des_fixed: Design a single-stage single-arm trial for a single binary...
In mjg211/singlearm: Design and analysis of single-arm clinical trials

Description Usage Arguments Details Value References See Also Examples

Determines single-stage single-arm clinical trial designs for a single binary primary endpoint, using either exact binomial calculations, or a normal approximation approach.

1 2	des_fixed(pi0 = 0.1, pi1 = 0.3, alpha = 0.05, beta = 0.2, Nmin = 1, Nmax = 30, exact = T, summary = F)

`pi0`	The (undesirable) response probability used in the definition of the null hypothesis. Defaults to 0.1.
`pi1`	The (desirable) response probability at which the trial is powered. Defaults to 0.3.
`alpha`	The desired maximal type-I error rate. Defaults to 0.05.
`beta`	The desired maximal type-II error rate. Defaults to 0.2.
`Nmin`	The minimal sample size to allow in considered designs. Defaults to 1.
`Nmax`	The maximal sample size to allow in considered designs. Defaults to 30.
`exact`	A logical variable indicating whether exact binomial calculations or a normal approximation approach should be used to determine the optimal design. Defaults to TRUE.
`summary`	A logical variable indicating whether a summary of the function's progress should be printed to the console. Defaults to FALSE.

des_fixed() supports the determination of single-stage single-arm clinical trial designs for a single binary primary endpoint. 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 single-stage single-arm design for a single binary endpoint is ultimately indexed by three parameters: a, r, and n.

With these parameters, and denoting the number of responses after m outcomes have been observed by s_m, the testing rules for the trial are as follows

If s_n ≤ a, then do not reject H₀.
Else if s_n ≥ r, then reject H₀.

The purpose of this function is then to determine (optimise) a, r, and n, accounting for the chosen restrictions placed on these parameters.

The arguments Nmin and Nmax allow restrictions to be placed on n. Precisely, Nmin and Nmax set an inclusive range of allowed values for n.

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

The optimal design is then the one that minimises n. In the case where there are multiple feasible designs with the same minimal value of n, the optimal design is the one amongst these which maximises P(π₁).

If exact is set to TRUE then exact binomial probability calculations are used to identify the optimal design. Otherwise, a normal approximation approach is used. Note that setting exact = TRUE is recommended.

A list of class "sa_des_fixed" containing the following elements

A tibble in the slot $des summarising the characteristics of the identified optimal design. This will be NULL if no feasible design was identified in the considered range for n.
A tibble in the slot $feasible, consisting of the identified designs which met the required operating characteristics.
Each of the input variables as specified, subject to internal modification.

A'Hern RP (2001) Sample size tables for exact single-stage phase II designs. Statistics in Medicine 20:859-66.

Fleming TR (1982) One-sample multiple testing procedure for phase II clinical trials. Biometrics 38:143-51.

opchar_fixed, est_fixed, pval_fixed, ci_fixed, and their associated plot family of functions. Note that similar functionality is available through ph2single.

# The optimal design for the default parameters
des    <- des_fixed()
# The optimal single-stage design for a 10% type-I error rate
des_10 <- des_fixed(alpha = 0.1)