Computer programs for group sequential tests

We are making available for downloading some of the FORTRAN code used to construct group sequential tests and to calculate their properties.

Copyright, 24 August 1999, C Jennison. c.jennison@bath.ac.uk

All rights reserved.

This code is released on an "as is" basis. There is no warranty. Users are warned that the developers are not liable for any errors or damages that occur as a result of using this code.

Programs presented here perform calculations to construct and evaluate group sequential tests. They are provided as a service to readers.

The programs are presented using the notation of the book and, in particular, the method of computation for normally distributed test statistics is as described in our Chapter 19.

We have called on functions and subroutines in the NAG library for certain standard calculations and you will need to substitute these if you do not have access to the NAG library. We have created simple functions and subroutines which do nothing other than call the NAG library so that there is just one place to make each replacement.

To retrieve subroutines or a main program

• Click on the highlighted name. A listing will appear in the window.
• Click on File (top left hand corner) and select the Save option to save as a FORTRAN file in text format. The program should be ready to compile and use.

Programs for normal response variables

• subroutines a collection of subroutines (all together in a single file)

  • gst1 calculates properties of a specified group sequential one-sided test.
  • gst2 calculates properties of a specified group sequential two-sided test.
  • ersp2 creates boundaries for a two-sided error spending test.
  • norcdf returns the cumulative distribution of a standard normal distribution.
  • invnor returns a quantile of the standard normal distribution.

• Main programs

  • main creates one-sided Pampallona & Tsiatis tests and calls the subroutine GST1 to evaluate the tests' properties.
  • main2 creates two-sided boundaries of Pocock, O'Brien & Fleming and, Wang & Tsiatis tests and calls the subroutine GST2 to evaluate the tests' properties.
  • maines2 creates two-sided boundaries using an error spending function and calls the subroutine GST2 to evaluate the tests' properties.

Programs for binomial response variables

• bsubroutines a collection of subroutines (all together in a single file)

  • bgst calculates exit probabilities through upper and lower boundaries for a group sequential test with Bernoulli responses.
  • bpci calculates probabilities of a group sequential test for Bernoulli responses terminating in a more extreme state than a particular observed outcome.
  • bprcal calculates the distribution and cumulative distribution function of a Binomial(n,p) random variable.
  • findci calculates a confidence interval for a Bernoulli success probability on termination of a group sequential test.

• Main programs

  • bmain1 produces a table of confidence intervals for outcomes of a 7 stage test taken from MIL STD 105D, plan Q 1.0.
  • bmain produces a table of confidence intervals for outcomes of a 3 stage test taken from Fleming (Biometrics, 1982).
  • bmain3 calculates error rates and expected sample sizes under two values of the success probability for a 3 stage test taken from Fleming (Biometrics, 1982).
  • bmain4 produces a table of confidence intervals for outcomes of a 2 stage test with early stopping at stage 1 only for a low number of successes.