two_stage_curtail_trial: Create a two stage curtailed trial design
In kaneplusplus/curtail: One and Two Stage Curtailed Trial Design

Description Usage Arguments Details Examples

The two_stage_curtail_trial function creates a two-stage trial object containing design parameters and statistical properties of one or more nested two-stage designs

1 2	two_stage_curtail_trial(p1_null, p2_null, p1_alt, p2_alt, n1, n2, n_total, r1, r2, prob_early, alpha)

`p1_null`	probability of a successful outcome in Stage 1 under the null hypothesis
`p2_null`	probability of a successful outcome in Stage 2 under the null hypothesis
`p1_alt`	probability of a successful outcome in Stage 1 under the alternative hypothesis
`p2_alt`	probability of a successful outcome in Stage 2 under the alternative hypothesis
`n1`	planned maximum sample size for Stage 1
`n2`	planned maximum sample size for Stage 2
`n_total`	planned maximum sample size for both stages of the trial (n1 + n2)
`r1`	the minimum number of Stage 1 successes needed to continue to Stage 2
`r2`	the minimum number of Stage 2 successes needed to reject the null hypothesis
`prob_early`	desired probability of early stopping in the trial under p1_null (default is 0.1)
`alpha`	desired significance level (default is 0.1)

There are many different ways that the user can specify the parameters to create a two-stage curtailed trial design. We have broken these down into different cases below. Cases 1 - 3 assume that a specific value of n1 and n2 are provided, in which case the trial object is created for that one specific design. In cases 4 and 5, an n_total is specified instead of n1 and n2 and the trial object created contains all possible designs (values of n1 and n2) for the given total sample size. The minimax_design and optimal_design functions can be applied to the trial object in cases 4 and 5 to find the minimax and optimal designs. Any specification of parameters that do not match one of the cases below will result in an error.

Case 1: User specifies p1_null, p2_null, p1_alt, p2_alt, n1, n2, r1, r2

Case 2: User specifies p1_null, p2_null, p1_alt, p2_alt, n1, n2 (default values of prob_early and alpha = 0.1 will be used to calcuate the critical values r1 and r2)

Case 3: User specifies p1_null, p2_null, p1_alt, p2_alt, n1, n2, prob_early, alpha Case 3a: User inputs p1_null, p2_null, p1_alt, p2_alt, n1, n2, prob_early (default value of alpha = 0.1 is used) Case 3b: User inputs p1_null, p2_null, p1_alt, p2_alt, n1, n2, alpha (default value of prob_early = 0.1 is used)

Case 4: User inputs p1_null, p2_null, p1_alt, p2_alt, n_total, prob_early, alpha Case 4a: User inputs p1_null, p2_null, p1_alt, p2_alt, n_total, prob_early (default value of alpha = 0.1 is used) Case 4b: User inputs p1_null, p2_null, p1_alt, p2_alt, n_total, alpha (default value of prob_early = 0.1 is used)

Case 5: User inputs p1_null, p2_null, p1_alt, p2_alt, n_total (default values of prob_early and alpha = 0.1 are used)

Case 1:
trial <- two_stage_curtail_trial(p1_null = 0.8, p2_null = 0.2, 
p1_alt = 0.8, p2_alt = 0.4, n1 = 6, n2 = 30, r1 = 4, r2 = 11)

Case 2:
trial <- two_stage_curtail_trial(p1_null = 0.8, p2_null = 0.2, 
p1_alt = 0.8, p2_alt = 0.4, n1 = 6, n2 = 30)

Case 3
trial <- two_stage_curtail_trial(p1_null = 0.8, p2_null = 0.2, 
p1_alt = 0.8, p2_alt = 0.4, n1 = 6, n2 = 30, prob_early = 0.2, alpha = 0.05)

Case 3a:
trial <- two_stage_curtail_trial(p1_null = 0.8, p2_null = 0.2, 
p1_alt = 0.8, p2_alt = 0.4, n1 = 6, n2 = 30, prob_early = 0.2)

Case 3b:
trial <- two_stage_curtail_trial(p1_null = 0.8, p2_null = 0.2, 
p1_alt = 0.8, p2_alt = 0.4, n1 = 6, n2 = 30, alpha = 0.05)

Case 4
trials <- two_stage_curtail_trial(p1_null = 0.8, p2_null=0.2, 
p1_alt = 0.8, p2_alt = 0.4, n_total=36, prob_early=0.2, alpha=0.05)

Case 4a:
trials <- two_stage_curtail_trial(p1_null = 0.8, p2_null=0.2, 
p1_alt = 0.8, p2_alt = 0.4, n_total=36, prob_early=0.2)

Case 4b:
trials <- two_stage_curtail_trial(p1_null = 0.8, p2_null=0.2, 
p1_alt = 0.8, p2_alt = 0.4, n_total=36, alpha = 0.05)

Case 5
trials <- two_stage_curtail_trial(p1_null = 0.8, p2_null=0.2, 
p1_alt = 0.8, p2_alt = 0.4, n_total=36, prob_early=0.2, alpha=0.05)