Sample.Size: Sample size calculation
In Sample.Size: Sample size calculation
Description
Usage
Arguments
Value
Author(s)
Examples
Description
Computes the required sample size using the optimal designs with multiple constraints proposed in Mayo et al.(2010). This optimal method is designed for two-arm, randomized phase II clinical trials, and the required sample size can be optimized either using fixed or flexible randomization allocation ratios.
Usage
1
Sample.Size(pi_c, pi_e, gamma_c, gamma_e, gamma_delta, Allratio_c = NA, Allratio_e = NA)
Arguments
pi_c
Response rate for control
pi_e
Response rate for experiment
gamma_c
Upper bound for gammaC
gamma_e
Upper bound for gammaE
gamma_delta
Upper bound for gammaDelta
Allratio_c
Allocation Design
Allratio_e
Allocation Design
Value
Prints required sample sizes, 1 to 1 allocation design and 1 to 3 allocation design
Author(s)
Wei Jiang, Jonathan Mahnken, Matthew Mayo
Maintainer: Wei Jiang<wjiang@kumc.edu>
Examples
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Sample.Size(0.3, 0.6, 0.15, 0.15, 0.15, Allratio_c = 1, Allratio_e = 3)
Sample.Size(0.3, 0.6, 0.15, 0.15, 0.15)
## The function is currently defined as
function (pi_c, pi_e, gamma_c, gamma_e, gamma_delta, Allratio_c = NA,
Allratio_e = NA)
{
c1 <- 1
e1 <- 1
dmax1 <- ceiling(max(((pi_c * (1 - pi_c))/(c1 * gamma_c^2)),
((pi_e * (1 - pi_e))/(e1 * gamma_e^2)), ((pi_c * (1 -
pi_c) + (c1/e1) * pi_e * (1 - pi_e))/(c1 * gamma_delta^2))))
nc_fixed1 <- c1 * dmax1
ne_fixed1 <- e1 * dmax1
n_fixed1 <- nc_fixed1 + ne_fixed1
nc_ast <- (pi_c * (1 - pi_c) + sqrt(pi_c * (1 - pi_c) * pi_e *
(1 - pi_e)))/gamma_delta^2
ne_ast <- pi_e * (1 - pi_e) * (gamma_delta^2 - pi_c * (1 -
pi_c) * nc_ast^(-1))^(-1)
nc_prime <- pi_c * (1 - pi_c)/gamma_c^2
fnc_prime <- pi_e * (1 - pi_e) * (gamma_delta^2 - pi_c *
(1 - pi_c) * nc_prime^(-1))^(-1)
ne_prime <- pi_e * (1 - pi_e)/gamma_e^2
fne_prime <- pi_c * (1 - pi_c) * (gamma_delta^2 - pi_e *
(1 - pi_e) * ne_prime^(-1))^(-1)
if (nc_ast > nc_prime & ne_ast > ne_prime) {
c1 <- ceiling(nc_ast)
e1 <- floor(ne_ast)
c2 <- floor(nc_ast)
e2 <- ceiling(ne_ast)
dmax1 <- max(((pi_c * (1 - pi_c))/(c1 * gamma_c^2)),
((pi_e * (1 - pi_e))/(e1 * gamma_e^2)), ((pi_c *
(1 - pi_c) + (c1/e1) * pi_e * (1 - pi_e))/(c1 *
gamma_delta^2)))
dmax2 <- max(((pi_c * (1 - pi_c))/(c2 * gamma_c^2)),
((pi_e * (1 - pi_e))/(e2 * gamma_e^2)), ((pi_c *
(1 - pi_c) + (c2/e2) * pi_e * (1 - pi_e))/(c2 *
gamma_delta^2)))
if (dmax1 <= 1) {
nc_flex <- ceiling(nc_ast)
ne_flex <- floor(ne_ast)
n_flex <- nc_flex + ne_flex
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
}
else if (dmax2 <= 1) {
nc_flex <- floor(nc_ast)
ne_flex <- ceiling(ne_ast)
n_flex <- nc_flex + ne_flex
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
}
else {
nc_flex <- ceiling(nc_ast)
ne_flex <- ceiling(ne_ast)
n_flex <- nc_flex + ne_flex
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
}
}
else if (nc_ast <= nc_prime & ne_ast > ne_prime) {
c1 <- ceiling(nc_prime)
e1 <- floor(max(fnc_prime, ne_prime))
dmax1 <- max(((pi_c * (1 - pi_c))/(c1 * gamma_c^2)),
((pi_e * (1 - pi_e))/(e1 * gamma_e^2)), ((pi_c *
(1 - pi_c) + (c1/e1) * pi_e * (1 - pi_e))/(c1 *
gamma_delta^2)))
if (dmax1 <= 1) {
nc_flex <- ceiling(nc_prime)
ne_flex <- floor(max(fnc_prime, ne_prime))
n_flex <- nc_flex + ne_flex
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
}
else {
nc_flex <- ceiling(nc_prime)
ne_flex <- ceiling(max(fnc_prime, ne_prime))
n_flex <- nc_flex + ne_flex
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
}
}
else if (nc_ast > nc_prime & ne_ast <= ne_prime) {
c1 <- floor(max(fne_prime, nc_prime))
e1 <- ceiling(ne_prime)
dmax1 <- max(((pi_c * (1 - pi_c))/(c1 * gamma_c^2)),
((pi_e * (1 - pi_e))/(e1 * gamma_e^2)), ((pi_c *
(1 - pi_c) + (c1/e1) * pi_e * (1 - pi_e))/(c1 *
gamma_delta^2)))
if (dmax1 <= 1) {
nc_flex <- floor(max(fne_prime, nc_prime))
ne_flex <- ceiling(ne_prime)
n_flex <- nc_flex + ne_flex
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
}
else {
nc_flex <- ceiling(max(fne_prime, nc_prime))
ne_flex <- ceiling(ne_prime)
n_flex <- nc_flex + ne_flex
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
}
}
else if (nc_ast <= nc_prime & ne_ast <= ne_prime) {
nc_flex <- ceiling(nc_prime)
ne_flex <- ceiling(ne_prime)
n_flex <- nc_flex + ne_flex
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
}
cat("Specified values for parameters:", "\n")
cat("Response rates:", "\n", paste("control =", pi_c, "experiment =",
pi_e), "\n")
cat("Upper bounds for constriants:", "\n", "gammaC =", gamma_c,
"gammaE =", gamma_e, "gammaDelta =", gamma_delta, "\n",
"\n", "\n")
cat("Required sample sizes:", "\n")
cat("[1] Optimal Design:", "\n", paste("nc =", nc_flex, "ne =",
ne_flex, "n =", n_flex), "\n")
cat("[2] 1 to 1 Allocation Design:", "\n", paste("nc =",
nc_fixed1, "ne =", ne_fixed1, "n =", n_fixed1), "\n")
if (!is.na(Allratio_c) | !is.na(Allratio_e)) {
c <- Allratio_c
e <- Allratio_e
dmax <- ceiling(max(((pi_c * (1 - pi_c))/(c * gamma_c^2)),
((pi_e * (1 - pi_e))/(e * gamma_e^2)), ((pi_c * (1 -
pi_c) + (c/e) * pi_e * (1 - pi_e))/(c * gamma_delta^2))))
nc_fixed <- c * dmax
ne_fixed <- e * dmax
n_fixed <- nc_fixed + ne_fixed
sample_fixed2 <- data.frame(nc_fixed, ne_fixed, n_fixed)
cat(paste("[3]", c, "to", e, "Allocation Design:"), "\n",
paste("nc =", nc_fixed, "ne =", ne_fixed, "n =",
n_fixed), "\n")
}
}
Sample.Size documentation built on May 1, 2019, 7:57 p.m.
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Description Usage Arguments Value Author(s) Examples
Description
Computes the required sample size using the optimal designs with multiple constraints proposed in Mayo et al.(2010). This optimal method is designed for two-arm, randomized phase II clinical trials, and the required sample size can be optimized either using fixed or flexible randomization allocation ratios.
Usage
1 | Sample.Size(pi_c, pi_e, gamma_c, gamma_e, gamma_delta, Allratio_c = NA, Allratio_e = NA)
|
Arguments
pi_c |
Response rate for control |
pi_e |
Response rate for experiment |
gamma_c |
Upper bound for gammaC |
gamma_e |
Upper bound for gammaE |
gamma_delta |
Upper bound for gammaDelta |
Allratio_c |
Allocation Design |
Allratio_e |
Allocation Design |
Value
Prints required sample sizes, 1 to 1 allocation design and 1 to 3 allocation design
Author(s)
Wei Jiang, Jonathan Mahnken, Matthew Mayo Maintainer: Wei Jiang<wjiang@kumc.edu>
Examples
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 | Sample.Size(0.3, 0.6, 0.15, 0.15, 0.15, Allratio_c = 1, Allratio_e = 3)
Sample.Size(0.3, 0.6, 0.15, 0.15, 0.15)
## The function is currently defined as
function (pi_c, pi_e, gamma_c, gamma_e, gamma_delta, Allratio_c = NA,
Allratio_e = NA)
{
c1 <- 1
e1 <- 1
dmax1 <- ceiling(max(((pi_c * (1 - pi_c))/(c1 * gamma_c^2)),
((pi_e * (1 - pi_e))/(e1 * gamma_e^2)), ((pi_c * (1 -
pi_c) + (c1/e1) * pi_e * (1 - pi_e))/(c1 * gamma_delta^2))))
nc_fixed1 <- c1 * dmax1
ne_fixed1 <- e1 * dmax1
n_fixed1 <- nc_fixed1 + ne_fixed1
nc_ast <- (pi_c * (1 - pi_c) + sqrt(pi_c * (1 - pi_c) * pi_e *
(1 - pi_e)))/gamma_delta^2
ne_ast <- pi_e * (1 - pi_e) * (gamma_delta^2 - pi_c * (1 -
pi_c) * nc_ast^(-1))^(-1)
nc_prime <- pi_c * (1 - pi_c)/gamma_c^2
fnc_prime <- pi_e * (1 - pi_e) * (gamma_delta^2 - pi_c *
(1 - pi_c) * nc_prime^(-1))^(-1)
ne_prime <- pi_e * (1 - pi_e)/gamma_e^2
fne_prime <- pi_c * (1 - pi_c) * (gamma_delta^2 - pi_e *
(1 - pi_e) * ne_prime^(-1))^(-1)
if (nc_ast > nc_prime & ne_ast > ne_prime) {
c1 <- ceiling(nc_ast)
e1 <- floor(ne_ast)
c2 <- floor(nc_ast)
e2 <- ceiling(ne_ast)
dmax1 <- max(((pi_c * (1 - pi_c))/(c1 * gamma_c^2)),
((pi_e * (1 - pi_e))/(e1 * gamma_e^2)), ((pi_c *
(1 - pi_c) + (c1/e1) * pi_e * (1 - pi_e))/(c1 *
gamma_delta^2)))
dmax2 <- max(((pi_c * (1 - pi_c))/(c2 * gamma_c^2)),
((pi_e * (1 - pi_e))/(e2 * gamma_e^2)), ((pi_c *
(1 - pi_c) + (c2/e2) * pi_e * (1 - pi_e))/(c2 *
gamma_delta^2)))
if (dmax1 <= 1) {
nc_flex <- ceiling(nc_ast)
ne_flex <- floor(ne_ast)
n_flex <- nc_flex + ne_flex
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
}
else if (dmax2 <= 1) {
nc_flex <- floor(nc_ast)
ne_flex <- ceiling(ne_ast)
n_flex <- nc_flex + ne_flex
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
}
else {
nc_flex <- ceiling(nc_ast)
ne_flex <- ceiling(ne_ast)
n_flex <- nc_flex + ne_flex
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
}
}
else if (nc_ast <= nc_prime & ne_ast > ne_prime) {
c1 <- ceiling(nc_prime)
e1 <- floor(max(fnc_prime, ne_prime))
dmax1 <- max(((pi_c * (1 - pi_c))/(c1 * gamma_c^2)),
((pi_e * (1 - pi_e))/(e1 * gamma_e^2)), ((pi_c *
(1 - pi_c) + (c1/e1) * pi_e * (1 - pi_e))/(c1 *
gamma_delta^2)))
if (dmax1 <= 1) {
nc_flex <- ceiling(nc_prime)
ne_flex <- floor(max(fnc_prime, ne_prime))
n_flex <- nc_flex + ne_flex
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
}
else {
nc_flex <- ceiling(nc_prime)
ne_flex <- ceiling(max(fnc_prime, ne_prime))
n_flex <- nc_flex + ne_flex
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
}
}
else if (nc_ast > nc_prime & ne_ast <= ne_prime) {
c1 <- floor(max(fne_prime, nc_prime))
e1 <- ceiling(ne_prime)
dmax1 <- max(((pi_c * (1 - pi_c))/(c1 * gamma_c^2)),
((pi_e * (1 - pi_e))/(e1 * gamma_e^2)), ((pi_c *
(1 - pi_c) + (c1/e1) * pi_e * (1 - pi_e))/(c1 *
gamma_delta^2)))
if (dmax1 <= 1) {
nc_flex <- floor(max(fne_prime, nc_prime))
ne_flex <- ceiling(ne_prime)
n_flex <- nc_flex + ne_flex
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
}
else {
nc_flex <- ceiling(max(fne_prime, nc_prime))
ne_flex <- ceiling(ne_prime)
n_flex <- nc_flex + ne_flex
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
}
}
else if (nc_ast <= nc_prime & ne_ast <= ne_prime) {
nc_flex <- ceiling(nc_prime)
ne_flex <- ceiling(ne_prime)
n_flex <- nc_flex + ne_flex
sample_flex <- data.frame(nc_flex, ne_flex, n_flex)
}
cat("Specified values for parameters:", "\n")
cat("Response rates:", "\n", paste("control =", pi_c, "experiment =",
pi_e), "\n")
cat("Upper bounds for constriants:", "\n", "gammaC =", gamma_c,
"gammaE =", gamma_e, "gammaDelta =", gamma_delta, "\n",
"\n", "\n")
cat("Required sample sizes:", "\n")
cat("[1] Optimal Design:", "\n", paste("nc =", nc_flex, "ne =",
ne_flex, "n =", n_flex), "\n")
cat("[2] 1 to 1 Allocation Design:", "\n", paste("nc =",
nc_fixed1, "ne =", ne_fixed1, "n =", n_fixed1), "\n")
if (!is.na(Allratio_c) | !is.na(Allratio_e)) {
c <- Allratio_c
e <- Allratio_e
dmax <- ceiling(max(((pi_c * (1 - pi_c))/(c * gamma_c^2)),
((pi_e * (1 - pi_e))/(e * gamma_e^2)), ((pi_c * (1 -
pi_c) + (c/e) * pi_e * (1 - pi_e))/(c * gamma_delta^2))))
nc_fixed <- c * dmax
ne_fixed <- e * dmax
n_fixed <- nc_fixed + ne_fixed
sample_fixed2 <- data.frame(nc_fixed, ne_fixed, n_fixed)
cat(paste("[3]", c, "to", e, "Allocation Design:"), "\n",
paste("nc =", nc_fixed, "ne =", ne_fixed, "n =",
n_fixed), "\n")
}
}
|
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