### Boundary Adjustments for Minimum Error Spending

In a group sequential clinical trial, boundary values created from a design such as an O’Brien-Fleming design might be too conservative in early stages. Thus the trial is unlikely to stop in early stages. Lan and DeMets (1983, p. 662) suggest truncating boundary values to a number such as 3.5 for the trial to have a reasonable probability of stopping at early stages. Instead of truncating boundary values by a specified number, the ERRSPENDMIN= option provides individual minimum error spending at each interim stage to stop the trial early.

For a K-stage trial, denote the derived cumulative error spending at stage k after adjusting for information levels by . Also denote the specified minimum error spending at interim stage k by . Then the cumulative error spending at stage 1 is . If , the error spending values at subsequent interim stages are adjusted proportionally by

for .

The process is repeated at each subsequent interim stage. That is, at stage , denote the updated cumulative spending at stage j by , . Then the cumulative error spending at stage k is . If , the error spending values at subsequent interim stages are adjusted proportionally by

for .

Note that the ERRSPENDMIN= option is applicable only to the boundaries specified in the BOUNDARYKEY= option. That is, the ERRSPENDMIN= option is applicable to the boundaries with BOUNDARYKEY=ALPHA or BOUNDARYKEY=BOTH, and it is applicable to the boundaries with BOUNDARYKEY=BETA or BOUNDARYKEY=BOTH.