# Group Sequential Methods

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## Chapter: Biostatistics for the Health Sciences: Tests of Hypotheses

In the hypothesis testing problems that we have studied, the critical value of the test statistic and the power of the test are based on predetermined sample sizes.

GROUP SEQUENTIAL METHODS

In the hypothesis testing problems that we have studied, the critical value of the test statistic and the power of the test are based on predetermined sample sizes. In some clinical trials, the sample size may not be fixed but allowed to be determined as the data are collected. When decisions are made after each new sample, such procedures are called sequential methods. More practical than making decisions after each new sample is to allow decisions to be made in steps as specified groups of samples are collected.

The statistical theory that underlies these techniques was developed in Great Britain and the United States during World War II. It was used extensively in quality assurance testing during the war. The goal was to waste as little ammunition as possible during testing.

In clinical trials, group sequential methods are used to stop trials early for either lack of efficacy or for safety reasons, or if medication is found to be highly effective. Sequential methods have advantages over fixed-sample-size trials in that they can lead to trials that tend to have smaller sample sizes than their fixed-sample-size counterparts. Since the actual sample size is unknown at the beginning of the trial, we can determine only a mean or a distribution of possible sample sizes that could result from the outcome of the trial.

Another reason for taking such a stepwise approach is that we may not have a good estimate of the population variances for the data prior to the trial. The accrual of some data enables us to estimate unknown parameters such as these variances; these data help us to determine more accurately the sample size we really need. If a bad initial guess in a fixed sample size trial gives too small a variance, we will have less power than we had planned for. On the other hand, if we conservatively overes-timate the variance, our fixed sample size test will use more samples than we actu ally need and thus cost more than is really necessary. Two-stage sampling and group sequential sampling provide methodology to overcome such problems.

In recent years, statistical software has been developed to design group sequen-tial trials. EaSt by Cytel, S + SeqTrial by Insightful Corporation (producers of Splus), and PEST by John Whitehead are representative packages that are discussed in Chapter 16. Among the texts that describe sequential and group sequential meth-ods, one of the best recent ones is by Jennison and Turnbull (2000).

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