Example 78.5 Creating Designs Using Haybittle-Peto Methods

This example requests two 3-stage group sequential designs for normally distributed statistics. Each design uses a Haybittle-Peto method with a two-sided alternative and early stopping to reject the hypothesis. One design uses the specified interim boundary values and derives the final-stage boundary value for the specified and errors. The other design uses the specified boundary values and derives the overall and errors.

The following statements specify the interim boundary values and derive the final-stage boundary value for the specified and :

ods graphics on;
proc seqdesign altref=0.25
               errspend
               stopprob
               plots=errspend
               ;
   OneSidedPeto: design nstages=3
                 method=peto( z=3)
                 alt=upper   stop=reject
                 alpha=0.05  beta=0.10;
run;
ods graphics off;

The "Design Information" table in Output 78.5.1 displays design specifications and maximum information in percentage of its corresponding fixed-sample design.

The "Method Information" table in Output 78.5.2 displays the and errors and the derived drift parameter, which is the standardized alternative reference at the final stage.

With the STOPPROB option, the "Expected Cumulative Stopping Probabilities" table in Output 78.5.3 displays the expected stopping stage and cumulative stopping probability to reject the null hypothesis at each stage under various hypothetical references , where is the alternative reference and are the default values in the CREF= option.

The "Boundary Information" table in Output 78.5.4 displays information level, alternative references, and boundary values. By default (or equivalently if you specify BOUNDARYSCALE=STDZ), the standardized scale is used to display the alternative references and boundary values. The resulting standardized alternative reference at stage is given by , where is the alternative reference and is the information level at stage , .

At each interim stage, if the standardized statistic , the trial is stopped and the null hypothesis is rejected. If the statistic , the trial continues to the next stage. At the final stage, the null hypothesis is rejected if the statistic . Otherwise, the hypothesis is accepted. Note that the boundary values at the final stage, , are close to the critical values in the corresponding fixed-sample design.

The "Error Spending Information" in Output 78.5.5 displays cumulative error spending at each stage for each boundary. The stage spending corresponds to the one-sided -value for a standardized statistic, .

With the specified ODS GRAPHICS ON statement, a detailed boundary plot with the rejection and acceptance regions is displayed, as shown in Output 78.5.6. With the STOP=REJECT option, the interim rejection boundaries are displayed.

Output 78.5.6 Boundary Plot

With the PLOTS=ERRSPEND option, the procedure displays a plot of error spending for each boundary, as shown in Output 78.5.7. The error spending values in the "Error Spending Information" in Output 78.5.4 are displayed in the plot. As expected, the error spending at each of the first two stages is small, with the standardized boundary value .

Output 78.5.7 Error Spending Plot

The following statements specify the boundary values and derive the and errors from these completely specified boundary values:

ods graphics on;
proc seqdesign altref=0.25
               maxinfo=200
               errspend
               stopprob
               plots=errspend
               ;
   OneSidedPeto: design nstages=3
                 method=peto(z=3 2.5 2)
                 alt=upper  stop=reject
                 boundarykey=none
                 ;
run;
ods graphics off;

The "Design Information" table in Output 78.5.8 displays design specifications and derived and error levels.

The "Method Information" table in Output 78.5.9 displays the and errors and the derived drift parameter for each boundary.

With the STOPPROB option, the "Expected Cumulative Stopping Probabilities" table in Output 78.5.10 displays the expected stopping stage and cumulative stopping probability to reject the null hypothesis at each stage under various hypothetical references , where is the alternative reference and are the default values in the CREF= option.

The "Boundary Information" table in Output 78.5.11 displays information level, alternative references, and boundary values.

The "Error Spending Information" in Output 78.5.12 displays cumulative error spending at each stage for each boundary. The first-stage spending corresponds to the one-sided -value for a standardized statistic, .

With the specified ODS GRAPHICS ON statement, a detailed boundary plot with the rejection and acceptance regions is displayed, as shown in Output 78.5.13. With the STOP=REJECT option, the interim rejection boundaries are displayed.

Output 78.5.13 Boundary Plot

With the PLOTS=ERRSPEND option, the procedure displays a plot of error spending for each boundary, as shown in Output 78.5.14. The error spending values in the "Error Spending Information" table in Output 78.5.10 are displayed in the plot.

Output 78.5.14 Error Spending Plot