The SEQDESIGN Procedure

This example requests three 4-stage Whitehead’s triangular designs for normally distributed statistics. Each design has a one-sided alternative hypothesis with early stopping to reject or accept the null hypothesis . Note that Whitehead’s triangular designs are different from unified family triangular designs.

The following statements invoke the SEQDESIGN procedure and specify three Whitehead’s triangular designs:

ods graphics on;
proc seqdesign altref=0.693147
               bscale=score
               plots=combinedboundary
               ;
   BoundaryKeyNone:  design nstages=4
                            method=whitehead
                            boundarykey=none
                            alt=upper   stop=both
                            alpha=0.05  beta=0.20
                            ;
   BoundaryKeyAlpha: design nstages=4
                            method=whitehead
                            boundarykey=alpha
                            alt=upper   stop=both
                            alpha=0.05  beta=0.20
                            ;

   BoundaryKeyBeta:  design nstages=4
                            method=whitehead
                            boundarykey=beta
                            alt=upper   stop=both
                            alpha=0.05  beta=0.20
                            ;
run;

Whitehead methods with early stopping to reject or accept the null hypothesis create boundaries that approximately satisfy the Type I and Type II error probability specification. The BOUNDARYKEY=NONE option specifies no adjustment to the boundary value at the final stage to maintain either a Type I or a Type II error probability level.

The "Design Information" table in Output 101.7.1 displays design specifications and maximum information. Note that with the BOUNDARYKEY=NONE option, the derived errors and are not the same as the specified errors and .

The "Method Information" table in Output 101.7.2 displays the derived and errors and the derived drift parameter. The derived errors and are not exactly the same as the specified errors and with the BOUNDARYKEY=NONE option.

The "Boundary Information" table in Output 101.7.3 displays information level, alternative reference, and boundary values. With the specified BOUNDARYSCALE=SCORE option, the alternative reference and boundary values are displayed with the score statistics scale.

With ODS Graphics enabled, a detailed boundary plot with the rejection and acceptance regions is displayed, as shown in Output 101.7.4.

Output 101.7.4: Boundary Plot

The second design uses the BOUNDARYKEY=ALPHA option to adjust the boundary value at the final stage to maintain the Type I error probability level.

The "Design Information" table in Output 101.7.5 displays design specifications and the derived maximum information. Note that with the BOUNDARYKEY=ALPHA option, the specified Type I error probability is maintained.

The "Method Information" table in Output 101.7.6 displays the specified and derived and errors and the derived drift parameter. The derived Type I error probability is the same as the specified and the derived Type II error probability is not the same as the specified with the BOUNDARYKEY=ALPHA option.

The "Boundary Information" table in Output 101.7.7 displays information level, alternative reference, and boundary values.

With ODS Graphics enabled, a detailed boundary plot with the rejection and acceptance regions is displayed, as shown in Output 101.7.8.

Output 101.7.8: Boundary Plot

The third design specifies the BOUNDARYKEY=BETA option to derive the boundary values to maintain the Type II error probability level .

The "Design Information" table in Output 101.7.9 displays design specifications and the derived maximum information. Note that with the BOUNDARYKEY=BETA option, the specified Type II error probability is maintained.

The "Method Information" table in Output 101.7.10 displays the and errors and the derived drift parameter. The derived Type II error probability is the same as the specified and the derived Type I error probability is not the same as the specified with the BOUNDARYKEY=BETA option.

The "Boundary Information" table in Output 101.7.11 displays information level, alternative reference, and boundary values.

With ODS Graphics enabled, a detailed boundary plot with the rejection and acceptance regions is displayed, as shown in Output 101.7.12.

Output 101.7.12: Boundary Plot

With the PLOTS=COMBINEDBOUNDARY option, a combined plot of group sequential boundaries for all designs is displayed, as shown in Output 101.7.13. It shows that three designs are similar, with a slightly smaller boundary value at the final stage for the design with the BOUNDARYKEY=NONE option.

Output 101.7.13: Combined Boundary Plot