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 87.9 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 87.9: 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 $\alpha$ and derives Type II error probability $\beta$ . The BOUNDARYKEY=BETA option maintains the Type II error probability level $\beta$ and derives Type I error probability $\alpha$ .

If the Haybittle-Peto method is used for all boundaries, the BOUNDARYKEY=NONE option uses the specified $\alpha$ boundary value (STOP=REJECT or STOP=BOTH) and the specified $\beta$ 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 87.10 lists applicable boundary keys for a design that uses Whitehead methods.

Table 87.10: Applicable Boundary Keys for Whitehead Methods

	Specified Parameters		Boundary Keys
Early Stopping	(Alt Ref – Max Info)	Tau	Alpha	Beta	None	Both
Reject $H_{0}$	X	X	X	X
Accept $H_{0}$	X	X	X	X
Reject/Accept $H_{0}$	X	0.25	X	X
Reject $H_{0}$		X				X
Accept $H_{0}$		X				X
Reject/Accept $H_{0}$		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 $\alpha$ and derives Type II error probability $\beta$ . The BOUNDARYKEY=BETA option maintains the Type II error probability level $\beta$ and derives the Type I error probability $\alpha$ .

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 $\alpha$ and Type II error probability level $\beta$ , respectively, by adjusting boundary values at the final stage.