Two-stage designs

TwoStageDesign is the fundamental design class of the adoptr package. Formally, we represent a generic two-stage design as a five-tuple (n₁, c₁^f, c₁^e, n₂(·), c₂(·)). Here, n₁ is the first-stage sample size (per group), c₁^f and c₁^e are boundaries for early stopping for futility and efficacy, respectively. Since the trial design is a two-stage design, the elements n₂(·) (stage-two sample size) and c₂(·) (stage-two critical value) are functions of the first-stage outcome X₁=x₁. X₁ denotes the first-stage test statistic. A brief description on this definition of two-stage designs can be read here. For available methods, see the 'See Also' section at the end of this page.

TwoStageDesign(n1, ...)

# S4 method for numeric
TwoStageDesign(
  n1,
  c1f,
  c1e,
  n2_pivots,
  c2_pivots,
  order = NULL,
  event_rate,
  ...
)

# S4 method for TwoStageDesign
summary(object, ..., rounded = TRUE)

Arguments

n1

stage-one sample size

...

further optional arguments

c1f

early futility stopping boundary

c1e

early efficacy stopping boundary

n2_pivots

numeric vector, stage-two sample size on the integration pivot points

c2_pivots

numeric vector, stage-two critical values on the integration pivot points

order

integer, integration order of the employed Gaussian quadrature integration rule to evaluate scores. Automatically set to length(n2_pivots) if
length(n2_pivots) == length(c2_pivots) > 1, otherwise c2 and n2 are taken to be constant in stage-two and replicated to match the number of pivots specified by order

event_rate

probability that a subject in either group will eventually have an event, only needs to be specified for time-to-event endpoints.

object

object to show

rounded

should rounded n-values be used?

Details

summary can be used to quickly compute and display basic facts about a TwoStageDesign. An arbitrary number of names UnconditionalScore objects can be provided via the optional arguments ... and are included in the summary displayed using print.

Slots

n1

cf. parameter 'n1'

c1f

cf. parameter 'c1f'

c1e

cf. parameter 'c1e'

n2_pivots

vector of length 'order' giving the values of n2 at the pivot points of the numeric integration rule

c2_pivots

vector of length order giving the values of c2 at the pivot points of the numeric integration rule

x1_norm_pivots

normalized pivots for integration rule (in [-1, 1]) the actual pivots are scaled to the interval [c1f, c1e] and can be obtained by the internal method
adoptr:::scaled_integration_pivots(design)

weights

weights of of integration rule at x1_norm_pivots for approximating integrals over x1

tunable

named logical vector indicating whether corresponding slot is considered a tunable parameter (i.e. whether it can be changed during optimization via minimize or not; cf.
make_fixed)

See also

For accessing sample sizes and critical values safely, see methods in n and c2; for modifying behaviour during optimizaton see make_tunable; to convert between S4 class represenation and numeric vector, see tunable_parameters; for simulating from a given design, see simulate; for plotting see plot,TwoStageDesign-method. Both group-sequential and one-stage designs (!) are implemented as subclasses of TwoStageDesign.

Examples

design <- TwoStageDesign(50, 0, 2, 50.0, 2.0, 5)
pow    <- Power(Normal(), PointMassPrior(.4, 1))
summary(design, "Power" = pow)
#> TwoStageDesign: n1 =  50
#> 
          futility |            continue           | efficacy
#> 
      x1:    -0.00 |  0.09  0.46  1.00  1.54  1.91 |  2.00
#> 
  c2(x1):     +Inf | +2.00 +2.00 +2.00 +2.00 +2.00 |  -Inf
#> 
  n2(x1):        0 |    50    50    50    50    50 |     0
#> 
   Power:      0.739
#>