1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
|
"epi.sscompb" <- function(N = NA, treat, control, 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(treat) & !is.na(control) & !is.na(n) & !is.na(power)){
stop("Error: at least one of treat, n and power must be NA.")
}
# Sample size.
if (!is.na(treat) & !is.na(control) & is.na(n) & !is.na(power)) {
z.beta <- qnorm(power, mean = 0, sd = 1)
delta <- abs(treat - control)
lambda <- treat / control
# Woodward (2014) page 312,
n <- (1 / delta^2) * ((z.alpha * sqrt(treat * (1 - treat))) + (z.beta * sqrt(control * (1 - control))))^2
# From Woodward's spreadsheet. Changed 130814:
# lambda <- treat / control
# Pc <- control * (r * lambda + 1) / (r + 1)
# T1 <- (r + 1) / (r * (lambda - 1)^2 * control^2)
# T2 <- (r + 1) * Pc *(1 - Pc)
# T3 <- lambda * control * (1 - lambda * control) + r * control * (1 - control)
# n <- T1 * (z.alpha * sqrt(T2) + z.beta * sqrt(T3))^2
n1 <- (n / (1 + r)) * design
n0 <- r * n1
n.total <- n0 + n1
p1 <- n1 / n.total
p0 <- n0 / n.total
# Finite population correction:
n.total <- ifelse(is.na(N), n.total, (n.total * N) / (n.total + (N - 1)))
n1 <- ifelse(is.na(N), n1, p1 * n.total)
n0 <- ifelse(is.na(N), n0, p0 * n.total)
# Fractional:
n1 <- ifelse(nfractional == TRUE, n1, ceiling(n1))
n0 <- ifelse(nfractional == TRUE, n0, ceiling(n0))
n.total <- n1 + n0
rval <- list(n.total = n.total, n.treat = n1, n.control = n0, power = power, lambda = sort(c(lambda, 1 / lambda)))
}
# Power.
else
if (!is.na(treat) & !is.na(control) & !is.na(n) & is.na(power)) {
if(nfractional == TRUE){
n1 <- n / (r + 1)
n1 <- n1 * design
n0 <- r * n1
n.total <- n1 + n0
}
if(nfractional == FALSE){
n1 <- n / (r + 1)
n1 <- ceiling(n1 * design)
n0 <- ceiling(r * n1)
n.total <- n1 + n0
}
# From Woodward's spreadsheet. Changed 130814:
# lambda <- control / treat
# Pc <- treat * (r * lambda + 1) / (r + 1)
# T1 <- ifelse(lambda >= 1, treat * (lambda - 1) * sqrt(n * r), treat * (1 - lambda) * sqrt(n * r))
# T2 <- z.alpha * (r + 1) * sqrt(Pc * (1 - Pc))
# T3 <- (r + 1) * (lambda * treat * (1 - lambda * treat) + r * treat * (1 - treat))
# z.beta <- (T1 - T2) / sqrt(T3)
delta <- abs(treat - control)
lambda <- treat / control
z.beta <- ((delta * sqrt(n)) - (z.alpha * sqrt(treat * (1 - treat)))) / (sqrt(control * (1 - control)))
power <- pnorm(z.beta, mean = 0, sd = 1)
rval <- list(n.total = n.total, n.treat = n1, n.control = n0, power = power, lambda = sort(c(lambda, 1 / lambda)))
}
# Lambda:
else
if (is.na(treat) & !is.na(control) & !is.na(n) & !is.na(power)) {
z.beta <- qnorm(power, mean = 0, sd = 1)
if(nfractional == TRUE){
n1 <- n / (r + 1)
n1 <- n1 * design
n0 <- r * n1
n.total <- n1 + n0
}
if(nfractional == FALSE){
n1 <- n / (r + 1)
n1 <- ceiling(n1 * design)
n0 <- ceiling(r * n1)
n.total <- n1 + n0
}
# Here we use the formulae for study power (Woodward page 312) and then solve for treat which then allows us to calculate lambda.
Pfun <- function(treat, control, n, r, z.alpha) {
delta <- treat - control
lambda <- treat / control
z.beta <- ((delta * sqrt(n)) - (z.alpha * sqrt(treat * (1 - treat)))) / (sqrt(control * (1 - control)))
# lambda <- control / treat
# Pc <- treat * (r * lambda + 1) / (r + 1)
# T1 <- treat * (lambda - 1) * sqrt(n * r)
# T2 <- z.alpha * (r + 1) * sqrt(Pc * (1 - Pc))
# T3 <- (r + 1) * (lambda * treat * (1 - lambda * treat) + r * treat * (1 - treat))
# z.beta <- (T1 - T2) / sqrt(T3)
pnorm(z.beta, mean = 0, sd = 1) - power
}
etreat <- uniroot(Pfun, control = control, n = n, r = r, z.alpha = z.alpha, interval = c(1e-06, 1))$root
rval <- list(n.total = n.total, n.treat = n1, n.control = n0, power = power, lambda = sort(c(etreat / control, control / etreat)))
}
rval
}
|
