# weibPmatch: Compute the shape or scale parameter for a Weibull... In OptInterim: Optimal Two and Three Stage Designs for Single-Arm and Two-Arm Randomized Controlled Trials with a Long-Term Binary Endpoint

## Description

Determine the shape or scale parameter of a Weibull distribution so it has event-free rate P0 at time x. If the shape is specified, the scale parameter is computed, and if the scale is specified, the shape parameter is computed.

## Usage

 `1` ```weibPmatch(x, p0, shape, scale) ```

## Arguments

 `x` Pre-specified time for the event-free endpoint (e.g., 1 year). `p0` Event-free rate at time x. `shape` If specified, the necessary scale parameter is computed `scale` If specified, the necessary shape parameter is computed

## Details

The time and event-free rate must be supplied. Either the shape or scale parameter must also be specified, but not both. The R parameterization of the Weibull distribution is used.

## Value

A single numerical value is returned, either the shape or scale parameter, depending on which is specified by the user.

## Author(s)

Bo Huang <[email protected]> and Neal Thomas <[email protected]>

## References

Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.

`weibull.plot`,`pweibull`, `OptimDes`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```param <- c(1, 1.09, 2, 1.40) x<-1 p0<-pweibull(x,param[1],param[2],lower=FALSE) p1<-pweibull(x,param[3],param[4],lower=FALSE) weibull.plot(param,x) ### equivalent to simple call paramNew<-c(param[1], weibPmatch(x,p0,param[1]), param[3], weibPmatch(x,p1,param[3])) weibull.plot(paramNew, x) ### null curve with different shape paramNew<-c(3.0, weibPmatch(x,p0,3.0), param[3], weibPmatch(x,p1,param[3])) weibull.plot(paramNew, x) ### alternative curve with different scale paramNew<-c(param[1], param[2], weibPmatch(x,p1,scale=2), 2) weibull.plot(paramNew, x) ```