The SEQTEST Procedure

Analysis after a Sequential Test

At the end of a trial, the hypothesis is either rejected or accepted. But the $\text{[math]}$ -value, median, and confidence limits depend on the ordering the sample space $\text{[math]}$ , where $\text{[math]}$ is the stage number and $\text{[math]}$ is the standardized $\text{[math]}$ statistic.

Following the notations used in Jennison and Turnbull (2000, pp. 179–180), $\text{[math]}$ if $\text{[math]}$ has a higher order or more extreme than $\text{[math]}$ . Then for a given ordering, the $\text{[math]}$ -value, median, and confidence limits associated with the observed statistics $\text{[math]}$ can be derived.

$\text{[math]}$ -value

With the observed pair of statistics $\text{[math]}$ when the trial is stopped, a one-sided upper $\text{[math]}$ -value is computed as

$\text{[math]}$

A one-sided lower $\text{[math]}$ -value is computed as

$\text{[math]}$

A two-sided $\text{[math]}$ -value is twice the smaller of the lower and upper $\text{[math]}$ -values.

Median Unbiased Estimate

With the observed pair $\text{[math]}$ , a median unbiased estimate $\text{[math]}$ is computed from

$\text{[math]}$

Confidence Limits

With the observed pair $\text{[math]}$ , a lower $\text{[math]}$ confidence limit for $\text{[math]}$ , $\text{[math]}$ , is computed from

$\text{[math]}$

Similarly, an upper $\text{[math]}$ confidence limit for $\text{[math]}$ , $\text{[math]}$ , is computed from

$\text{[math]}$