The SEQDESIGN Procedure
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Overview
- Getting Started
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Syntax
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Details
Fixed-Sample Clinical Trials One-Sided Fixed-Sample Tests in Clinical Trials Two-Sided Fixed-Sample Tests in Clinical Trials Group Sequential Methods Statistical Assumptions for Group Sequential Designs Boundary Scales Boundary Variables Type I and Type II Errors Unified Family Methods Haybittle-Peto Method Whitehead Methods Error Spending Methods Acceptance (beta) Boundary Boundary Adjustments for Overlapping Lower and Upper beta Boundaries Specified and Derived Parameters Applicable Boundary Keys Sample Size Computation Applicable One-Sample Tests and Sample Size Computation Applicable Two-Sample Tests and Sample Size Computation Applicable Regression Parameter Tests and Sample Size Computation Aspects of Group Sequential Designs Summary of Methods in Group Sequential Designs Table Output ODS Table Names Graphics Output ODS Graphics Acknowledgments
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Examples
Creating Fixed-Sample Designs Creating a One-Sided O’Brien-Fleming Design Creating Two-Sided Pocock and O’Brien-Fleming Designs Generating Graphics Display for Sequential Designs Creating Designs Using Haybittle-Peto Methods Creating Designs with Various Stopping Criteria Creating Whitehead’s Triangular Designs Creating a One-Sided Error Spending Design Creating Designs with Various Number of Stages Creating Two-Sided Error Spending Designs with and without Overlapping Lower and Upper beta Boundaries Creating a Two-Sided Asymmetric Error Spending Design with Early Stopping to Reject H0 Creating a Two-Sided Asymmetric Error Spending Design with Early Stopping to Reject or Accept H0
- References
| Statistical Assumptions for Group Sequential Designs |
The SEQDESIGN procedure assumes that with a total number of stages 
, the sequence of the standardized test statistics 
has the canonical joint distribution with information levels 
for the parameter 
(Jennison and Turnbull 2000, p. 49):
is multivariate normal 
, 
In terms of the maximum likelihood estimator, 
, 
, the canonical joint distribution can be expressed as follows:
is multivariate normal 
,
Furthermore, in terms of the score statistics 
, , the canonical joint distribution can be expressed as follows:
is multivariate normal 
,
That is, the increments 
, 
, ..., and 
are independently distributed.
If the test statistic is computed from the data that are not from a normal distribution, such as a binomial distribution, then it is assumed that the test statistic is computed from a large sample such that the statistic has an approximately normal distribution.
If the increments , , ..., and are not independently distributed, then it is inappropriate to use group sequential methods in the SEQDESIGN procedure. One such example is the Gehan statistic, which is a weighted log-rank statistic for censored data. Refer to Jennison and Turnbull (2000, pp. 232–233, 276–277) and Proschan, Lan, and Wittes (2006, pp. 150–151) for a description of statistics with nonindependent increments.
If a trial stops at an early interim stage with only a small number of responses observed, it can lead to a distrust of the statistical findings, which rely on the assumption that the sample is large (Whitehead 1997, p. 167). A group sequential design can be specified such that at the first interim analysis, there are a sufficient number of responses to ensure that the analysis to be conducted is both reliable and persuasive (Whitehead 1997, p. 167).
Alternatively, a method such as the O’Brien-Fleming method can be used to derive conservative stopping boundary values at very early stages to make the early stop less likely. That is, the trial is stopped in early stages only with overwhelming evidence.
A simple example of the group sequential tests is the test for a normal mean, 
. Suppose 
are 
observations of a response variable Y in a data set from a normal distribution with an unknown mean 
and a known variance 
. Then the maximum likelihood estimate of is the sample mean
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The sample mean has a normal distribution with mean and variance 
:
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An equivalent hypothesis for is 
, where 
. The MLE statistic for ,
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where the information 
.
For a group sequential test with stages, there are 
observations available at these stages. At stage 
, the sample mean is computed as
 |
where 
is the value of the 
th observation available at the th stage and 
is the cumulative sample size at stage , which includes the 
observations collected at previous stages and the 
observations collected at the current stage.
The maximum likelihood estimate
 |
where the information
 |
is the inverse of the variance.
Thus, the standardized statistic
 |
The covariance of 
and 
, can be expressed as
 |
where 
and 
.
Since 
is independent of 
, 
and
 |
Thus the statistics has the canonical joint distribution with information levels for the parameter . See the section Applicable One-Sample Tests and Sample Size Computation, the section Applicable Two-Sample Tests and Sample Size Computation, and the section Applicable Regression Parameter Tests and Sample Size Computation for more examples of applicable tests in group sequential trials.