Power and Sample Size of Several Stratified Re-estimation Designs

Evaluates a set of stratified designs with blinded sample size re-estimation over a common set of scenarios of true pooled response probabilities of the strata, by calling StratPowerBSSR for each design, and returns the results as one data frame with a row for each design and each scenario.

Usage

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

Arguments

design: Data frame with one row per design. Its columns are arguments of StratPowerBSSR other than p and n.interim, for example Test, Delta.A, omega or N.max. An argument with one value per stratum is given by one column per stratum, named with the suffixes .S1, .S2, ..., for example N1.S1 and N1.S2; a column without the suffix gives a value common to the strata, where the argument allows it (r and Delta.T). The interim group sizes are given by the columns n1.interim.S1, ... and n2.interim.S1, ..., and the planned group sizes either by N1.S1, ... and N2.S1, ... or by the planning probabilities p.plan.S1, ..., see Details. A missing value in a column means that the argument is not given for that design
p: True pooled response probabilities of the strata at which every design is evaluated: a vector with one element per stratum, or a matrix with one row per scenario and one column per stratum. Every design must have this number of strata. Scenarios in which a response probability of a group falls outside the unit interval are dropped for that design, and every design needs at least one scenario that is kept
Delta.T: True treatment effect, a single value common to the strata or one value per stratum. The default of NULL uses the assumed effect Delta.A of each design. It can also be given in design, but not in both places
type1: Logical. If TRUE, the largest type I error rate of each design and of the fixed design is added, as computed by StratTypeIErrorBSSR with its default grid of theta and, with two strata, the certified maximum. With three or more strata the rates are simulated at every point of the grid, which takes long. 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 names of the arguments of StratPowerBSSR. An argument with one value per stratum is given here as a vector, for example N1 = c(20, 20), and the interim group sizes as n1.interim and n2.interim. An argument may not be given both here and in design

Value

An object of class bbssr_sgrid, which inherits from bbssr_grid: a data frame with one row for each design and each scenario in which the response probabilities lie in the unit interval, containing the index design of the design, the columns of design (other than the group sizes and Delta.T), and:

N1.S1, ..., N2.S1, ...: Planned group sizes
n1.interim.S1, ..., n2.interim.S1, ...: Interim group sizes
Delta.T.S1, ...: True treatment effect in the strata
scenario: Row of p
p.S1, ..., p1.S1, ..., p2.S1, ...: True pooled response probabilities of the strata and those of the two groups
power.BSSR, power.TRAD: Power of the design with re-estimation and of the fixed design
se.BSSR, se.TRAD: Monte Carlo standard errors, present when a design has them (three or more strata, or a random allocation) and NA for the other designs
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, see summary.bbssr_spowerbssr

The attribute designs has one row per design with its index, the columns of design other than the group sizes and Delta.T, the planned and interim group sizes and the true effect and, with type1 = TRUE, the largest type I error rates TIE.BSSR and TIE.TRAD, the probabilities theta.S1.BSSR, ... and theta.S1.TRAD, ... at which they occur, the certified upper bounds bound.BSSR and bound.TRAD (NA without the certificate) and, with a random allocation, the standard errors se.BSSR and se.TRAD at the largest rates. Warnings and errors raised while a design is evaluated are prefixed with the index of the design. summary.bbssr_grid summarizes each design over the scenarios, and plot.bbssr_sgrid draws the results.

Details

When a design has the planning probabilities p.plan.S1, ... instead of the planned group sizes, the planning probabilities of the two groups of each stratum are obtained from them and the assumed effect Delta.A, as in the re-estimation, and the planned group sizes are those of StratSampleSize with the fractions frac, which must then be given, the allocation ratio, the test, the level and the target power of the design, the method ss.method of the re-estimation and the fixed allocation.

Designs with a random allocation (alloc) or with three or more strata use the random numbers of R in the order of the designs, so a call to set.seed() before StratGridBSSR makes the results reproducible.

Author

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

Examples

design <- data.frame(Test = c('CMH', 'Strat-Fisher'))
grid <- StratGridBSSR(design, p = rbind(c(0.3, 0.5), c(0.4, 0.6)), Delta.A = 0.3,
                      N1 = c(10, 10), N2 = c(10, 10), omega = 0.5, r = 1,
                      alpha = 0.05, tar.power = 0.8, ss.method = 'standard')
summary(grid)
#>   design         Test N1.S1 N1.S2 N2.S1 N2.S2 n1.interim.S1 n1.interim.S2
#> 1      1          CMH    10    10    10    10             5             5
#> 2      2 Strat-Fisher    10    10    10    10             5             5
#>   n2.interim.S1 n2.interim.S2 Delta.T.S1 Delta.T.S2 power.BSSR.min
#> 1             5             5        0.3        0.3      0.7704415
#> 2             5             5        0.3        0.3      0.6828610
#>   power.BSSR.max power.TRAD.min power.TRAD.max  E.N.max
#> 1      0.7708956      0.6171045      0.6468430 59.74021
#> 2      0.6870437      0.4897454      0.5188663 59.74021

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


# Planned group sizes from the planning probabilities of the strata
design <- data.frame(Delta.A = c(0.25, 0.3), p.plan.S1 = 0.3, p.plan.S2 = 0.5)
grid <- StratGridBSSR(design, p = c(0.3, 0.5), frac = c(0.5, 0.5), omega = 0.5, r = 1,
                      alpha = 0.025, tar.power = 0.8, Test = 'CMH',
                      ss.method = 'standard')
attr(grid, 'designs')
#>   design Delta.A p.plan.S1 p.plan.S2 N1.S1 N1.S2 N2.S1 N2.S2 n1.interim.S1
#> 1      1    0.25       0.3       0.5    29    29    29    29            15
#> 2      2    0.30       0.3       0.5    20    20    20    20            10
#>   n1.interim.S2 n2.interim.S1 n2.interim.S2 Delta.T.S1 Delta.T.S2
#> 1            15            15            15       0.25       0.25
#> 2            10            10            10       0.30       0.30
# }