The SEQTEST Procedure

Information Level Adjustments at Future Stages

In a group sequential clinical trial, the information level for the observed test statistic at the current stage generally does not match the corresponding information level in the BOUNDARY= data set. By default (or equivalently if you specify INFOADJ=PROP), the SEQTEST procedure accommodates the observed information level by adjusting the information levels at future interim stages. The adjustment of information levels depends on the boundary key to be maintained in the boundary adjustments, which in turn is determined by the BOUNDARYKEY= option.

If you specify BOUNDARYKEY=ALPHA (which is the default) or BOUNDARYKEY=BETA, the maximum information level (the information level at the final stage) provided in the BOUNDARY= data set is maintained. In this case, if an observed information level at the current stage is different from the level provided in the BOUNDARY= data set, you can use the INFOADJ= option to determine whether the information levels at subsequent interim stages are to be adjusted. Specifying INFOADJ=NONE preserves the levels provided in the BOUNDARY= data set without adjustment. Specifying INFOADJ=PROP proportionally adjusts the levels provided in the BOUNDARY= data set as follows.

Denote the information level at stage k for the K-stage design that is stored in the BOUNDARY= data set by upper I Subscript k, k equals 1 comma 2 comma ellipsis comma upper K. Also denote the information level that corresponds to the test statistic at an interim stage k 0 by upper I prime Subscript k 0, 1 less-than-or-equal-to k 0 less-than-or-equal-to left-parenthesis upper K minus 1 right-parenthesis. Then for the updated design, the information level at stage k, k equals k 0 plus 1 comma ellipsis comma left-parenthesis upper K minus 1 right-parenthesis, is computed as

upper I prime Subscript k Baseline equals upper I prime Subscript k 0 Baseline plus left-parenthesis upper I Subscript upper K Baseline minus upper I prime Subscript k 0 right-parenthesis StartFraction upper I Subscript k Baseline minus upper I Subscript k 0 Baseline Over upper I Subscript upper K Baseline minus upper I Subscript k 0 Baseline EndFraction

Note that if upper I prime Subscript k 0 Baseline greater-than-or-equal-to upper I Subscript upper K, the information level at stage k 0 reaches the maximum information level in the design, the trial stops at stage k 0, and no future information levels are derived.

If you specify BOUNDARYKEY=BOTH, the maximum information level for the trial is recomputed to maintain the alpha and beta levels simultaneously. In this case, the INFOADJ=NONE option is not applicable, and the INFOADJ=PROP option is used to proportionally adjust the information levels at future interim stages with the updated maximum information upper I prime Subscript upper K. That is, with an updated upper I prime Subscript upper K, the information level at a future interim stage k is computed as

upper I prime Subscript k Baseline equals upper I prime Subscript k 0 Baseline plus left-parenthesis upper I prime Subscript upper K Baseline minus upper I prime Subscript k 0 right-parenthesis StartFraction upper I Subscript k Baseline minus upper I Subscript k 0 Baseline Over upper I Subscript upper K Baseline minus upper I Subscript k 0 Baseline EndFraction

Because PROC SEQTEST computes a new maximum information level when you specify BOUNDARYKEY=BOTH, you can use this option even if the original design is ceiling-adjusted (that is, if you specified the CEILADJDESIGN=INCLUDE suboption in the SAMPLESIZE statement in PROC SEQDESIGN). In this regard, the BOUNDARYKEY=BOTH option in PROC SEQTEST differs from the BOUNDARYKEY=BOTH option in PROC SEQDESIGN.

Last updated: December 09, 2022