Power and Sample Size of Several Blinded Sample Size Re-estimation Designs

Evaluates a set of designs with blinded sample size re-estimation (BSSR) for a binary endpoint over a common set of true pooled response probabilities, by calling BinaryPowerBSSR for each design, and returns the results as one data frame with a row for each design and each probability.

Usage

BinaryGridBSSR(design, p, Delta.T = NULL, type1 = FALSE, verbose = FALSE, ...)

Arguments

design: Data frame with one row per design. Its columns are arguments of BinaryPowerBSSR other than p and n.interim, for example Test, Delta.A, omega or r. The interim sample sizes are given by the two columns n1.interim and n2.interim, and the initial sample sizes either by the columns N1 and N2 or by a column p.plan, see Details. A missing value in a column means that the argument is not given for that design, so that designs specified by omega and by the interim sample sizes can share one data frame
p: Vector of true pooled response probabilities at which every design is evaluated. Values at which a response probability falls outside the unit interval are dropped for that design, and every design needs at least one value that is kept
Delta.T: True treatment effect. The default of NULL uses the assumed effect Delta.A of each design. It can also be given as a column of design, but not in both places
type1: Logical. If TRUE, the largest type I error rate of each design and of the corresponding fixed-sample design is added, as computed by BinaryTypeIErrorBSSR with its default grid of theta and the certified maximum. It is taken over the common response probability, over the boundary of the null hypothesis for a design with a non-inferiority margin, or over both boundaries for a test of equivalence. Default is FALSE
verbose: Logical. If TRUE, a message is issued as each design is evaluated. Default is FALSE
...: Arguments shared by all designs, with the same names as the columns of design. An argument may not be given both here and as a column

Value

An object of class bbssr_grid, a data frame with one row for each design and each element of p that gives response probabilities inside the unit interval, containing the index design of the design, the columns of design (other than the sample sizes and Delta.T), and:

N1, N2: Initial sample sizes
n1.interim, n2.interim: Interim sample sizes
Delta.T: True treatment effect
p, p1, p2: True pooled response probability and those of the two groups
power.BSSR, power.TRAD: Power of the BSSR design and of the fixed-sample design with the initial sample sizes
E.N, SD.N: Expected value and standard deviation of the final total sample size
N.q25, N.q50, N.q75: Quartiles of the final total sample size
P.N.max: Probability that the final total sample size is the largest the design can reach

The attribute designs has one row per design with its index, the columns of design other than the sample sizes and Delta.T, the initial and interim sample sizes and the true effect and, with type1 = TRUE, the largest type I error rates TIE.BSSR and TIE.TRAD and the values theta.BSSR and theta.TRAD at which they occur. When a design tests equivalence, the columns boundary.BSSR and boundary.TRAD give the boundary, 'lower' or 'upper', of each largest rate, and are NA for the other designs. Warnings and errors raised while a design is evaluated are prefixed with the index of the design.

Details

When design has a column p.plan instead of the initial sample sizes, the planning proportions of the two groups are obtained from the pooled proportion p.plan and the assumed effect Delta.A, as in the re-estimation, and the initial sample sizes are those of BinarySampleSize with the test, the level, the target power and the allocation ratio of the design, the method ss.method of the re-estimation and the rounding rule of the design. The test Test and the level alpha of the final analysis are used even when the re-estimation uses another test ss.Test or level ss.alpha.

The quartiles and P.N.max are those of summary.bbssr_powerbssr. The p-values of each test are kept for the rest of the session, so designs that share sample sizes are evaluated faster after the first one.

Author

Gosuke Homma (my.name.is.gosuke@gmail.com)

Examples

design <- expand.grid(Test = c('Chisq', 'Fisher'), omega = c(0.3, 0.5),
                      stringsAsFactors = FALSE)
grid <- BinaryGridBSSR(design, p = c(0.3, 0.4, 0.5), Delta.A = 0.3, N1 = 30, N2 = 30,
                       r = 1, alpha = 0.025, tar.power = 0.8, ss.method = 'standard')
summary(grid)
#>   design   Test omega N1 N2 n1.interim n2.interim Delta.T power.BSSR.min
#> 1      1  Chisq   0.3 30 30          9          9     0.3      0.7716927
#> 2      2 Fisher   0.3 30 30          9          9     0.3      0.6913132
#> 3      3  Chisq   0.5 30 30         15         15     0.3      0.7885735
#> 4      4 Fisher   0.5 30 30         15         15     0.3      0.7026320
#>   power.BSSR.max power.TRAD.min power.TRAD.max  E.N.max
#> 1      0.7932220      0.6617280      0.7369757 81.24550
#> 2      0.7225466      0.5593173      0.6447901 81.24550
#> 3      0.7982702      0.6617280      0.7369757 83.27159
#> 4      0.7265063      0.5593173      0.6447901 83.27159

# \donttest{
plot(grid, colour.by = 'Test', facet.by = 'omega')


# Initial sample sizes from a planning proportion, and the largest type I error rates
design <- data.frame(Delta.A = c(0.2, 0.3), p.plan = 0.4)
grid <- BinaryGridBSSR(design, p = c(0.3, 0.5), omega = 0.5, r = 1, alpha = 0.025,
                       tar.power = 0.8, Test = 'Chisq', ss.method = 'standard',
                       type1 = TRUE)
attr(grid, 'designs')
#>   design Delta.A p.plan N1 N2 n1.interim n2.interim Delta.T   TIE.BSSR
#> 1      1     0.2    0.4 93 93         47         47     0.2 0.03034393
#> 2      2     0.3    0.4 41 41         21         21     0.3 0.02633609
#>   theta.BSSR   TIE.TRAD theta.TRAD
#> 1 0.07944775 0.02614329   0.351347
#> 2 0.39979935 0.02990483   0.500000
# }