The SEQDESIGN Procedure

Specified and Derived Parameters

In the SEQDESIGN procedure, the type of alternative hypothesis (ALT= option) and the condition for early stopping (STOP= option) must be specified for each sequential design. The drift parameters are derived for each design specified. Other parameters, such as Type I error probability $\alpha $, Type II error probability $\beta $, the alternative reference $\theta _1$, and maximum information are either specified or derived in the SEQDESIGN procedure.

Table 89.8 summarizes the available combinations for the specified and derived parameters in the SEQDESIGN procedure.

Table 89.8: Specified and Derived Parameters in the SEQDESIGN Procedure

Specified Parameters

 

Derived Parameters

Alt Ref

Max Info

Alpha

Beta

 

Alt Ref

Max Info

Alpha

Beta

Drift

Z

X

X

 

      

     

X

X

Z

X

 

X

     

X

 

X

Z

X

         

X

X

X

Z

 

X

X

   

X

   

X

 

X

X

X

 

X

     

X

   

X

X

         

X


The symbol "X" indicates that the parameter is either specified or derived in the design and the symbol "Z" indicates that the alternative reference is either specified explicitly with the ALTREF= option or derived from the SAMPLESIZE statement. The drift parameter is always derived in the SEQDESIGN procedure.

For example, if the ALTREF= option is specified without the MAXINFO= option being specified, then the maximum information is derived in the SEQDESIGN procedure with the specified $\alpha $ and $\beta $, as illustrated in Example 89.5.

The drift parameter is the standardized reference difference at the final stage. For a design, the drift parameter is

\[ d_{l} = \theta _{1l} \sqrt {I_{X}} \]

if it has a lower alternative, and

\[ d_{u} = \theta _{1u} \sqrt {I_{X}} \]

if it has an upper alternative, where $I_{X}$ is the maximum information and $\theta _{1l}$ and $\theta _{1u}$ are the lower and upper alternative references, respectively.

If the alternative reference and the maximum information are not both specified, then the specified $\alpha $ and $\beta $ are used to derive the drift parameter. Then if either the alternative reference or the maximum information is specified, the other is derived from the drift parameter.

If both the alternative reference and the maximum information are specified, then either the $\alpha $ error or the $\beta $ error is derived in the procedure. However, for a Haybittle-Peto method with the BOUNDARYKEY=NONE option, both $\alpha $ and $\beta $ errors are derived from the completely specified boundary values.

For a nonsymmetric two-sided design with different lower and upper specifications (such as different lower and upper $\alpha $ errors, $\beta $ errors, or alternative references in absolute values), the derived lower and upper boundaries are not symmetric. If the alternative references $\theta _{1l}$ and $\theta _{1u}$ are not both specified, then the SEQDESIGN procedure assumes symmetric alternative references, $\theta _1= \theta _{1u}= -\theta _{1l}$, for the computation of the boundary values.