feasibility_check: Check feasibility of power constraints
In aaronjfisher/designOptim: Design optimizer

Description Usage Arguments Details Value

Functions to check feasibility of a design, adjust the design in order to make it feasible, or adjust the constraints so that they can be achieved. Here, "feasibility" means that there exists a 1-stage design at the supplied sample size that meets the supplied power and Type I error constraints.

feasibility_check(FWER, p1, trial_method, r1 = 0.5, r2 = 1 - r1, n_total,
  cases, npoints_sqrt = 10, trial_args = list())

min_n_feasible(min_n = 100, max_n = min_n * 10, step_n = 5,
  showiter = FALSE, trial_method, ...)

max_power_feasible(n_total, cases, p1, trial_method, step_multiplier = 0.01,
  showiter = FALSE, FWER = 0.025, npoints_sqrt = 10, ...)

`FWER`	the required familywise Type I error rate for the trial
`p1`	population proportion in subpopulation 1
`trial_method`	the type of trial to run. 'cov' for covariance based, 'MB' for Maurer Bretz, and 'covMB' for a combination approach.
`r1`	probability of being randomized to treatment in subpopulation 1
`r2`	probability of being randomized to treatment in subpopulation 2
`n_total`	the total sample size for the 1-stage trial
`cases`	a list of power constraints, of the same format as those passed to `optimizeTrial`
`npoints_sqrt`	`feasibility_check` determines feasibility by searching over a grid of points for the alpha to be allocated between the two trials. Determines the number of grid points to search over. The search will be conducted over a triangle of points, with `(npoints_sqrt^2)/2` points.
`trial_args`	either an empty list (for trial_method=='cov'), or a list containing graph edges for alpha reallocation (for trial_method=='MB').
`min_n`	smallest sample size to consider for a 1-stage trial
`max_n`	largest sample size to consider
`step_n`	the step size for sample size. For example, if `step=20` then we will search in increments of 20 people.
`showiter`	passed to `binsearch`, determines whether to show progress.
`...`	passed to `feasibility_check`
`step_multiplier`	the step size

feasibility_check checks whether it is possible to meet a set of power constraints while maintaining a given familywise Type I error rate (FWER) and total sample size.

min_n_feasible implements a binary search to find the smallest sample size that meets the power constraints and FWER specified. In each iteration of the search, min_n_feasible calls feasibility_check.

Given a sample size and set of power cases, max_power_feasible finds the number m between 0 and 1 such that if all of the minimum power thresholds are multiplied by m, then these power constraints will be satisfied at the supplied value of n_total. In other words, it finds the factor by which the power constraints must be relaxed.

feasibility_check returns a named vector, with the first element being 1 if the trial is feasible, and zero otherwise. The remaining elements of this vector tell the alpha allocated to each hypothesis in one particular setup that results in a feasible trial.
min_n_feasible returns the smallest sample size that meets the power constraints and FWER specified, as well as the output from feasibility_check at that sample size.
max_power_feasible returns the multiplier m and a list of modified cases in which each power threshold has been multiplied by m.