The SEQDESIGN Procedure
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Overview
- Getting Started
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Syntax
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DetailsFixed-Sample Clinical TrialsOne-Sided Fixed-Sample Tests in Clinical TrialsTwo-Sided Fixed-Sample Tests in Clinical TrialsGroup Sequential MethodsStatistical Assumptions for Group Sequential DesignsBoundary ScalesBoundary VariablesType I and Type II ErrorsUnified Family MethodsHaybittle-Peto MethodWhitehead MethodsError Spending MethodsAcceptance (beta) BoundaryBoundary Adjustments for Overlapping Lower and Upper beta BoundariesSpecified and Derived ParametersApplicable Boundary KeysSample Size ComputationApplicable One-Sample Tests and Sample Size ComputationApplicable Two-Sample Tests and Sample Size ComputationApplicable Regression Parameter Tests and Sample Size ComputationAspects of Group Sequential DesignsSummary of Methods in Group Sequential DesignsTable OutputODS Table NamesGraphics OutputODS Graphics
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ExamplesCreating Fixed-Sample DesignsCreating a One-Sided O’Brien-Fleming DesignCreating Two-Sided Pocock and O’Brien-Fleming DesignsGenerating Graphics Display for Sequential DesignsCreating Designs Using Haybittle-Peto MethodsCreating Designs with Various Stopping CriteriaCreating Whitehead’s Triangular DesignsCreating a One-Sided Error Spending DesignCreating Designs with Various Number of StagesCreating Two-Sided Error Spending Designs with and without Overlapping Lower and Upper beta BoundariesCreating a Two-Sided Asymmetric Error Spending Design with Early Stopping to Reject H0Creating a Two-Sided Asymmetric Error Spending Design with Early Stopping to Reject or Accept H0Creating a Design with a Nonbinding Beta BoundaryComputing Sample Size for Survival Data
- References
Boundary Adjustments for Overlapping Lower and Upper 
Boundaries
For the fixed boundary shape methods and Whitehead methods, the boundary values for all stages are derived simultaneously
for each boundary. For a two-sided design with STOP=ACCEPT or STOP=BOTH, simultaneous derivation might result in overlapping
of the lower and upper 
boundaries. That is, at an interim stage k, the lower boundary value might be greater than its corresponding upper boundary value. In this case, these two boundary values are set to missing and the design does not stop at stage k to accept the null hypothesis (Jennison and Turnbull, 2000, p. 113).
For the error spending methods, the boundary values are derived sequentially for the stages. For a two-sided design with STOP=ACCEPT
or STOP=BOTH, a small spending at an interim stage might result in overlapping of the lower and upper boundaries for the two corresponding one-sided tests. Specifically, this form of overlapping occurs at an interim stage k if the upper boundary value derived from the one-sided test for the upper alternative is less than the lower boundary value derived from the one-sided test for the lower alternative (Kittelson and Emerson 1999, pp. 881–882; Rudser and Emerson 2007, p. 6). You can use the BETAOVERLAP= option to specify how this type of overlapping is to be handled.
If BETAOVERLAP=ADJUST (which is the default) is specified, the procedure derives the boundary values for the two-sided design
and then checks for overlapping of the two one-sided boundaries at interim stages. If overlapping occurs at a particular stage, the boundary values for the two-sided design are set to missing (so the trial does not stop to accept the null hypothesis at
this stage), and the spending values at subsequent stages are adjusted proportionally as follows.
If the boundary values are set to missing at stage k in a K-stage trial, the adjusted spending value at stage k, 
, is updated for these missing boundary values, and then the spending values at subsequent stages are adjusted proportionally by
![\[ e’_{j} = e’_{k} + \frac{e_{j}-e_{k}}{e_{K}-e_{k}} \; (e_{K}-e’_{k}) \]](images/statug_seqdesign0584.png){kind=small} |
for 
, where 
and 
are the cumulative spending values st stage j before and after the adjustment, respectively.
After all these adjusted spending values are computed, the boundary values are then further modified for these adjusted spending values.
If you specify BETAOVERLAP=NOADJUST, no adjustment is made when overlapping of one-sided boundaries occurs. The BETAOVERLAP= option is illustrated in Example 83.10.