des_admissable: Design an admissable group sequential single-arm trial for a...
In mjg211/singlearm: Design and analysis of single-arm clinical trials

Description Usage Arguments Details Value See Also Examples

Determines admissable group sequential single-arm clinical trial designs for a single binary primary endpoint, using exact binomial calculations.

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des_admissable(J = 2, pi0 = 0.1, pi1 = 0.3, alpha = 0.05,
  beta = 0.2, Nmin = 1, Nmax = 50, futility = T, efficacy = F,
  equal_n = F, ensign = F, summary = F)

`J`	The maximal number of stages to allow.
`pi0`	The (undesirable) response probability used in the definition of the null hypothesis.
`pi1`	The (desiable) response probability at which the trial is powered.
`alpha`	The desired maximal type-I error-rate.
`beta`	The desired maximal type-II error-rate.
`Nmin`	The minimal total sample size to allow in considered designs.
`Nmax`	The maximal total sample size to allow in considered designs.
`futility`	A logical variable indicating whether early stopping for futility should be allowed.
`efficacy`	A logical variable indicating whether early stopping for efficacy should be allowed.
`equal_n`	A logical variable indicating that the sample size of each stage should be equal.
`ensign`	A logical variable indicating that the design of Ensign et al (1994) should be mimicked, and the first stage futility boundary forced to be 0.
`summary`	A logical variable indicating a summary of the function's progress should be printed to the console.

des_admissable() supports the determination of admissable group sequential single-arm clinical trial designs for a single binary primary endpoint. For all supported designs, the following hypotheses are tested for the response probability π

H₀ : π ≤ π ₀, H₁ : π > π₀,

for π₀, specified using the argument pi0.

In each instance, the optimal design is required to meet the following operating characteristics

P(π₀) ≤ α, P(π₁) ≥ 1 - β,

where P(π) is the probability of rejecting H₀ when the true response probability is π, and the values of α and β are specified using the arguments alpha and beta respectively. Moreover, π₁, satisfying π₀ < π₁, is specified using the argument pi1.

A group sequential single-arm design for a single binary endpoint, with a maximum of J allowed stages (specifying J through the argument J) is then indexed by three vectors: a = (a₁,…,a_J), r = (r₁,…,r_J), and n = (n₁,…,n_J).

With these vectors, and denoting the number of responses after m patients have been observed by s_m, the stopping rules for a trial are then as follows

For j = 1,…,J - 1
- If s_{N_j} ≤ a_j, then stop the trial and do not reject H₀.
- Else if s_{N_j} ≥ r_j, then stop the trial and reject H₀.
- Else if a_j < s_{N_j} < r_j, then continute to stage j + 1.
For j = J
- If s_{N_j} ≤ a_j, then do not reject H₀.
- Else if s_{N_j} ≥ r_j, then reject H₀.

Here, N_j = n₁ + &ctdot; + n_j.

The purpose of this function is then to optimise a , r , and n , accounting for the chosen restrictions placed on these vectors, and the chosen optimality criteria.

The arguments Nmin, Nmax, and equal_n allow restrictions to be placed on n. Precisely, Nmin and Nmax set an inclusive range of allowed values for N_J, while if set to TRUE, equal_n enforces that n ₁ = &ctdot; = n_J.

The arguments futility, efficacy, and ensign allow restrictions to be placed on a and r. If futility is set to FALSE, early stopping for futility (to not reject H₀) is prevented by enforcing a₁ = &ctdot; = a_{J - 1} = -∞. Similarly, if efficacy is set to FALSE, early stopping for efficacy (to reject H₀) is prevented by enforcing r₁ = &ctdot; = r_{J - 1} = ∞. Finally, if set to TRUE, ensign enforces the restriction that a₁ = 0, as suggested for 3-stage designs by Ensign et al (1994).

Note that to ensure a decision is made about H₀, this function enforces that a_J + 1 = r_J.

To describe the admissability criteria, denote the expected sample size when the true response probability is π by ESS(π). Then, the following admissability criteria are currently supported:

The designs which minimise w₀ESS(π₀) + w₁ESS(π₁) + (1 - w₀ - w₁)N_J for 0 ≤ w₀ + w₁ ≤ 1.

A list of class "sa_des_admissable" containing the following elements

A list of lists in the slot $des containing details of the identified admissable design(s). Each element will contain details of each admissable design.
A tibble in the slot $feasible, consisting of the identified designs which met the required operating characteristics.
A tibble in the slot $admissable, summarising the performance of the admissable designs.
A tibble in the slot $weights containing details of which design is admissable for each considered combination of w ₀ and w₁.
Each of the input variables as specified.