The curtail package is used for the planning of one- and two- stage clinical trials with curtailed sampling. Under curtailed sampling, an early decision in the trial is allowed as soon as any predefined statistical endpoint is reached. The package provides functions to help select a design, including visualizations to compare criteria for different choices of parameters, and functions to calculate power, significance, and expected sample size, among others.

In the one-stage design, patients are assumed to be enrolled into the trial
sequentially up to a maximum number of patients. A critical value of
observed patient successes needed to deem the therapy superior is set prior
to the start of the study. The `power_significance_plot`

and
`power_significance_ROC`

functions provide visualizations to compare
power and significance levels for various choices of critical values. Also,
the `critical_values`

function will calculate the critical value to
maintain a desired significance level. Under curtailed sampling, the study
ends as soon as enough the observed patient successes meets the critical
value or as soon as too many patient failures have been observed. The
smallest number of patient enrollees needed to reach a decision under
curtailed sampling is described by the Stopped Negative Binomial
distribution. This package also provides density and other related
functions for the Stopped Negative Binomial Distribution.

The two-stage design presented in this package is a modification of Simon's
two-stage design with separate, but nested, criteria for early stopping in
Stage 1 and efficacy in Stage 2. The two-stage design has two critical
values which can both be determined with the `critical_values`

function to maintain a desired significance level and probability of early
stopping. These critical values are set prior to the start of the study to
determine the number of patient successes in the first stage needed to
continue the trial to the second stage and the critical number of efficacy
successes throughout the trial needed to deem the therapy superior. Under
curtailed sampling, early decisions can be made in Stage 1 and Stage 2.
The `best_designs`

function finds the optimal and minimax design
for a fixed total sample size. Other functions are provided to calculate the
expected sample size, power, significance, and probability of early
stopping in the trial given a choice of design parameters.

One-Stage Design Function Calls

critical_values: finds the minimum number of successes to reject the null hypothesis with significance level alpha

single_stage_significance: computes the probability of rejecting the null hypothesis assuming the null probability of success

single_stage_power: computes the probability of rejecting the null hypothesis assuming an alternative probability of success

single_stage_expected_sample_size: computes the mean and standard deviation of the sample size for the one-stage design

zplot: visualize the Stopped Negative Binomial process with horizontal axis counting patient successes and vertical axis counting patient failures

kplot: visualize the Stopped Negative Binomial process with horizontal axis counting patients enrolled and vertical axis counting the number of successes

power_significance_plot: Plot power and significance across all trial designs with a fixed maximum number of patients

power_significance_ROC: ROC curve of Power vs. 1-Significance for all trial designs with a fixed number of maximum patients

#' Stopped Negative Binomial Distribution Function Calls

dsnb: density for the Stopped Negative Binomial Distribution

psnb: distribution function for the Stopped Negative Binomial Distribution

qsnb: quantile function for the Stopped Negative Binomial Distribution

rsnb: randomly generated value from the Stopped Negative Binomial distribution

esnb: expected value of the Stopped Negative Binomial distribution

vsnb: variance of the Stopped Negative Binomial distribution

dsnb_stacked: computes the density stacked by responders and non- responders

stacked_plot: stacked plot of the probability mass function for the snb showing the contributions from N (the top barrier) and R (the right barrier)

dsnb_plot: plot of the probability mass function for the Stopped Negative Binomial

dsnb_stack_plot: The stacked plot of the probability mass function for the SNB showing the contributions from N (the top barrier) and R (the right barrier) by color.

Two-Stage Design Function Calls

critical_values: finds the critical values the number of Stage 1 successes to continue to Stage 2 and the minimum number of Stage 2 successes to the reject the null hypothesis

prob_early_stop: computes the probability of stopping the trial after Stage 1

expected_stage1_sample_size: computes the expected sample size and standard deviation for Stage 1 of the two-stage design under curtailed sampling

expected_total_sample_size: computes the expected number of patients who are enrolled and followed to their endpoint before critical endpoints in Stage 1 and Stage 2 are achieved

all_minimax_designs: computes the minimax probability for each possible design for a a given total n

all_optimal_designs: computes the expected curtailed sample size for each possible design for a a given total n

best_designs: finds the minimax and optimal designs for a given total n

plot.ph2_design: plots the optimal and minimax criteria for each possible design over different values of n1

minimax_design: computes the minimax probability for a given design with specified n1 and n2

Acknowledgements: This work was partially supported through a Patient-Centered Outcomes Research Institute (PCORI) Award (ME-1511-32832).

Disclaimer: All statements in this report, including its findings and conclusions, are solely those of the authors and do not necessarily represent the views of the Patient-Centered Outcomes Research Institute (PCORI), its Board of Governors or Methodology Committee.

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