exactprob {BinGSD} | R Documentation |

Calculate boundary crossing probabilities of single-arm group sequential design with binary endpoint using binomial distribution

exactprob(K = 0, p_0, p_1, n.I, u_K, lowerbounds, d = NULL)

`K` |
The maximum number of analyses, including the interim and the final. Should be an integer within (1,20]. K will be rounded to the nearest whole number if it is not an integer. The default is 0. |

`p_0` |
The response rate or the probability of success under null hypothesis. Should be a scalar within (0,1). |

`p_1` |
A scalar or vector representing response rate or probability of success under the alternative hypothesis. The value(s) should be within (p_0,1). It is a mandatory input. |

`n.I` |
A vector of length K which contains sample sizes required at each analysis. Should be a positive and increasing sequence. |

`u_K` |
The upper boundary for the last analysis. |

`lowerbounds` |
Non-decreasing lower boundaries for each analysis, in which each element is no less than -1 (no lower bound). With length K, the last lower bound must be identical to u_K. With length K-1, the last element must be no greater than u_K and u_K will be automatically added into the sequence. Note the lower bound must be less than the corresponding sample size. |

`d` |
An object of the class exactdesign. |

This function is similar to `asymprob`

except that the former uses binomial distribution and the latter
uses the normal asymptotic distribution. With `K=0`

(as default), `d`

must be an object of class exactdesign. Meanwhile, other
arguments except for `p_1`

will be inherited from `d`

and the input values will be
ignored. With `K!=0`

, the probabilities are derived from the input arguments. In
this circumstance, all the arguments except for `d`

are required.

The computation is based on the single-arm group sequential exact test
described in `exactdesign`

. Therefore, for the output matrix of
upper bound crossing probabilities, the values for the first K-1 analyses are
zero since there is only one upper bound for the last analysis.

An object of the class exactprob. This class contains:

p_0: As input with

`d=NULL`

or as in`d`

.p_1: As input.

K: K used in computation.

n.I: As input with

`d=NULL`

or as in`d`

.u_K: As input with

`d=NULL`

or as in`d`

.lowerbounds: lowerbounds used in computation.

problow: Probabilities of crossing the lower bounds at each analysis.

probhi: Probability of crossing the upper bounds at each analysis.

Christopher Jennison, Bruce W. Turnbull. Group Sequential Methods with Applications to Clinical Trials. Chapman and Hall/CRC, Boca Raton, FL, 2000.

Keaven M. Anderson, Dan (Jennifer) Sun, Zhongxin (John) Zhang. gsDesign: An R Package for Designing Group Sequential Clinical Trials. R package version 3.0-1.

The calculation of boundary crossing probabilities here borrowed strength from the
source code of function `gsBinomialExact`

in package gsDesign and we really appreciate
their work.

`exactdesign`

, `exactcp`

, `asymprob`

.

I=c(0.2,0.4,0.6,0.8,0.99) beta=0.2 betaspend=c(0.1,0.2,0.3,0.3,0.2) alpha=0.05 p_0=0.3 p_1=0.5 K=4.6 tol=1e-6 tt1=asymdesign(I,beta,betaspend,alpha,p_0,p_1,K,tol) tt2=exactdesign(tt1) tt3=exactprob(p_1=c(0.4,0.5,0.6,0.7,0.8,0.9),d=tt2) tt3=exactprob(K=5,p_0=0.4,p_1=c(0.5,0.6,0.7,0.8),n.I=c(15,20,25,30,35),u_K=15, lowerbounds=c(3,5,10,12,15))

[Package *BinGSD* version 0.0.1 Index]