# The SEQDESIGN Procedure

### 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 101.9 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.

Table 101.9: Applicable Boundary Keys for Designs without Whitehead Methods

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 101.10 lists applicable boundary keys for a design that uses Whitehead methods.

Table 101.10: Applicable Boundary Keys for 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.