exactprob {BinGSD}

Boundary crossing probabilities computation using exact test.

Description

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

Usage

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

Arguments

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.

Details

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.

Value

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.

Reference

• 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.

Note

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.

See Also

exactdesign, exactcp, asymprob.

Examples

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))