 is the treatment group. The outcome in the study is proportion of
# subjects with serious outcomes or death. A negative value for the difference
# in proportions between groups (Group 2 proportion - Group 1 proportion)
# indicates the treatment group has a better outcome. In this table, the
# proportion of subjects in Group 1 with serious outcomes or death is set
# to 3%, 6.5%, and 12%, and the difference in proportions between the two
# groups is set to -2.8 percentage points, -1.4 percentage points, and 0.
ciTableProp(n1 = 935, p1.hat = c(0.03, 0.065, 0.12), n2 = 935,
p2.hat.minus.p1.hat = c(-0.028, -0.014, 0), digits = 3)
# Diff=-0.028 Diff=-0.014 Diff=0
#P1.hat=0.030 [-0.040, -0.015] [-0.029, 0.001] [-0.015, 0.015]
#P1.hat=0.065 [-0.049, -0.007] [-0.036, 0.008] [-0.022, 0.022]
#P1.hat=0.120 [-0.057, 0.001] [-0.044, 0.016] [-0.029, 0.029]
#==========
# Show how the returned data frame has to be modified for cases of small
# sample sizes where not all user-supplied differenes are possible.
ciTableProp(n1 = 5, n2 = 5, p1.hat = c(0.3, 0.6, 0.12), p2.hat = c(0.2, 0.1, 0))
# Diff CI Diff CI Diff CI
#P1.hat=0.4 0.2 [-0.61, 1.00] 0.0 [-0.61, 0.61] 0 [-0.61, 0.61]
#P1.hat=0.6 0.2 [-0.55, 0.95] 0.2 [-0.55, 0.95] 0 [-0.61, 0.61]
#P1.hat=0.2 0.2 [-0.55, 0.95] 0.2 [-0.55, 0.95] 0 [-0.50, 0.50]
#==========
# Suppose we are planning a study to compare the proportion of nondetects at
# a background and downgradient well, and we can use ciTableProp to look how
# the confidence interval for the difference between the two proportions using
# say 36 quarterly samples at each well varies with the observed estimated
# proportions. Here we'll let the argument "p1.hat" denote the proportion of
# nondetects observed at the downgradient well and set this equal to
# 20%, 40% and 60%. The argument "p2.hat.minus.p1.hat" represents the proportion
# of nondetects at the background well minus the proportion of nondetects at the
# downgradient well.
ciTableProp(n1 = 36, p1.hat = c(0.2, 0.4, 0.6), n2 = 36,
p2.hat.minus.p1.hat = c(0.3, 0.15, 0))
# Diff=0.31 Diff=0.14 Diff=0
#P1.hat=0.19 [ 0.07, 0.54] [-0.09, 0.37] [-0.18, 0.18]
#P1.hat=0.39 [ 0.06, 0.55] [-0.12, 0.39] [-0.23, 0.23]
#P1.hat=0.61 [ 0.09, 0.52] [-0.10, 0.38] [-0.23, 0.23]
# We see that even if the observed difference in the proportion of nondetects
# is about 15 percentage points, all of the confidence intervals for the
# difference between the proportions of nondetects at the two wells contain 0,
# so if a difference of 15 percentage points is important to substantiate, we
# may need to increase our sample sizes.
# }
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