Description Usage Arguments Value References Examples

Finds the probability that a sequence of standard normal random variables *z_1, z_2,…,z_m* derived from a normal stochastic process with independent increments will cross a lower and and upper boundary.

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`a` |
Lower boundary as a numeric vector of length |

`b` |
Upper boundary as a numeric vector of length |

`t` |
Information times as a numeric vector of length |

`int` |
number of intervals that the Z-space is partitioned into for calculation purposes, increasing this will improve accuracy, this is also a numeric vector of length |

Produces a numeric vector of length *2 m* the first *m* components are the probability that the *z_k* will be less than *a_k* for some *k≤ i* and be less than *b_k* for all *k ≤ i*. The second *m* components are the probability that the *z_k* will be greater than *b_k* for some *k≤ i* and be greater than *a_k* for all *k ≤ i*.

Note that the last probability in the sequence is the overall significance level of a sequential design that uses `a`

and `b`

as upper and lower boundaries. To get power you subtract the *μ √(t)* from `a`

and `b`

where *μ* is the mean of *z_m* under the alternative hypothesis.

Schoenfeld, David A. "A simple algorithm for designing group sequential clinical trials." Biometrics 57.3 (2001): 972-974.

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