Design a two-stage two-arm randomised clinical trial assuming a Bernoulli distributed primary outcome variable

Source: R/des_two_stage.R

des_two_stage determines two-stage two-arm randomised clinical trial designs, assuming the primary outcome variable is Bernoulli distributed. It supports a flexible framework for specifying which scenarios to control the type-I and type-II error-rates for, and allows for design determination assuming a variety of test statistics. In all instances, des_two_stage computes the optimal required sample size in each arm in each stage, the associated optimal stopping boundaries, and returns information on key operating characteristics.

des_two_stage(
  type = "binomial",
  alpha = 0.1,
  beta = 0.2,
  delta = 0.2,
  ratio = 1,
  Pi0 = 0.1,
  Pi1 = Pi0[1],
  nCmax = 50L,
  equal = T,
  w = c(1, 0, 0, 0, 0),
  piO = Pi0[1],
  efficacy = FALSE,
  futility = TRUE,
  efficacy_type = 0L,
  efficacy_param = NULL,
  futility_type = 1L,
  futility_param = 0L,
  summary = FALSE
)

Arguments

type

A character string indicating the chosen design framework/test statistic to assume. Must be one of "barnard", "binomial", "fisher", or "sat". Defaults to "binomial".
alpha

A numeric indicating the chosen value for α, the significance level (i.e., the type-I error-rate). Defaults to 0.1.
beta

A numeric indicating the chosen value for β, used in the definition of the desired power (i.e., the type-II error-rate). Defaults to 0.2.
delta

A numeric indicating the chosen value for δ, the treatment effect assumed in the power calculation. Defaults to 0.2.
ratio

A numeric indicating the chosen value for r, the allocation ratio to the experimental arm, relative to the control arm. Defaults to 1.
Pi0

A numeric vector indicating the chosen values of the control arm response rate to control the type-I error-rate to level α for. Must either be of length one, indicating a single point, or of length two. In this case, the elements indicate the range of possible response rates to allow for. Defaults to 0.1.
Pi1

A numeric vector indicating the chosen values of the control arm response rate to allow for in the power calculations. Must either be of length one, indicating a single point, or of length two. In this case, the elements indicate the range of possible response rates to allow for. Defaults to Pi0[1].
nCmax

A numeric indicating the maximum value of the sample size in the control arm (across both stages) to consider in the search procedure. Defaults to 50L.
equal

A logical variable indicating whether the sample size of the two stages should be equal. Defaults to TRUE.
w

A numeric vector indicating the weights to use in the optimality criteria. Must be of length five, with all elements greater than or equal to zero, and at least one of the first four elements strictly positive. Defaults to c(1, 0, 0, 0, 0).
piO

A numeric indicating the value of the control arm response rate to assume in the optimality criteria. Defaults to Pi0[1].
efficacy

Only used if type is one of "barnard", "binomial", or "sat". Then, it is a logical variable indicating whether to include early stopping for efficacy in the design. Defaults to FALSE.
futility

Only used if type is one of "barnard", "binomial", or "sat". Then, it is a logical variable indicating whether to include early stopping for futility in the design. Defaults to TRUE.
efficacy_type

Only used if type is "fisher". Then, it is a numeric indicating whether, and which type of, early stopping for efficacy to include in the design. See the vignette for details. Defaults to 0L.
efficacy_param

Only used if type is "fisher" and efficacy_type is not equal to 0L. Then, it is a numeric that influences the precise way in which an efficacy boundary is specified. See the vignette for details. Defaults to NULL.
futility_type

Only used if type is "fisher". Then, it is a numeric indicating whether, and which type of, early stopping for futility to include in the design. See the vignette for details. Defaults to 1L.
futility_param

Only used if type is "fisher" and futility_type is not equal to 0L. Then, it is a numeric that influences the precise way in which a futility boundary is specified. See the vignette for details. Defaults to 1L.
summary

A logical variable indicating whether a summary of the function's progress should be printed to the console. Defaults to FALSE.

Value

A list with additional class "ph2rand_des", containing each of the input parameters along with several additional variables, including

  • A list in the slot $boundaries giving the rejection boundaries of the optimal design. The names of these elements depends on the value of type.

  • A tibble in the slot $feasible summarising the operating characteristics of the feasible designs.

  • A numeric vector in the slot $nC giving the sample sizes in the control arm in each stage for the optimal design.

  • A numeric vector in the slot $nE giving the sample sizes in the experimental arm in each stage for the optimal design.

  • A tibble in the slot $opchar summarising the operating characteristics of the optimal design.

See also

des_one_stage, opchar, pmf, terminal, plot.ph2rand_des, summary.ph2rand_des.

Examples

# The design for the default parameters
des       <- des_two_stage()
# Controlling the type-I/II error-rates over a range of possible response
# rates
des_range <- des_two_stage(Pi0 = c(0, 1),
                           Pi1 = c(0, 0.8))