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
| Applicable One-Sample Tests and Sample Size Computation |
The SEQDESIGN procedure provides sample size computation for two one-sample tests: normal mean and binomial proportion. The required sample size depends on the variance of the response variable—that is, the sample proportion for a binomial proportion test.
In a typical clinical trial, a hypothesis is designed to reject, not accept, the null hypothesis to show the evidence for the alternative hypothesis. Thus, in most cases, the proportion under the alternative hypothesis is used to derive the required sample size. For a test of the binomial proportion, the REF=NULLPROP and REF=PROP options use proportions under the null and alternative hypotheses, respectively.
Test for a Normal Mean
The MODEL=ONESAMPLEMEAN option in the SAMPLESIZE statement derives the sample size required to test a normal mean by using the sample mean statistic for the null hypothesis 
. At stage 
, the sample mean is computed as
 |
where 
is the value of the 
th observation available in the th stage and 
is the cumulative sample size at stage .
An equivalent hypothesis is 
, where 
.
The MLE statistic for 
,
 |
where the information
 |
is the inverse of the variance.
That is, the standardized statistic
 |
Thus, to test the hypothesis 
against a two-sided alternative 
, 
is rejected at stage if the statistic 
is less than or equal to the lower 
boundary value or if is greater than or equal to the upper boundary value at stage .
If the variance 
is unknown, the sample variance can be used if it is assumed that the sample variance is computed from a large sample such that the test statistic has an approximately normal distribution.
The maximum information is needed to derive the required sample size. If the maximum information is not specified or derived with the ALTREF= option in the procedure, the MEAN=
option in the SAMPLESIZE statement is used to specify the alternative reference and thus to derive the maximum information.
In the SEQDESIGN procedure, the computed total sample size
 |
where 
is the maximum information and 
is the specified standard deviation. With an available maximum information, you can specify the MODEL=ONESAMPLEMEAN( STDDEV= ) option in the SAMPLESIZE statement to compute the required total sample size and individual sample size at each stage. A procedure such as PROC MEANS can be used to derive a one-sample 
test for a normal mean.
Test for a Binomial Proportion
The MODEL=ONESAMPLEFREQ option in the SAMPLESIZE statement derives the sample size required to test a binomial proportion by using the null hypothesis 
, where 
is the proportion of a binomial population. At stage , the MLE for is computed as
 |
where is the value of the th observation available in the th stage and is the cumulative sample size at stage .
An equivalent hypothesis is , where 
. If 
is not close to 
or 
, then for a large sample, 
has an approximately normal distribution
 |
where the information 
is the inverse of the variance 
.
Then the standardized statistic
 |
In practice, the estimated sample proportion 
at stage can be used to derive the information 
and test statistic . Thus, to test the hypothesis against an upper alternative 
, is rejected at stage if the statistic is greater than or equal to the upper boundary at stage .
The maximum information is needed to derive the required sample size. If the maximum information is not specified or derived with the ALTREF= option in the procedure, the PROP= option in the SAMPLESIZE statement is used to specify the alternative reference and to derive the maximum information for the sample size calculation.
It is assumed that the sample size is sufficiently large such that the test statistic has an approximately normal distribution. With the hypotheses 
and 
, the SEQDESIGN procedure derives the total sample size
 |
where 
if REF=NULLPROP is specified. Otherwise, 
.
If the PROP= option in the SAMPLESIZE statement is not specified, then the alternative reference derived in the SEQDESIGN procedure is used to compute 
.
The ALTREF= option in the PROC statement can be used to specify 
. Otherwise, the PROP= option in the SAMPLESIZE statement must be specified.
For example, with 
, 
, and REF=PROP (which is the default),
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You can specify the MODEL=ONESAMPLEFREQ option in the SAMPLESIZE statement to compute the required total sample size and individual sample size at each stage. A procedure such as PROC GENMOD with the default DIST=NORMAL option in the MODEL statement can be used to derive the test for a binomial proportion.