The SEQTEST Procedure
- Overview
- Getting Started
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Syntax
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Details
Input Data Sets Boundary Variables Information Level Adjustments at Future Stages Boundary Adjustments for Information Levels Boundary Adjustments for Minimum Error Spending Boundary Adjustments for Overlapping Lower and Upper beta Boundaries Stochastic Curtailment Repeated Confidence Intervals Analysis after a Sequential Test Available Sample Space Orderings in a Sequential Test Applicable Tests and Sample Size Computation Table Output ODS Table Names Graphics Output ODS Graphics Acknowledgments
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Examples
Testing the Difference between Two Proportions Testing an Effect in a Regression Model Testing an Effect with Early Stopping to Accept H0 Testing a Binomial Proportion Comparing Two Proportions with a Log Odds Ratio Test Comparing Two Survival Distributions with a Log-Rank Test Testing an Effect in a Proportional Hazards Regression Model Testing an Effect in a Logistic Regression Model
- References
| Repeated Confidence Intervals |
In a group sequential test, repeated confidence intervals for a parameter 
are defined as a sequence of intervals 
, 
, for which a simultaneous coverage probability is maintained (Jennison and Turnbull 2000, p. 189). That is, a 
sequence of repeated confidence intervals has
 |
These confidence limits 
and 
can be created from observed statistic and boundary values at each stage.
Two-Sided Repeated Confidence Intervals
Two sequences of repeated confidence intervals can be derived for a two-sided test. One is a 
rejection repeated confidence intervals 
, , and the other is a 
acceptance repeated confidence intervals 
, , where 
and 
are the lower and upper Type I error probabilities for the test and 
and 
are the lower and upper Type II error probabilities for the test (Jennison and Turnbull 2000, p. 196).
The rejection lower and upper repeated confidence limits at stage 
are
 |
The hypothesis is rejected for upper alternative if the lower limit 
and is rejected for lower alternative if the upper limit 
. That is, the hypothesis is rejected if both 
and 
are not in a rejection repeated confidence interval .
The acceptance lower and upper repeated confidence limits at stage are
 |
The hypothesis is accepted if the lower limit 
and the upper limit 
. That is, a repeated confidence interval is contained in the interval 
.
One-Sided Repeated Confidence Intervals
Like the two-sided repeated confidence intervals, two sequences of repeated confidence intervals can be derived for a one-sided test. Suppose the one-sided test has an upper alternative 
. Then one sequence of repeated confidence intervals is a 
rejection repeated confidence intervals 
, , and the other is a 
acceptance repeated confidence intervals 
, , where and are the upper Type I and Type II error probabilities for the test. Thus, a sequence of repeated confidence intervals with confidence level greater than or equal to 
is given by 
.
The rejection lower repeated confidence limit and the acceptance upper repeated confidence limit at stage are
 |
The hypothesis is rejected if the lower limit . and it is accepted if the upper limit .