Applicable Boundary Keys |
In the SEQDESIGN procedure, the BOUNDARYKEY= option in the DESIGN statement specifies the types of errors to be maintained for the design. Table 80.9 lists applicable boundary keys for designs that use unified family and Haybittle-Peto methods, designs that use error spending methods, and designs that use the Haybittle-Peto method only.
Specified Parameters |
Boundary Keys |
||||
Method |
(Alt Ref – Max Info) |
Alpha |
Beta |
None |
Both |
Unified |
X |
X |
X |
||
Unified/Haybittle-Peto |
X |
X |
X |
||
Error spending |
X |
X |
X |
||
Haybittle-Peto |
X |
X |
X |
X |
|
Unified/Haybittle-Peto |
X |
||||
Error spending |
X |
||||
Haybittle-Peto |
X |
Note that the symbol "X" under "(Alt Ref – Max Info)" indicates that both the alternative reference and maximum information are specified, and the method "Unified/Haybittle-Peto" indicates that both the unified method and the Haybittle-Peto method are used in the same design.
If the ALTREF= and MAXINFO= options are both specified, then Type I and Type II error probability levels cannot be met simultaneously if both error probabilities are specified. The BOUNDARYKEY=ALPHA option maintains the Type I error probability level and derives Type II error probability . The BOUNDARYKEY=BETA option maintains the Type II error probability level and derives Type I error probability .
If the Haybittle-Peto method is used for all boundaries, the BOUNDARYKEY=NONE option uses the specified boundary value (STOP=REJECT or STOP=BOTH) and the specified boundary value (STOP=ACCEPT) at the final stage for the design.
If the ALTREF= and MAXINFO= options are not both specified, the BOUNDARYKEY=BOTH option derives boundary values that maintain both Type I and Type II error probability levels.
Table 80.10 lists applicable boundary keys for a design that uses Whitehead methods.
Specified Parameters |
Boundary Keys |
|||||
Early Stopping |
(Alt Ref – Max Info) |
Tau |
Alpha |
Beta |
None |
Both |
Reject |
X |
X |
X |
X |
||
Accept |
X |
X |
X |
X |
||
Reject/Accept |
X |
0.25 |
X |
X |
||
Reject |
X |
X |
||||
Accept |
X |
X |
||||
Reject/Accept |
0.25 |
X |
X |
X |
Note that the symbol "X" under "(Alt Ref – Max Info)" indicates that both alternative reference and maximum information are specified.
If the ALTREF= and MAXINFO= options are both specified, then Type I and Type II error probability levels cannot be achieved simultaneously if both are specified. the BOUNDARYKEY=ALPHA option maintains the Type I error probability level and derives Type II error probability . The BOUNDARYKEY=BETA option maintains the Type II error probability level and derives the Type I error probability .
If the ALTREF= and MAXINFO= options are not both specified, then for a design with the STOP=REJECT or STOP=ACCEPT option, the BOUNDARYKEY=BOTH option derives boundary values that maintain both Type I and Type II error probability levels. If the STOP=BOTH option is specified, Whitehead’s triangular method produces boundaries with approximate Type I and Type II error probabilities. The BOUNDARYKEY=NONE option specifies no adjustment to these boundaries. The BOUNDARYKEY=ALPHA and BOUNDARYKEY=BETA options maintain the Type I error probability level and Type II error probability level , respectively, by adjusting boundary values at the final stage.